Metrics for Hyperbolic arc-(co)secant

analyze4.0ms (0%)

Memory

-33.5MiB live, 6.1MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
0%	0%	50%	0%	0%	50%	0%	3
33.3%	12.5%	25%	0%	0%	62.5%	0%	4
60%	18.7%	12.5%	0%	0%	68.7%	0%	5
77.8%	21.9%	6.2%	0%	0%	71.8%	0%	6
88.2%	23.4%	3.1%	0%	0%	73.4%	0%	7
93.9%	24.2%	1.6%	0%	0%	74.2%	0%	8
96.9%	24.6%	0.8%	0%	0%	74.6%	0%	9
98.4%	24.8%	0.4%	0%	0%	74.8%	0%	10
99.2%	24.9%	0.2%	0%	0%	74.9%	0%	11
99.6%	24.9%	0.1%	0%	0%	74.9%	0%	12

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample1.3s (15.7%)

Memory

54.5MiB live, 1 030.8MiB allocated

Samples

938.0ms	8 256×	0	valid
2.0ms	29×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 702.0ms

ival-div: 261.0ms (37.2% of total)

ival-log: 134.0ms (19.1% of total)

ival-mult: 133.0ms (19% of total)

ival-sub: 70.0ms (10% of total)

ival-sqrt: 57.0ms (8.1% of total)

ival-add: 33.0ms (4.7% of total)

ival-true: 5.0ms (0.7% of total)

exact: 5.0ms (0.7% of total)

ival-assert: 3.0ms (0.4% of total)

Bogosity

preprocess940.0ms (11.7%)

Memory

-49.0MiB live, 778.7MiB allocated

Algorithm

1×	egg-herbie

Rules

28 400×	`lower-fma.f64`
28 400×	`lower-fma.f32`
3 690×	`lower-*.f32`
3 688×	`lower-*.f64`
2 256×	`lower-+.f32`

Iterations

Useful iterations: 14 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

Outputs

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

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

explain134.0ms (1.7%)

Memory

29.0MiB live, 335.5MiB allocated

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

48.0ms

512×

valid

Compiler

Compiled 136 to 40 computations (70.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 32.0ms

ival-div: 10.0ms (31.5% of total)

ival-log: 9.0ms (28.3% of total)

ival-sqrt: 4.0ms (12.6% of total)

ival-mult: 3.0ms (9.4% of total)

ival-sub: 3.0ms (9.4% of total)

ival-add: 2.0ms (6.3% of total)

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

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

exact: 0.0ms (0% of total)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

2.3MiB live, 2.3MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 14 to 9 computations (35.7% saved)

simplify592.0ms (7.4%)

Memory

-5.9MiB live, 878.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

28 400×	`lower-fma.f64`
28 400×	`lower-fma.f32`
3 690×	`lower-*.f32`
3 688×	`lower-*.f64`
2 256×	`lower-+.f32`

Iterations

Useful iterations: 14 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

localize33.0ms (0.4%)

Memory

3.2MiB live, 81.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
✓	accuracy	100.0%	(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)
✓	accuracy	100.0%	(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))

Samples

21.0ms

256×

valid

Compiler

Compiled 54 to 11 computations (79.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-div: 4.0ms (31.9% of total)

ival-log: 3.0ms (23.9% of total)

ival-sqrt: 2.0ms (15.9% of total)

ival-add: 1.0ms (8% of total)

ival-mult: 1.0ms (8% of total)

ival-sub: 1.0ms (8% of total)

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

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

exact: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory

11.0MiB live, 11.0MiB allocated

Counts

4 → 48

Calls

Call 1

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

Outputs
#<alt (+ (log 2) (* -1 (log x)))>
#<alt (+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 2))))>
#<alt (+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* -3/32 (pow x 2)) 1/4))))>
#<alt (+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -5/96 (pow x 2)) 3/32)) 1/4))))>
#<alt (log (sqrt -1))>
#<alt (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1))))>
#<alt (- (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1)))) (/ 1/6 (* (pow x 3) (pow (sqrt -1) 3))))>
#<alt (- (+ (log (sqrt -1)) (+ (/ 1 (* x (sqrt -1))) (* 3/40 (/ 1 (* (pow x 5) (pow (sqrt -1) 5)))))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))>
#<alt (log (* -1 (sqrt -1)))>
#<alt (- (log (* -1 (sqrt -1))) (/ 1 (* x (sqrt -1))))>
#<alt (+ (log (* -1 (sqrt -1))) (* -1 (/ (- (/ 1 (sqrt -1)) (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x)))>
#<alt (+ (log (* -1 (sqrt -1))) (* -1 (/ (- (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3)))) x)))>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (* -1/2 (pow x 2))) x)>
#<alt (/ (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) x)>
#<alt (/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) x)>
#<alt (sqrt -1)>
#<alt (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))>
#<alt (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))>
#<alt (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))>
#<alt (* -1 (sqrt -1))>
#<alt (- (* -1 (sqrt -1)) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))>
#<alt (- (+ (* -1 (sqrt -1)) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))) (/ 1/2 (* (pow x 2) (sqrt -1))))>
#<alt (- (+ (* -1 (sqrt -1)) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))>
#<alt (* x (sqrt -1))>
#<alt (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))>
#<alt (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))>
#<alt (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))>
#<alt (* -1 (* x (sqrt -1)))>
#<alt (* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))>
#<alt (* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))>
#<alt (* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
1.0ms	x	@	-inf	(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
1.0ms	x	@	0	(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
0.0ms	x	@	-inf	(/ (sqrt (- 1 (* x x))) x)
0.0ms	x	@	inf	(/ (sqrt (- 1 (* x x))) x)

rewrite269.0ms (3.4%)

Memory

6.8MiB live, 357.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 520×	`lower-fma.f64`
4 520×	`lower-fma.f32`
3 106×	`lower-*.f32`
3 104×	`lower-*.f64`
2 972×	`lower-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	30
0	16	30
1	69	30
2	624	28
3	7596	28
0	8354	28

Stop Event

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

Counts

4 → 154

Calls

Call 1

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

Outputs
(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x))
(+.f64 (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x)) #s(literal 0 binary64))
(+.f64 (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) x)) (log.f64 (.f64 (/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) x) (/.f64 x (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))))))))
(+.f64 (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) x)) (log.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) x) (/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x))))
(+.f64 #s(literal 0 binary64) (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x)))
(+.f64 (log.f64 (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x)) (neg.f64 (.f64 #s(literal 2 binary64) (log.f64 x))))
(+.f64 (log.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64)))) (neg.f64 (log.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) (*.f64 x x))))))
(+.f64 (log.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) (.f64 x x)))) (log.f64 (.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) x) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) (.f64 x x)))))))
(+.f64 (log.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) (.f64 x x)))) (log.f64 (/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) x) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) (*.f64 x x))))))
(+.f64 (log.f64 (/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 x x))) (log.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))))
(+.f64 (neg.f64 (log.f64 x)) (log1p.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(+.f64 (neg.f64 (log.f64 x)) (log.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))))))
(+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))))
(+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 (+.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) #s(literal -1 binary64))))
(+.f64 (log1p.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (neg.f64 (log.f64 x)))
(+.f64 (neg.f64 (.f64 #s(literal 2 binary64) (log.f64 x))) (log.f64 (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x)))
(+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))))))
(+.f64 (log.f64 (pow.f64 x #s(literal -1/2 binary64))) (log.f64 (.f64 (pow.f64 x #s(literal -1/2 binary64)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))))))
(+.f64 (log.f64 (+.f64 x (/.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))))) (log.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (*.f64 x x))))
(+.f64 (log.f64 (+.f64 (neg.f64 x) (/.f64 (neg.f64 x) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))))) (log.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (*.f64 x (neg.f64 x)))))
(+.f64 (log.f64 (neg.f64 (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x))) (log.f64 (/.f64 #s(literal 1 binary64) (.f64 x (neg.f64 x)))))
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(/.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (fma.f64 (.f64 x x) (*.f64 x (neg.f64 x)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (.f64 (sqrt.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (neg.f64 x)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64))))
(/.f64 (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (*.f64 x (neg.f64 x)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(pow.f64 (/.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x))
(.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))))
(.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) #s(literal -1 binary64)))
(.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x)))
(.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) (/.f64 #s(literal -1 binary64) x))
(.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) x))
(.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) x)))
(.f64 (pow.f64 x #s(literal -1/2 binary64)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(.f64 (neg.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x)) #s(literal -1 binary64))
(.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))))
(.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/4 binary64)) x) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/4 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) x))
(.f64 (pow.f64 (/.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) #s(literal -1/2 binary64)))
(.f64 (.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/4 binary64))) (.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64))))
(.f64 (.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (pow.f64 x #s(literal -1/2 binary64))) (.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) (pow.f64 x #s(literal -1/2 binary64))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/4 binary64))) (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/4 binary64)))
(.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)))
(exp.f64 (.f64 #s(literal 1/2 binary64) (log1p.f64 (.f64 x (neg.f64 x)))))
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(neg.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) (*.f64 x (neg.f64 x)) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x (neg.f64 x)) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (neg.f64 x)) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x (fma.f64 x (*.f64 x x) x) #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x (neg.f64 x)) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (neg.f64 x)) #s(literal 1 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 x (fma.f64 x (*.f64 x x) x) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (*.f64 x x))))) (sqrt.f64 (fma.f64 x (neg.f64 x) #s(literal -1 binary64))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (neg.f64 x)) #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 x (fma.f64 x (*.f64 x x) x) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x (neg.f64 x)) #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))
(/.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (neg.f64 x)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64))))
(/.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (.f64 x x) (*.f64 x (neg.f64 x)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (.f64 (sqrt.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (neg.f64 x)) #s(literal 1 binary64))) #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64))))
(/.f64 (.f64 (sqrt.f64 (fma.f64 (.f64 x x) (*.f64 x (neg.f64 x)) #s(literal 1 binary64))) #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log1p.f64 (*.f64 x (neg.f64 x)))) #s(literal 1/2 binary64))
(.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))))
(.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))))
(.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) #s(literal -1 binary64))
(.f64 (sqrt.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (neg.f64 x)) #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (neg.f64 x)) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64)))))
(.f64 (sqrt.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (neg.f64 x)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64)))))
(.f64 (sqrt.f64 (fma.f64 (.f64 x x) (*.f64 x (neg.f64 x)) #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 (.f64 x x) (*.f64 x (neg.f64 x)) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))
(.f64 (sqrt.f64 (fma.f64 (.f64 x x) (*.f64 x (neg.f64 x)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))
(.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/4 binary64))) (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(neg.f64 (*.f64 x (neg.f64 x)))
(/.f64 x (/.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 x x) #s(literal 1 binary64))
(/.f64 (*.f64 x (neg.f64 x)) #s(literal -1 binary64))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(.f64 #s(literal 1 binary64) (.f64 x x))
(*.f64 x x)
(.f64 (.f64 x x) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (.f64 x (neg.f64 x)))
(*.f64 (neg.f64 x) (neg.f64 x))

simplify357.0ms (4.4%)

Memory

-11.9MiB live, 561.1MiB allocated

Algorithm

1×	egg-herbie

Rules

13 898×	`lower-fma.f64`
13 898×	`lower-fma.f32`
3 290×	`lower-*.f64`
3 290×	`lower-*.f32`
1 616×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	127	618
1	328	598
2	901	582
3	2639	570
4	7140	570
0	8341	547

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

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

eval27.0ms (0.3%)

Memory: -19.3MiB live, 58.7MiB allocated
Compiler: Compiled 4 936 to 811 computations (83.6% saved)

prune45.0ms (0.6%)

Memory

7.2MiB live, 46.5MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	197	5	202
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	198	5	203

Accuracy

100.0%

Counts

203 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(+.f64 (neg.f64 (log.f64 x)) (log1p.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
▶	54.1%	(neg.f64 (log.f64 (/.f64 (.f64 x x) (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x))))
▶	100.0%	(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x))
▶	98.8%	(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)))
▶	0.0%	(log.f64 (sqrt.f64 #s(literal -1 binary64)))

Compiler

Compiled 106 to 70 computations (34% saved)

simplify323.0ms (4%)

Memory

4.6MiB live, 368.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(log1p.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
✓	cost-diff	0	(log.f64 x)
✓	cost-diff	0	(neg.f64 (log.f64 x))
✓	cost-diff	128	(+.f64 (neg.f64 (log.f64 x)) (log1p.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(log.f64 (/.f64 (.f64 x x) (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x)))
✓	cost-diff	128	(neg.f64 (log.f64 (/.f64 (.f64 x x) (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x))))
✓	cost-diff	512	(/.f64 (.f64 x x) (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)))
✓	cost-diff	896	(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(sqrt.f64 #s(literal -1 binary64))
✓	cost-diff	0	(log.f64 (sqrt.f64 #s(literal -1 binary64)))
✓	cost-diff	0	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
✓	cost-diff	0	(/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x)
✓	cost-diff	0	(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x))

Rules

9 146×	`lower-fma.f32`
9 144×	`lower-fma.f64`
2 788×	`lower-*.f32`
2 786×	`lower-*.f64`
1 726×	`lower-/.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	22	177
0	42	169
1	61	164
2	81	164
3	106	162
4	154	158
5	210	158
6	381	158
7	1119	158
8	3043	158
9	4702	158
0	8103	158

Stop Event

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

Calls

Call 1

Inputs
(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x))
(/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x)
(+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
#s(literal 1 binary64)
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 x x)
x
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(sqrt.f64 #s(literal -1 binary64))
#s(literal -1 binary64)
(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)))
(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(neg.f64 (log.f64 (/.f64 (.f64 x x) (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x))))
(log.f64 (/.f64 (.f64 x x) (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x)))
(/.f64 (.f64 x x) (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x))
(*.f64 x x)
x
(fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
#s(literal 1 binary64)
(+.f64 (neg.f64 (log.f64 x)) (log1p.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(neg.f64 (log.f64 x))
(log.f64 x)
x
(log1p.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
#s(literal 1 binary64)
(*.f64 x x)

Outputs
(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x))
(/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x)
(+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
#s(literal 1 binary64)
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 x x)
x
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(sqrt.f64 #s(literal -1 binary64))
#s(literal -1 binary64)
(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)))
(log.f64 (/.f64 #s(literal 2 binary64) x))
(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 2 binary64) x)
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(neg.f64 (log.f64 (/.f64 (.f64 x x) (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x))))
(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x))
(log.f64 (/.f64 (.f64 x x) (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x)))
(log.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))))
(/.f64 (.f64 x x) (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x))
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(*.f64 x x)
x
(fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
#s(literal 1 binary64)
(+.f64 (neg.f64 (log.f64 x)) (log1p.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(-.f64 (log1p.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (log.f64 x))
(neg.f64 (log.f64 x))
(log.f64 x)
x
(log1p.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
#s(literal 1 binary64)
(*.f64 x x)

localize100.0ms (1.3%)

Memory

-0.3MiB live, 157.2MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
✓	accuracy	100.0%	(neg.f64 (log.f64 x))
✓	accuracy	100.0%	(log1p.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
✓	accuracy	100.0%	(log.f64 x)
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
✓	accuracy	100.0%	(neg.f64 (log.f64 (/.f64 (.f64 x x) (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x))))
✓	accuracy	100.0%	(log.f64 (/.f64 (.f64 x x) (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x)))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)
✓	accuracy	100.0%	(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)))
✓	accuracy	100.0%	(sqrt.f64 #s(literal -1 binary64))
✓	accuracy	100.0%	(log.f64 (sqrt.f64 #s(literal -1 binary64)))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
✓	accuracy	100.0%	(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x))

Samples

61.0ms

256×

invalid

Compiler

Compiled 187 to 25 computations (86.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 47.0ms

ival-add: 17.0ms (36.4% of total)

ival-log: 12.0ms (25.7% of total)

ival-div: 5.0ms (10.7% of total)

ival-mult: 3.0ms (6.4% of total)

ival-log1p: 3.0ms (6.4% of total)

ival-sqrt: 3.0ms (6.4% of total)

ival-neg: 2.0ms (4.3% of total)

ival-sub: 1.0ms (2.1% of total)

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

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

exact: 0.0ms (0% of total)

series137.0ms (1.7%)

Memory

-9.4MiB live, 179.8MiB allocated

Counts

14 → 144

Calls

Call 1

Inputs
#<alt (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x))>
#<alt (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))>
#<alt (*.f64 x x)>
#<alt (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))>
#<alt (log.f64 (sqrt.f64 #s(literal -1 binary64)))>
#<alt (sqrt.f64 #s(literal -1 binary64))>
#<alt (log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)))>
#<alt (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x))>
#<alt (/.f64 #s(literal 1 binary64) x)>
#<alt (log.f64 (/.f64 (.f64 x x) (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x)))>
#<alt (neg.f64 (log.f64 (/.f64 (.f64 x x) (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x))))>
#<alt (log.f64 x)>
#<alt (log1p.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))>
#<alt (neg.f64 (log.f64 x))>

Outputs
#<alt (+ (log 2) (* -1 (log x)))>
#<alt (+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 2))))>
#<alt (+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* -3/32 (pow x 2)) 1/4))))>
#<alt (+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -5/96 (pow x 2)) 3/32)) 1/4))))>
#<alt (log (sqrt -1))>
#<alt (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1))))>
#<alt (- (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1)))) (/ 1/6 (* (pow x 3) (pow (sqrt -1) 3))))>
#<alt (- (+ (log (sqrt -1)) (+ (/ 1 (* x (sqrt -1))) (* 3/40 (/ 1 (* (pow x 5) (pow (sqrt -1) 5)))))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))>
#<alt (log (* -1 (sqrt -1)))>
#<alt (- (log (* -1 (sqrt -1))) (/ 1 (* x (sqrt -1))))>
#<alt (+ (log (* -1 (sqrt -1))) (* -1 (/ (- (/ 1 (sqrt -1)) (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x)))>
#<alt (+ (log (* -1 (sqrt -1))) (* -1 (/ (- (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3)))) x)))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))>
#<alt (* x (sqrt -1))>
#<alt (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))>
#<alt (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))>
#<alt (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))>
#<alt (* -1 (* x (sqrt -1)))>
#<alt (* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))>
#<alt (* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))>
#<alt (* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt 2>
#<alt (+ 2 (* -1/2 (pow x 2)))>
#<alt (+ 2 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))>
#<alt (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))>
#<alt (* x (sqrt -1))>
#<alt (* x (+ (sqrt -1) (/ 1 x)))>
#<alt (* x (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (/ 1 x))))>
#<alt (* x (- (+ (sqrt -1) (+ (/ 1 x) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))>
#<alt (* -1 (* x (sqrt -1)))>
#<alt (* -1 (* x (- (sqrt -1) (/ 1 x))))>
#<alt (* -1 (* x (+ (sqrt -1) (* -1 (/ (- 1 (* 1/2 (/ 1 (* x (sqrt -1))))) x)))))>
#<alt (* -1 (* x (+ (sqrt -1) (* -1 (/ (+ 1 (* -1 (/ (- (* 1/2 (/ 1 (sqrt -1))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x))) x)))))>
#<alt (+ (log 2) (* -1 (log x)))>
#<alt (+ (log 2) (* -1 (log x)))>
#<alt (+ (log 2) (* -1 (log x)))>
#<alt (+ (log 2) (* -1 (log x)))>
#<alt (+ (log 2) (log (/ 1 x)))>
#<alt (+ (log 2) (log (/ 1 x)))>
#<alt (+ (log 2) (log (/ 1 x)))>
#<alt (+ (log 2) (log (/ 1 x)))>
#<alt (+ (log -2) (log (/ -1 x)))>
#<alt (+ (log -2) (log (/ -1 x)))>
#<alt (+ (log -2) (log (/ -1 x)))>
#<alt (+ (log -2) (log (/ -1 x)))>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (+ (log 1/2) (log x))>
#<alt (+ (log 1/2) (+ (log x) (* 1/4 (pow x 2))))>
#<alt (+ (log 1/2) (+ (log x) (* (pow x 2) (+ 1/4 (* 3/32 (pow x 2))))))>
#<alt (+ (log 1/2) (+ (log x) (* (pow x 2) (+ 1/4 (* (pow x 2) (+ 3/32 (* 5/96 (pow x 2))))))))>
#<alt (log (/ 1 (sqrt -1)))>
#<alt (- (log (/ 1 (sqrt -1))) (/ 1 (* x (sqrt -1))))>
#<alt (- (+ (log (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 3) (pow (sqrt -1) 3)))) (/ 1 (* x (sqrt -1))))>
#<alt (- (+ (log (/ 1 (sqrt -1))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3))))) (+ (/ 1 (* x (sqrt -1))) (* 3/40 (/ 1 (* (pow x 5) (pow (sqrt -1) 5))))))>
#<alt (log (/ -1 (sqrt -1)))>
#<alt (+ (log (/ -1 (sqrt -1))) (/ 1 (* x (sqrt -1))))>
#<alt (+ (log (/ -1 (sqrt -1))) (* -1 (/ (- (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (/ 1 (sqrt -1))) x)))>
#<alt (+ (log (/ -1 (sqrt -1))) (* -1 (/ (- (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3))) (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1)))) x)))>
#<alt (* -1 (+ (log 1/2) (log x)))>
#<alt (- (* -1/4 (pow x 2)) (+ (log 1/2) (log x)))>
#<alt (- (* (pow x 2) (- (* -3/32 (pow x 2)) 1/4)) (+ (log 1/2) (log x)))>
#<alt (- (* (pow x 2) (- (* (pow x 2) (- (* -5/96 (pow x 2)) 3/32)) 1/4)) (+ (log 1/2) (log x)))>
#<alt (* -1 (log (/ 1 (sqrt -1))))>
#<alt (- (/ 1 (* x (sqrt -1))) (log (/ 1 (sqrt -1))))>
#<alt (- (/ 1 (* x (sqrt -1))) (+ (log (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 3) (pow (sqrt -1) 3)))))>
#<alt (- (+ (/ 1 (* x (sqrt -1))) (* 3/40 (/ 1 (* (pow x 5) (pow (sqrt -1) 5))))) (+ (log (/ 1 (sqrt -1))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3))))))>
#<alt (* -1 (log (/ -1 (sqrt -1))))>
#<alt (* -1 (+ (log (/ -1 (sqrt -1))) (/ 1 (* x (sqrt -1)))))>
#<alt (- (* -1 (/ (- (/ 1 (sqrt -1)) (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x)) (log (/ -1 (sqrt -1))))>
#<alt (- (* -1 (/ (- (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3)))) x)) (log (/ -1 (sqrt -1))))>
#<alt (log x)>
#<alt (log x)>
#<alt (log x)>
#<alt (log x)>
#<alt (* -1 (log (/ 1 x)))>
#<alt (* -1 (log (/ 1 x)))>
#<alt (* -1 (log (/ 1 x)))>
#<alt (* -1 (log (/ 1 x)))>
#<alt (+ (log -1) (* -1 (log (/ -1 x))))>
#<alt (+ (log -1) (* -1 (log (/ -1 x))))>
#<alt (+ (log -1) (* -1 (log (/ -1 x))))>
#<alt (+ (log -1) (* -1 (log (/ -1 x))))>
#<alt (log 2)>
#<alt (+ (log 2) (* -1/4 (pow x 2)))>
#<alt (+ (log 2) (* (pow x 2) (- (* -3/32 (pow x 2)) 1/4)))>
#<alt (+ (log 2) (* (pow x 2) (- (* (pow x 2) (- (* -5/96 (pow x 2)) 3/32)) 1/4)))>
#<alt (+ (log (sqrt -1)) (* -1 (log (/ 1 x))))>
#<alt (+ (log (sqrt -1)) (+ (* -1 (log (/ 1 x))) (/ 1 (* x (sqrt -1)))))>
#<alt (- (+ (log (sqrt -1)) (+ (* -1 (log (/ 1 x))) (/ 1 (* x (sqrt -1))))) (/ 1/6 (* (pow x 3) (pow (sqrt -1) 3))))>
#<alt (- (+ (log (sqrt -1)) (+ (* -1 (log (/ 1 x))) (+ (/ 1 (* x (sqrt -1))) (* 3/40 (/ 1 (* (pow x 5) (pow (sqrt -1) 5))))))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))>
#<alt (+ (log (sqrt -1)) (* -1 (log (/ -1 x))))>
#<alt (- (+ (log (sqrt -1)) (* -1 (log (/ -1 x)))) (/ 1 (* x (sqrt -1))))>
#<alt (+ (log (sqrt -1)) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (/ 1 (sqrt -1)) (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x))))>
#<alt (+ (log (sqrt -1)) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3)))) x))))>
#<alt (* -1 (log x))>
#<alt (* -1 (log x))>
#<alt (* -1 (log x))>
#<alt (* -1 (log x))>
#<alt (log (/ 1 x))>
#<alt (log (/ 1 x))>
#<alt (log (/ 1 x))>
#<alt (log (/ 1 x))>
#<alt (* -1 (+ (log -1) (* -1 (log (/ -1 x)))))>
#<alt (* -1 (+ (log -1) (* -1 (log (/ -1 x)))))>
#<alt (* -1 (+ (log -1) (* -1 (log (/ -1 x)))))>
#<alt (* -1 (+ (log -1) (* -1 (log (/ -1 x)))))>

Calls

36 calls:

Time	Variable		Point	Expression
46.0ms	x	@	0	(log (+ (/ 1 x) (/ 1 x)))
29.0ms	x	@	-inf	(log x)
22.0ms	x	@	-inf	(log (+ (/ 1 x) (/ 1 x)))
11.0ms	x	@	inf	(log x)
11.0ms	x	@	0	(log x)

rewrite73.0ms (0.9%)

Memory

8.0MiB live, 94.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

384×	`lower-/.f32`
378×	`lower-/.f64`
364×	`lower-*.f32`
362×	`lower-*.f64`
302×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	92
0	40	87
1	132	82
0	975	82

Stop Event

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

Counts

14 → 120

Calls

Call 1

Inputs
(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x))
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(*.f64 x x)
(+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(sqrt.f64 #s(literal -1 binary64))
(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)))
(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
(log.f64 (/.f64 (.f64 x x) (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x)))
(neg.f64 (log.f64 (/.f64 (.f64 x x) (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x))))
(log.f64 x)
(log1p.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(neg.f64 (log.f64 x))

Outputs
(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x))
(+.f64 (log1p.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (neg.f64 (log.f64 x)))
(-.f64 (log1p.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (log.f64 x))
(-.f64 #s(literal 0 binary64) (log.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))))
(-.f64 (log.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))) (log.f64 (neg.f64 x)))
(neg.f64 (log.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))))
(/.f64 (-.f64 (pow.f64 (log1p.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) #s(literal 3 binary64)) (pow.f64 (log.f64 x) #s(literal 3 binary64))) (fma.f64 (log1p.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) (log1p.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) (fma.f64 (log.f64 x) (log.f64 x) (.f64 (log1p.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (log.f64 x)))))
(/.f64 (-.f64 (.f64 (log1p.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) (log1p.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))))) (.f64 (log.f64 x) (log.f64 x))) (+.f64 (log1p.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (log.f64 x)))
(exp.f64 (.f64 (log1p.f64 (neg.f64 (.f64 x x))) #s(literal 1/2 binary64)))
(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (sqrt.f64 (fma.f64 (.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x))))) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))))
(.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1 binary64))
(.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(pow.f64 x #s(literal 2 binary64))
(.f64 #s(literal 1 binary64) (.f64 x x))
(*.f64 x x)
(.f64 (.f64 x x) #s(literal 1 binary64))
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(+.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))))) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))))
(fma.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/4 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x)))))
(/.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1 binary64)) (-.f64 (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))))
(/.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))))))
(/.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))) (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))))
(/.f64 (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1 binary64))) (neg.f64 (-.f64 (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x)))) (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))))))
(/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64)) (-.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1 binary64)))
(.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))))
(.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))))
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal -1 binary64))
(pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)))
(log.f64 (/.f64 #s(literal 2 binary64) x))
(+.f64 (log.f64 #s(literal 2 binary64)) (neg.f64 (log.f64 x)))
(-.f64 (log.f64 (+.f64 x x)) (*.f64 #s(literal 2 binary64) (log.f64 x)))
(-.f64 (log.f64 (.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (log.f64 (+.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))))
(-.f64 (log.f64 #s(literal 0 binary64)) (log.f64 #s(literal 0 binary64)))
(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 0 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 0 binary64)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 x)) (/.f64 #s(literal 1 binary64) x))
(fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(fma.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (+.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))))
(/.f64 #s(literal 2 binary64) x)
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (+.f64 x x) (*.f64 x x))
(/.f64 (.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))))
(/.f64 #s(literal -2 binary64) (neg.f64 x))
(/.f64 (fma.f64 #s(literal 1 binary64) (neg.f64 x) (.f64 x #s(literal -1 binary64))) (neg.f64 (.f64 x x)))
(/.f64 (+.f64 (neg.f64 x) (.f64 (neg.f64 x) #s(literal 1 binary64))) (neg.f64 (.f64 x x)))
(/.f64 (fma.f64 #s(literal -1 binary64) (neg.f64 x) (.f64 (neg.f64 x) #s(literal -1 binary64))) (.f64 (neg.f64 x) (neg.f64 x)))
(/.f64 (neg.f64 (+.f64 x x)) (neg.f64 (*.f64 x x)))
(/.f64 (neg.f64 (.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (neg.f64 (+.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))))
(/.f64 (/.f64 (+.f64 x x) x) x)
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(.f64 (+.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 (.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))))
(exp.f64 (neg.f64 (log.f64 x)))
(neg.f64 (/.f64 #s(literal -1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 x)))
(/.f64 #s(literal -1 binary64) (neg.f64 x))
(pow.f64 x #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64)))
(log.f64 (/.f64 (.f64 x x) (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x)))
(+.f64 (log.f64 x) (log.f64 (/.f64 x (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))))
(+.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) (log.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x))))
(+.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) (neg.f64 (log.f64 (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x))))
(-.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) (log.f64 (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x)))
(-.f64 #s(literal 0 binary64) (log.f64 (/.f64 (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x) (.f64 x x))))
(-.f64 (log.f64 (neg.f64 (.f64 x x))) (log.f64 (neg.f64 (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x))))
(fma.f64 #s(literal 2 binary64) (log.f64 x) (log.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))))
(fma.f64 #s(literal 2 binary64) (log.f64 x) (neg.f64 (log.f64 (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))))
(neg.f64 (log.f64 (/.f64 (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x) (.f64 x x))))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 3 binary64)) (pow.f64 (log.f64 (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x)) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) (.f64 #s(literal 2 binary64) (log.f64 x)) (fma.f64 (log.f64 (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x)) (log.f64 (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x)) (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) (log.f64 (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) (.f64 #s(literal 2 binary64) (log.f64 x))) (.f64 (log.f64 (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x)) (log.f64 (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x)))) (fma.f64 #s(literal 2 binary64) (log.f64 x) (log.f64 (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))))
(log.f64 (/.f64 (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x) (.f64 x x)))
(+.f64 #s(literal 0 binary64) (log.f64 (/.f64 (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x) (.f64 x x))))
(+.f64 (-.f64 #s(literal 0 binary64) (.f64 #s(literal 2 binary64) (log.f64 x))) (log.f64 (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x)))
(-.f64 #s(literal 0 binary64) (log.f64 (/.f64 (.f64 x x) (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x))))
(neg.f64 (log.f64 (/.f64 (.f64 x x) (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 (/.f64 (.f64 x x) (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x))) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 (log.f64 (/.f64 (.f64 x x) (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x))) (log.f64 (/.f64 (.f64 x x) (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x))) (.f64 #s(literal 0 binary64) (log.f64 (/.f64 (.f64 x x) (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (log.f64 (/.f64 (.f64 x x) (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x))) (log.f64 (/.f64 (.f64 x x) (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x))))) (+.f64 #s(literal 0 binary64) (log.f64 (/.f64 (.f64 x x) (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))))
(.f64 #s(literal -1 binary64) (log.f64 (/.f64 (.f64 x x) (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))))
(.f64 (log.f64 (/.f64 (.f64 x x) (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))) #s(literal -1 binary64))
(log.f64 x)
(log.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(-.f64 (log1p.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))))) (log1p.f64 (-.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))))
(-.f64 (log1p.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) (log1p.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))))))
(log1p.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(log.f64 (/.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 0 binary64) (neg.f64 (log.f64 x)))
(-.f64 #s(literal 0 binary64) (log.f64 x))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (neg.f64 x)))
(neg.f64 (log.f64 x))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 x) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 (log.f64 x) (log.f64 x) (*.f64 #s(literal 0 binary64) (log.f64 x)))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (log.f64 x) (log.f64 x))) (+.f64 #s(literal 0 binary64) (log.f64 x)))
(*.f64 #s(literal -1 binary64) (log.f64 x))
(*.f64 (log.f64 x) #s(literal -1 binary64))

simplify445.0ms (5.6%)

Memory

24.0MiB live, 497.6MiB allocated

Algorithm

1×	egg-herbie

Rules

18 210×	`lower-fma.f64`
18 210×	`lower-fma.f32`
3 534×	`lower-+.f64`
3 534×	`lower-+.f32`
3 124×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	228	1462
1	658	1391
2	1766	1344
3	5138	1320
0	8341	1280

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 144

Calls

Call 1

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

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

eval44.0ms (0.5%)

Memory: -24.3MiB live, 51.2MiB allocated
Compiler: Compiled 5 528 to 815 computations (85.3% saved)

prune36.0ms (0.4%)

Memory

-0.5MiB live, 49.5MiB allocated

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	375	5	380
Fresh	0	0	0
Picked	4	1	5
Done	0	0	0
Total	379	6	385

Accuracy

100.0%

Counts

385 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	0.0%	(*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal -1 binary64)))
▶	100.0%	(neg.f64 (log.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))))
▶	99.2%	(log.f64 (/.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) x))
▶	54.1%	(log.f64 (/.f64 (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x) (.f64 x x)))
✓	100.0%	(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x))
▶	98.8%	(log.f64 (/.f64 #s(literal 2 binary64) x))

Compiler

Compiled 108 to 74 computations (31.5% saved)

simplify242.0ms (3%)

Memory

23.7MiB live, 216.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
✓	cost-diff	0	(fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)
✓	cost-diff	0	(log.f64 (/.f64 (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x) (.f64 x x)))
✓	cost-diff	512	(/.f64 (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x) (.f64 x x))
✓	cost-diff	0	(*.f64 x #s(literal -1/2 binary64))
✓	cost-diff	0	(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
✓	cost-diff	0	(/.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) x)
✓	cost-diff	0	(log.f64 (/.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) x))
✓	cost-diff	0	(/.f64 #s(literal 2 binary64) x)
✓	cost-diff	0	(log.f64 (/.f64 #s(literal 2 binary64) x))
✓	cost-diff	0	(log.f64 #s(literal -1 binary64))
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal -1 binary64)))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
✓	cost-diff	0	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
✓	cost-diff	0	(log.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))))
✓	cost-diff	128	(neg.f64 (log.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))))

Rules

6 182×	`lower-fma.f32`
6 178×	`lower-fma.f64`
1 998×	`lower--.f32`
1 996×	`lower--.f64`
1 974×	`lower-*.f32`

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	24	155
0	44	153
1	63	153
2	73	153
3	90	152
4	124	150
5	167	150
6	359	150
7	1119	148
8	3218	148
9	4852	148
0	8188	148

Stop Event

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

Calls

Call 1

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

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

localize130.0ms (1.6%)

Memory

-28.0MiB live, 93.0MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(-.f64 #s(literal 1 binary64) (*.f64 x x))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
✓	accuracy	100.0%	(log.f64 (/.f64 (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x) (.f64 x x)))
✓	accuracy	100.0%	(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
✓	accuracy	100.0%	(/.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) x)
✓	accuracy	100.0%	(*.f64 x #s(literal -1/2 binary64))
✓	accuracy	100.0%	(log.f64 (/.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) x))
✓	accuracy	100.0%	(/.f64 #s(literal 2 binary64) x)
✓	accuracy	100.0%	(log.f64 (/.f64 #s(literal 2 binary64) x))
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal -1 binary64)))
✓	accuracy	100.0%	(log.f64 #s(literal -1 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
✓	accuracy	100.0%	(neg.f64 (log.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))))
✓	accuracy	100.0%	(log.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))))

Samples

74.0ms

256×

invalid

Compiler

Compiled 163 to 28 computations (82.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 60.0ms

ival-mult: 33.0ms (55.1% of total)

ival-log: 12.0ms (20% of total)

ival-div: 6.0ms (10% of total)

ival-add: 3.0ms (5% of total)

ival-sqrt: 2.0ms (3.3% of total)

ival-sub: 1.0ms (1.7% of total)

exact: 1.0ms (1.7% of total)

ival-neg: 1.0ms (1.7% of total)

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

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

series22.0ms (0.3%)

Memory

-0.3MiB live, 37.6MiB allocated

Counts

14 → 144

Calls

Call 1

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

Outputs
#<alt (+ (log 1/2) (log x))>
#<alt (+ (log 1/2) (+ (log x) (* 1/4 (pow x 2))))>
#<alt (+ (log 1/2) (+ (log x) (* (pow x 2) (+ 1/4 (* 3/32 (pow x 2))))))>
#<alt (+ (log 1/2) (+ (log x) (* (pow x 2) (+ 1/4 (* (pow x 2) (+ 3/32 (* 5/96 (pow x 2))))))))>
#<alt (log (/ 1 (sqrt -1)))>
#<alt (- (log (/ 1 (sqrt -1))) (/ 1 (* x (sqrt -1))))>
#<alt (- (+ (log (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 3) (pow (sqrt -1) 3)))) (/ 1 (* x (sqrt -1))))>
#<alt (- (+ (log (/ 1 (sqrt -1))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3))))) (+ (/ 1 (* x (sqrt -1))) (* 3/40 (/ 1 (* (pow x 5) (pow (sqrt -1) 5))))))>
#<alt (log (/ -1 (sqrt -1)))>
#<alt (+ (log (/ -1 (sqrt -1))) (/ 1 (* x (sqrt -1))))>
#<alt (+ (log (/ -1 (sqrt -1))) (* -1 (/ (- (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (/ 1 (sqrt -1))) x)))>
#<alt (+ (log (/ -1 (sqrt -1))) (* -1 (/ (- (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3))) (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1)))) x)))>
#<alt (* -1 (+ (log 1/2) (log x)))>
#<alt (- (* -1/4 (pow x 2)) (+ (log 1/2) (log x)))>
#<alt (- (* (pow x 2) (- (* -3/32 (pow x 2)) 1/4)) (+ (log 1/2) (log x)))>
#<alt (- (* (pow x 2) (- (* (pow x 2) (- (* -5/96 (pow x 2)) 3/32)) 1/4)) (+ (log 1/2) (log x)))>
#<alt (* -1 (log (/ 1 (sqrt -1))))>
#<alt (- (/ 1 (* x (sqrt -1))) (log (/ 1 (sqrt -1))))>
#<alt (- (/ 1 (* x (sqrt -1))) (+ (log (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 3) (pow (sqrt -1) 3)))))>
#<alt (- (+ (/ 1 (* x (sqrt -1))) (* 3/40 (/ 1 (* (pow x 5) (pow (sqrt -1) 5))))) (+ (log (/ 1 (sqrt -1))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3))))))>
#<alt (* -1 (log (/ -1 (sqrt -1))))>
#<alt (* -1 (+ (log (/ -1 (sqrt -1))) (/ 1 (* x (sqrt -1)))))>
#<alt (- (* -1 (/ (- (/ 1 (sqrt -1)) (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x)) (log (/ -1 (sqrt -1))))>
#<alt (- (* -1 (/ (- (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3)))) x)) (log (/ -1 (sqrt -1))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))>
#<alt (* x (sqrt -1))>
#<alt (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))>
#<alt (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))>
#<alt (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))>
#<alt (* -1 (* x (sqrt -1)))>
#<alt (* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))>
#<alt (* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))>
#<alt (* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (+ (log 2) (* -1 (log x)))>
#<alt (+ (log 2) (* -1 (log x)))>
#<alt (+ (log 2) (* -1 (log x)))>
#<alt (+ (log 2) (* -1 (log x)))>
#<alt (+ (log 2) (log (/ 1 x)))>
#<alt (+ (log 2) (log (/ 1 x)))>
#<alt (+ (log 2) (log (/ 1 x)))>
#<alt (+ (log 2) (log (/ 1 x)))>
#<alt (+ (log -2) (log (/ -1 x)))>
#<alt (+ (log -2) (log (/ -1 x)))>
#<alt (+ (log -2) (log (/ -1 x)))>
#<alt (+ (log -2) (log (/ -1 x)))>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (+ (log 2) (* -1 (log x)))>
#<alt (+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 2))))>
#<alt (+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* -1/32 (pow x 2)) 1/4))))>
#<alt (+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -1/192 (pow x 2)) 1/32)) 1/4))))>
#<alt (+ (log -1/2) (* -1 (log (/ 1 x))))>
#<alt (- (+ (log -1/2) (* -1 (log (/ 1 x)))) (* 4 (/ 1 (pow x 2))))>
#<alt (+ (log -1/2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 4 (* 8 (/ 1 (pow x 2)))) (pow x 2)))))>
#<alt (- (+ (log -1/2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 8 (* 64/3 (/ 1 (pow x 2)))) (pow x 4))))) (* 4 (/ 1 (pow x 2))))>
#<alt (+ (log 1/2) (* -1 (log (/ -1 x))))>
#<alt (- (+ (log 1/2) (* -1 (log (/ -1 x)))) (* 4 (/ 1 (pow x 2))))>
#<alt (+ (log 1/2) (+ (* -1 (log (/ -1 x))) (* -1 (/ (+ 4 (* 8 (/ 1 (pow x 2)))) (pow x 2)))))>
#<alt (- (+ (log 1/2) (+ (* -1 (log (/ -1 x))) (* -1 (/ (+ 8 (* 64/3 (/ 1 (pow x 2)))) (pow x 4))))) (* 4 (/ 1 (pow x 2))))>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (/ 2 x)>
#<alt (/ (+ 2 (* -1/2 (pow x 2))) x)>
#<alt (/ (+ 2 (* -1/2 (pow x 2))) x)>
#<alt (/ (+ 2 (* -1/2 (pow x 2))) x)>
#<alt (* -1/2 x)>
#<alt (* x (- (* 2 (/ 1 (pow x 2))) 1/2))>
#<alt (* x (- (* 2 (/ 1 (pow x 2))) 1/2))>
#<alt (* x (- (* 2 (/ 1 (pow x 2))) 1/2))>
#<alt (* -1/2 x)>
#<alt (* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))>
#<alt (* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))>
#<alt (* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))>
#<alt 2>
#<alt (+ 2 (* -1/2 (pow x 2)))>
#<alt (+ 2 (* -1/2 (pow x 2)))>
#<alt (+ 2 (* -1/2 (pow x 2)))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))>
#<alt (* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))>
#<alt (* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))>
#<alt (* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))>
#<alt (* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))>
#<alt (+ (log 2) (* -1 (log x)))>
#<alt (+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 2))))>
#<alt (+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* -3/32 (pow x 2)) 1/4))))>
#<alt (+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -5/96 (pow x 2)) 3/32)) 1/4))))>
#<alt (log (sqrt -1))>
#<alt (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1))))>
#<alt (- (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1)))) (/ 1/6 (* (pow x 3) (pow (sqrt -1) 3))))>
#<alt (- (+ (log (sqrt -1)) (+ (/ 1 (* x (sqrt -1))) (* 3/40 (/ 1 (* (pow x 5) (pow (sqrt -1) 5)))))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))>
#<alt (log (* -1 (sqrt -1)))>
#<alt (- (log (* -1 (sqrt -1))) (/ 1 (* x (sqrt -1))))>
#<alt (+ (log (* -1 (sqrt -1))) (* -1 (/ (- (/ 1 (sqrt -1)) (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x)))>
#<alt (+ (log (* -1 (sqrt -1))) (* -1 (/ (- (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3)))) x)))>
#<alt 1>
#<alt (+ 1 (* -1 (pow x 2)))>
#<alt (+ 1 (* -1 (pow x 2)))>
#<alt (+ 1 (* -1 (pow x 2)))>
#<alt (* -1 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1))>
#<alt (* -1 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1))>

Calls

36 calls:

Time	Variable		Point	Expression
7.0ms	x	@	0	(log (/ 2 x))
6.0ms	x	@	-inf	(log (/ 2 x))
2.0ms	x	@	0	(log (/ (+ (* x (sqrt (- 1 (* x x)))) x) (* x x)))
1.0ms	x	@	inf	(log (/ (+ (* x (* x -1/2)) 2) x))
0.0ms	x	@	-inf	(log (/ (+ (* x (* x -1/2)) 2) x))

rewrite372.0ms (4.6%)

Memory

29.9MiB live, 426.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

8 584×	`lower-fma.f32`
8 580×	`lower-fma.f64`
4 662×	`lower-*.f32`
4 656×	`lower-*.f64`
3 370×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	90
0	44	90
1	149	89
2	958	89
0	8626	87

Stop Event

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

Counts

14 → 525

Calls

Call 1

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

Outputs
(log.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))))
(+.f64 (log.f64 x) (neg.f64 (log1p.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))))
(+.f64 #s(literal 0 binary64) (log.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))))
(+.f64 (log.f64 (neg.f64 x)) (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))))
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(.f64 (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (neg.f64 x) #s(literal -1 binary64))))
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(.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (*.f64 x x) x) #s(literal 1 binary64))) #s(literal 1 binary64)))
(.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64))))
(.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x))))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))
(.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/4 binary64))) (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64)))

simplify705.0ms (8.8%)

Memory

3.2MiB live, 752.7MiB allocated

Algorithm

1×	egg-herbie

Rules

23 688×	`lower-fma.f64`
23 688×	`lower-fma.f32`
3 906×	`lower-*.f64`
3 906×	`lower-*.f32`
3 346×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	232	1420
1	630	1349
2	1679	1326
3	4694	1310
0	8164	1261

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 144

Calls

Call 1

Inputs
(+ (log 1/2) (log x))
(+ (log 1/2) (+ (log x) (* 1/4 (pow x 2))))
(+ (log 1/2) (+ (log x) (* (pow x 2) (+ 1/4 (* 3/32 (pow x 2))))))
(+ (log 1/2) (+ (log x) (* (pow x 2) (+ 1/4 (* (pow x 2) (+ 3/32 (* 5/96 (pow x 2))))))))
(log (/ 1 (sqrt -1)))
(- (log (/ 1 (sqrt -1))) (/ 1 (* x (sqrt -1))))
(- (+ (log (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 3) (pow (sqrt -1) 3)))) (/ 1 (* x (sqrt -1))))
(- (+ (log (/ 1 (sqrt -1))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3))))) (+ (/ 1 (* x (sqrt -1))) (* 3/40 (/ 1 (* (pow x 5) (pow (sqrt -1) 5))))))
(log (/ -1 (sqrt -1)))
(+ (log (/ -1 (sqrt -1))) (/ 1 (* x (sqrt -1))))
(+ (log (/ -1 (sqrt -1))) (* -1 (/ (- (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (/ 1 (sqrt -1))) x)))
(+ (log (/ -1 (sqrt -1))) (* -1 (/ (- (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3))) (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1)))) x)))
(* -1 (+ (log 1/2) (log x)))
(- (* -1/4 (pow x 2)) (+ (log 1/2) (log x)))
(- (* (pow x 2) (- (* -3/32 (pow x 2)) 1/4)) (+ (log 1/2) (log x)))
(- (* (pow x 2) (- (* (pow x 2) (- (* -5/96 (pow x 2)) 3/32)) 1/4)) (+ (log 1/2) (log x)))
(* -1 (log (/ 1 (sqrt -1))))
(- (/ 1 (* x (sqrt -1))) (log (/ 1 (sqrt -1))))
(- (/ 1 (* x (sqrt -1))) (+ (log (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 3) (pow (sqrt -1) 3)))))
(- (+ (/ 1 (* x (sqrt -1))) (* 3/40 (/ 1 (* (pow x 5) (pow (sqrt -1) 5))))) (+ (log (/ 1 (sqrt -1))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3))))))
(* -1 (log (/ -1 (sqrt -1))))
(* -1 (+ (log (/ -1 (sqrt -1))) (/ 1 (* x (sqrt -1)))))
(- (* -1 (/ (- (/ 1 (sqrt -1)) (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x)) (log (/ -1 (sqrt -1))))
(- (* -1 (/ (- (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3)))) x)) (log (/ -1 (sqrt -1))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(* x (sqrt -1))
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(+ (log 2) (* -1 (log x)))
(+ (log 2) (* -1 (log x)))
(+ (log 2) (* -1 (log x)))
(+ (log 2) (* -1 (log x)))
(+ (log 2) (log (/ 1 x)))
(+ (log 2) (log (/ 1 x)))
(+ (log 2) (log (/ 1 x)))
(+ (log 2) (log (/ 1 x)))
(+ (log -2) (log (/ -1 x)))
(+ (log -2) (log (/ -1 x)))
(+ (log -2) (log (/ -1 x)))
(+ (log -2) (log (/ -1 x)))
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(+ (log 2) (* -1 (log x)))
(+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 2))))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* -1/32 (pow x 2)) 1/4))))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -1/192 (pow x 2)) 1/32)) 1/4))))
(+ (log -1/2) (* -1 (log (/ 1 x))))
(- (+ (log -1/2) (* -1 (log (/ 1 x)))) (* 4 (/ 1 (pow x 2))))
(+ (log -1/2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 4 (* 8 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log -1/2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 8 (* 64/3 (/ 1 (pow x 2)))) (pow x 4))))) (* 4 (/ 1 (pow x 2))))
(+ (log 1/2) (* -1 (log (/ -1 x))))
(- (+ (log 1/2) (* -1 (log (/ -1 x)))) (* 4 (/ 1 (pow x 2))))
(+ (log 1/2) (+ (* -1 (log (/ -1 x))) (* -1 (/ (+ 4 (* 8 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log 1/2) (+ (* -1 (log (/ -1 x))) (* -1 (/ (+ 8 (* 64/3 (/ 1 (pow x 2)))) (pow x 4))))) (* 4 (/ 1 (pow x 2))))
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(/ 2 x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(* -1/2 x)
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(* -1/2 x)
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
2
(+ 2 (* -1/2 (pow x 2)))
(+ 2 (* -1/2 (pow x 2)))
(+ 2 (* -1/2 (pow x 2)))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))
(+ (log 2) (* -1 (log x)))
(+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 2))))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* -3/32 (pow x 2)) 1/4))))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -5/96 (pow x 2)) 3/32)) 1/4))))
(log (sqrt -1))
(+ (log (sqrt -1)) (/ 1 (* x (sqrt -1))))
(- (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1)))) (/ 1/6 (* (pow x 3) (pow (sqrt -1) 3))))
(- (+ (log (sqrt -1)) (+ (/ 1 (* x (sqrt -1))) (* 3/40 (/ 1 (* (pow x 5) (pow (sqrt -1) 5)))))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))
(log (* -1 (sqrt -1)))
(- (log (* -1 (sqrt -1))) (/ 1 (* x (sqrt -1))))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (/ 1 (sqrt -1)) (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x)))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3)))) x)))
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))

Outputs
(+ (log 1/2) (log x))
(+.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 x))
(+ (log 1/2) (+ (log x) (* 1/4 (pow x 2))))
(+.f64 (log.f64 #s(literal 1/2 binary64)) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) (log.f64 x)))
(+ (log 1/2) (+ (log x) (* (pow x 2) (+ 1/4 (* 3/32 (pow x 2))))))
(+.f64 (log.f64 x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 3/32 binary64)) #s(literal 1/4 binary64))) (log.f64 #s(literal 1/2 binary64))))
(+ (log 1/2) (+ (log x) (* (pow x 2) (+ 1/4 (* (pow x 2) (+ 3/32 (* 5/96 (pow x 2))))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal 5/96 binary64) #s(literal 3/32 binary64)) #s(literal 1/4 binary64)) (+.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 x)))
(log (/ 1 (sqrt -1)))
(neg.f64 (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(- (log (/ 1 (sqrt -1))) (/ 1 (* x (sqrt -1))))
(-.f64 (/.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(- (+ (log (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 3) (pow (sqrt -1) 3)))) (/ 1 (* x (sqrt -1))))
(+.f64 (-.f64 (/.f64 #s(literal -1 binary64) (.f64 x (sqrt.f64 #s(literal -1 binary64)))) (log.f64 (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (.f64 x (sqrt.f64 #s(literal -1 binary64))))))
(- (+ (log (/ 1 (sqrt -1))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3))))) (+ (/ 1 (* x (sqrt -1))) (* 3/40 (/ 1 (* (pow x 5) (pow (sqrt -1) 5))))))
(+.f64 (/.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (.f64 x (sqrt.f64 #s(literal -1 binary64))))) (-.f64 (-.f64 (/.f64 #s(literal -1 binary64) (.f64 x (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal 3/40 binary64) (*.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))))) (log.f64 (sqrt.f64 #s(literal -1 binary64)))))
(log (/ -1 (sqrt -1)))
(neg.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(+ (log (/ -1 (sqrt -1))) (/ 1 (* x (sqrt -1))))
(-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(+ (log (/ -1 (sqrt -1))) (* -1 (/ (- (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (/ 1 (sqrt -1))) x)))
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 #s(literal -1 binary64)))) (-.f64 (/.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (.f64 x (sqrt.f64 #s(literal -1 binary64))))) (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))))))
(+ (log (/ -1 (sqrt -1))) (* -1 (/ (- (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3))) (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1)))) x)))
(-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64))))) (/.f64 #s(literal -3/40 binary64) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) (.f64 x (.f64 x (.f64 x x))))))) x) (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (+ (log 1/2) (log x)))
(-.f64 (neg.f64 (log.f64 x)) (log.f64 #s(literal 1/2 binary64)))
(- (* -1/4 (pow x 2)) (+ (log 1/2) (log x)))
(-.f64 (.f64 (.f64 x x) #s(literal -1/4 binary64)) (+.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 x)))
(- (* (pow x 2) (- (* -3/32 (pow x 2)) 1/4)) (+ (log 1/2) (log x)))
(-.f64 (.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -3/32 binary64) #s(literal -1/4 binary64))) (+.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 x)))
(- (* (pow x 2) (- (* (pow x 2) (- (* -5/96 (pow x 2)) 3/32)) 1/4)) (+ (log 1/2) (log x)))
(-.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -5/96 binary64)) #s(literal -3/32 binary64)) #s(literal -1/4 binary64)) (neg.f64 (log.f64 x))) (log.f64 #s(literal 1/2 binary64)))
(* -1 (log (/ 1 (sqrt -1))))
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(- (/ 1 (* x (sqrt -1))) (log (/ 1 (sqrt -1))))
(+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(- (/ 1 (* x (sqrt -1))) (+ (log (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 3) (pow (sqrt -1) 3)))))
(+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (.f64 x (sqrt.f64 #s(literal -1 binary64)))))) (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(- (+ (/ 1 (* x (sqrt -1))) (* 3/40 (/ 1 (* (pow x 5) (pow (sqrt -1) 5))))) (+ (log (/ 1 (sqrt -1))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3))))))
(+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (.f64 x (sqrt.f64 #s(literal -1 binary64)))))) (+.f64 (/.f64 #s(literal 3/40 binary64) (*.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (log.f64 (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (log (/ -1 (sqrt -1))))
(log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(* -1 (+ (log (/ -1 (sqrt -1))) (/ 1 (* x (sqrt -1)))))
(+.f64 (/.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(- (* -1 (/ (- (/ 1 (sqrt -1)) (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x)) (log (/ -1 (sqrt -1))))
(+.f64 (+.f64 (/.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (.f64 x (sqrt.f64 #s(literal -1 binary64))))) (/.f64 #s(literal -1 binary64) (.f64 x (sqrt.f64 #s(literal -1 binary64))))) (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(- (* -1 (/ (- (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3)))) x)) (log (/ -1 (sqrt -1))))
(+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64))))) (/.f64 #s(literal -3/40 binary64) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) (.f64 x (.f64 x (.f64 x x))))))) x) (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/8 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/16 binary64) #s(literal -1/8 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(* x (sqrt -1))
(*.f64 x (sqrt.f64 #s(literal -1 binary64)))
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(fma.f64 x (sqrt.f64 #s(literal -1 binary64)) (.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 #s(literal -1 binary64))))))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 #s(literal -1 binary64)))) (.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x (.f64 x (.f64 x x)))))) x))
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 #s(literal -1 binary64)))) (.f64 x (+.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) (pow.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x (.f64 x (*.f64 x x)))))))))
(* -1 (* x (sqrt -1)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(-.f64 (.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 #s(literal -1 binary64))))) (*.f64 x (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(fma.f64 x (-.f64 (/.f64 #s(literal -1/8 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x (.f64 x (.f64 x x))))) (sqrt.f64 #s(literal -1 binary64))) (.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 #s(literal -1 binary64))))))
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))
(.f64 x (-.f64 (/.f64 #s(literal -1/8 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x (.f64 x (.f64 x x))))) (+.f64 (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64)))))) (/.f64 #s(literal 1/16 binary64) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) (pow.f64 x #s(literal 6 binary64)))))))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(+ (log 2) (* -1 (log x)))
(-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (* -1 (log x)))
(-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (* -1 (log x)))
(-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (* -1 (log x)))
(-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (log (/ 1 x)))
(-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (log (/ 1 x)))
(-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (log (/ 1 x)))
(-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (log (/ 1 x)))
(-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log -2) (log (/ -1 x)))
(+.f64 (log.f64 #s(literal -2 binary64)) (neg.f64 (log.f64 (neg.f64 x))))
(+ (log -2) (log (/ -1 x)))
(+.f64 (log.f64 #s(literal -2 binary64)) (neg.f64 (log.f64 (neg.f64 x))))
(+ (log -2) (log (/ -1 x)))
(+.f64 (log.f64 #s(literal -2 binary64)) (neg.f64 (log.f64 (neg.f64 x))))
(+ (log -2) (log (/ -1 x)))
(+.f64 (log.f64 #s(literal -2 binary64)) (neg.f64 (log.f64 (neg.f64 x))))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(+ (log 2) (* -1 (log x)))
(-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 2))))
(-.f64 (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (log.f64 #s(literal 2 binary64))) (log.f64 x))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* -1/32 (pow x 2)) 1/4))))
(-.f64 (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/32 binary64)) #s(literal -1/4 binary64)) (log.f64 #s(literal 2 binary64))) (log.f64 x))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -1/192 (pow x 2)) 1/32)) 1/4))))
(-.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/192 binary64) #s(literal -1/32 binary64)) #s(literal -1/4 binary64)) (log.f64 #s(literal 2 binary64))) (log.f64 x))
(+ (log -1/2) (* -1 (log (/ 1 x))))
(+.f64 (log.f64 x) (log.f64 #s(literal -1/2 binary64)))
(- (+ (log -1/2) (* -1 (log (/ 1 x)))) (* 4 (/ 1 (pow x 2))))
(+.f64 (+.f64 (log.f64 x) (log.f64 #s(literal -1/2 binary64))) (/.f64 #s(literal -4 binary64) (*.f64 x x)))
(+ (log -1/2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 4 (* 8 (/ 1 (pow x 2)))) (pow x 2)))))
(+.f64 (log.f64 x) (+.f64 (log.f64 #s(literal -1/2 binary64)) (/.f64 (-.f64 #s(literal -4 binary64) (/.f64 #s(literal 8 binary64) (.f64 x x))) (.f64 x x))))
(- (+ (log -1/2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 8 (* 64/3 (/ 1 (pow x 2)))) (pow x 4))))) (* 4 (/ 1 (pow x 2))))
(+.f64 (log.f64 x) (+.f64 (log.f64 #s(literal -1/2 binary64)) (+.f64 (/.f64 (+.f64 #s(literal -8 binary64) (/.f64 #s(literal -64/3 binary64) (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -4 binary64) (*.f64 x x)))))
(+ (log 1/2) (* -1 (log (/ -1 x))))
(-.f64 (log.f64 #s(literal 1/2 binary64)) (neg.f64 (log.f64 (neg.f64 x))))
(- (+ (log 1/2) (* -1 (log (/ -1 x)))) (* 4 (/ 1 (pow x 2))))
(+.f64 (log.f64 #s(literal 1/2 binary64)) (-.f64 (/.f64 #s(literal -4 binary64) (*.f64 x x)) (neg.f64 (log.f64 (neg.f64 x)))))
(+ (log 1/2) (+ (* -1 (log (/ -1 x))) (* -1 (/ (+ 4 (* 8 (/ 1 (pow x 2)))) (pow x 2)))))
(+.f64 (/.f64 (-.f64 #s(literal -4 binary64) (/.f64 #s(literal 8 binary64) (.f64 x x))) (.f64 x x)) (-.f64 (log.f64 #s(literal 1/2 binary64)) (neg.f64 (log.f64 (neg.f64 x)))))
(- (+ (log 1/2) (+ (* -1 (log (/ -1 x))) (* -1 (/ (+ 8 (* 64/3 (/ 1 (pow x 2)))) (pow x 4))))) (* 4 (/ 1 (pow x 2))))
(+.f64 (-.f64 (log.f64 #s(literal 1/2 binary64)) (neg.f64 (log.f64 (neg.f64 x)))) (+.f64 (/.f64 (+.f64 #s(literal -8 binary64) (/.f64 #s(literal -64/3 binary64) (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -4 binary64) (*.f64 x x))))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) x)
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x) (*.f64 x #s(literal -1/2 binary64)))
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x) (*.f64 x #s(literal -1/2 binary64)))
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x) (*.f64 x #s(literal -1/2 binary64)))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x) (*.f64 x #s(literal -1/2 binary64)))
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x) (*.f64 x #s(literal -1/2 binary64)))
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x) (*.f64 x #s(literal -1/2 binary64)))
2
#s(literal 2 binary64)
(+ 2 (* -1/2 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
(+ 2 (* -1/2 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
(+ 2 (* -1/2 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
(* (pow x 2) (- (* 2 (/ 1 (pow x 2))) 1/2))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
(+ (log 2) (* -1 (log x)))
(-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 2))))
(-.f64 (fma.f64 x (*.f64 x #s(literal -1/4 binary64)) (log.f64 #s(literal 2 binary64))) (log.f64 x))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* -3/32 (pow x 2)) 1/4))))
(-.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -3/32 binary64) #s(literal -1/4 binary64))) (log.f64 #s(literal 2 binary64))) (log.f64 x))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -5/96 (pow x 2)) 3/32)) 1/4))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -5/96 binary64)) #s(literal -3/32 binary64)) #s(literal -1/4 binary64)) (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x)))
(log (sqrt -1))
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (log (sqrt -1)) (/ 1 (* x (sqrt -1))))
(+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(- (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1)))) (/ 1/6 (* (pow x 3) (pow (sqrt -1) 3))))
(+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (.f64 x (sqrt.f64 #s(literal -1 binary64)))))) (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(- (+ (log (sqrt -1)) (+ (/ 1 (* x (sqrt -1))) (* 3/40 (/ 1 (* (pow x 5) (pow (sqrt -1) 5)))))) (* 1/6 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))))
(+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (.f64 x (sqrt.f64 #s(literal -1 binary64)))))) (+.f64 (/.f64 #s(literal 3/40 binary64) (*.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (log.f64 (sqrt.f64 #s(literal -1 binary64)))))
(log (* -1 (sqrt -1)))
(log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))))
(- (log (* -1 (sqrt -1))) (/ 1 (* x (sqrt -1))))
(+.f64 (/.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (/ 1 (sqrt -1)) (* 1/6 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x)))
(+.f64 (+.f64 (/.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (.f64 x (sqrt.f64 #s(literal -1 binary64))))) (/.f64 #s(literal -1 binary64) (.f64 x (sqrt.f64 #s(literal -1 binary64))))) (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(+ (log (* -1 (sqrt -1))) (* -1 (/ (- (+ (/ 3/40 (* (pow x 4) (pow (sqrt -1) 5))) (/ 1 (sqrt -1))) (/ 1/6 (* (pow x 2) (pow (sqrt -1) 3)))) x)))
(+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64))))) (/.f64 #s(literal -3/40 binary64) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) (.f64 x (.f64 x (.f64 x x))))))) x) (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* -1 (pow x 2))
(*.f64 x (neg.f64 x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* -1 (pow x 2))
(*.f64 x (neg.f64 x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))

eval181.0ms (2.3%)

Memory: -18.3MiB live, 218.9MiB allocated
Compiler: Compiled 20 442 to 3 019 computations (85.2% saved)

prune105.0ms (1.3%)

Memory

14.7MiB live, 184.0MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	904	1	905
Fresh	0	0	0
Picked	1	4	5
Done	0	1	1
Total	905	6	911

Accuracy

100.0%

Counts

911 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	0.0%	(*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal -1 binary64)))
✓	100.0%	(neg.f64 (log.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))))
▶	98.8%	(neg.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))
✓	99.2%	(log.f64 (/.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) x))
✓	54.1%	(log.f64 (/.f64 (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x) (.f64 x x)))
✓	100.0%	(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x))

Compiler

Compiled 61 to 42 computations (31.1% saved)

simplify5.0ms (0.1%)

Memory

3.4MiB live, 3.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 x #s(literal 1/2 binary64))
✓	cost-diff	(log.f64 (*.f64 x #s(literal 1/2 binary64)))
✓	cost-diff	(neg.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))

Rules

8×	`lower-+.f64`
8×	`lower-*.f32`
8×	`lower-+.f32`
6×	`lower-*.f64`
6×	`sub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	14
0	8	14
1	13	14
2	15	14
3	17	14
4	19	14
5	23	14
6	28	14
0	28	14

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(neg.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))
(log.f64 (*.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)

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

localize41.0ms (0.5%)

Memory

1.1MiB live, 37.6MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x #s(literal 1/2 binary64))
✓	accuracy	100.0%	(neg.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(log.f64 (*.f64 x #s(literal 1/2 binary64)))

Samples

34.0ms

256×

valid

Compiler

Compiled 16 to 7 computations (56.3% saved)

Precisions

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

ival-mult: 25.0ms (85.9% of total)

ival-log: 3.0ms (10.3% of total)

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

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

exact: 0.0ms (0% of total)

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

series50.0ms (0.6%)

Memory

7.5MiB live, 85.4MiB allocated

Counts

3 → 36

Calls

Call 1

Inputs
#<alt (log.f64 (*.f64 x #s(literal 1/2 binary64)))>
#<alt (neg.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))>
#<alt (*.f64 x #s(literal 1/2 binary64))>

Outputs
#<alt (+ (log 1/2) (log x))>
#<alt (+ (log 1/2) (log x))>
#<alt (+ (log 1/2) (log x))>
#<alt (+ (log 1/2) (log x))>
#<alt (+ (log 1/2) (* -1 (log (/ 1 x))))>
#<alt (+ (log 1/2) (* -1 (log (/ 1 x))))>
#<alt (+ (log 1/2) (* -1 (log (/ 1 x))))>
#<alt (+ (log 1/2) (* -1 (log (/ 1 x))))>
#<alt (+ (log -1/2) (* -1 (log (/ -1 x))))>
#<alt (+ (log -1/2) (* -1 (log (/ -1 x))))>
#<alt (+ (log -1/2) (* -1 (log (/ -1 x))))>
#<alt (+ (log -1/2) (* -1 (log (/ -1 x))))>
#<alt (* -1 (+ (log 1/2) (log x)))>
#<alt (* -1 (+ (log 1/2) (log x)))>
#<alt (* -1 (+ (log 1/2) (log x)))>
#<alt (* -1 (+ (log 1/2) (log x)))>
#<alt (* -1 (+ (log 1/2) (* -1 (log (/ 1 x)))))>
#<alt (* -1 (+ (log 1/2) (* -1 (log (/ 1 x)))))>
#<alt (* -1 (+ (log 1/2) (* -1 (log (/ 1 x)))))>
#<alt (* -1 (+ (log 1/2) (* -1 (log (/ 1 x)))))>
#<alt (* -1 (+ (log -1/2) (* -1 (log (/ -1 x)))))>
#<alt (* -1 (+ (log -1/2) (* -1 (log (/ -1 x)))))>
#<alt (* -1 (+ (log -1/2) (* -1 (log (/ -1 x)))))>
#<alt (* -1 (+ (log -1/2) (* -1 (log (/ -1 x)))))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>

Calls

9 calls:

Time	Variable		Point	Expression
30.0ms	x	@	0	(log (* x 1/2))
14.0ms	x	@	-inf	(log (* x 1/2))
6.0ms	x	@	inf	(log (* x 1/2))
0.0ms	x	@	inf	(neg (log (* x 1/2)))
0.0ms	x	@	-inf	(neg (log (* x 1/2)))

rewrite188.0ms (2.3%)

Memory

-23.7MiB live, 209.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

2 296×	`lower-fma.f64`
2 296×	`lower-fma.f32`
2 120×	`lower-*.f32`
2 118×	`lower-*.f64`
1 196×	`lower-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	12
0	8	11
1	19	11
2	72	11
3	498	11
4	4576	11
0	9349	11

Stop Event

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

Counts

3 → 507

Calls

Call 1

Inputs
(log.f64 (*.f64 x #s(literal 1/2 binary64)))
(neg.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))
(*.f64 x #s(literal 1/2 binary64))

Outputs
(log.f64 (*.f64 x #s(literal 1/2 binary64)))
(+.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 0 binary64))
(+.f64 (log.f64 x) (log.f64 #s(literal 1/2 binary64)))
(+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64)))
(+.f64 (log.f64 x) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal -1 binary64)))
(+.f64 (log.f64 x) (*.f64 #s(literal 1 binary64) (log.f64 #s(literal 1/2 binary64))))
(+.f64 (log.f64 x) (+.f64 (log.f64 #s(literal 2 binary64)) #s(literal 0 binary64)))
(+.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 x))
(+.f64 #s(literal 0 binary64) (log.f64 (*.f64 x #s(literal 1/2 binary64))))
(+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
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(pow.f64 (pow.f64 (exp.f64 (pow.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3 binary64))) (pow.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal -3 binary64))) (log.f64 (*.f64 x #s(literal 1/2 binary64))))
(pow.f64 (pow.f64 (pow.f64 (.f64 x #s(literal 1/2 binary64)) (log.f64 (.f64 x #s(literal 1/2 binary64)))) (fma.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) (log.f64 x) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (log.f64 x) #s(literal 3 binary64)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)))))
(pow.f64 (pow.f64 (pow.f64 (.f64 x #s(literal 1/2 binary64)) (log.f64 (.f64 x #s(literal 1/2 binary64)))) (pow.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal -2 binary64))) (log.f64 (.f64 x #s(literal 1/2 binary64))))
(pow.f64 (pow.f64 (pow.f64 (.f64 x #s(literal 1/2 binary64)) (log.f64 (.f64 x #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (log.f64 x) #s(literal 3 binary64)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64))))) (fma.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) (log.f64 x) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64))))
(pow.f64 (pow.f64 (pow.f64 (.f64 x #s(literal 1/2 binary64)) (log.f64 (.f64 x #s(literal 1/2 binary64)))) (/.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) (+.f64 (pow.f64 (log.f64 x) #s(literal 6 binary64)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 6 binary64))))) (+.f64 (pow.f64 (log.f64 x) #s(literal 4 binary64)) (pow.f64 (.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) (log.f64 #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(pow.f64 (pow.f64 (pow.f64 (.f64 x #s(literal 1/2 binary64)) (log.f64 (.f64 x #s(literal 1/2 binary64)))) (/.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) (pow.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 4 binary64)))) (pow.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(pow.f64 (pow.f64 (pow.f64 (.f64 x #s(literal 1/2 binary64)) (log.f64 (.f64 x #s(literal 1/2 binary64)))) (pow.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal -3 binary64))) (pow.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(pow.f64 (pow.f64 (pow.f64 (.f64 x #s(literal 1/2 binary64)) (log.f64 (.f64 x #s(literal 1/2 binary64)))) (/.f64 (fma.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) (log.f64 x) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64))) (+.f64 (pow.f64 (log.f64 x) #s(literal 9 binary64)) (pow.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 9 binary64))))) (+.f64 (pow.f64 (log.f64 x) #s(literal 6 binary64)) (+.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 6 binary64)) (pow.f64 (.f64 (log.f64 x) (log.f64 #s(literal 1/2 binary64))) #s(literal 3 binary64)))))
(pow.f64 (pow.f64 (pow.f64 (.f64 x #s(literal 1/2 binary64)) (log.f64 (.f64 x #s(literal 1/2 binary64)))) (/.f64 (fma.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) (log.f64 x) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64))) (+.f64 (pow.f64 (log.f64 x) #s(literal 6 binary64)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 6 binary64))))) (+.f64 (pow.f64 (log.f64 x) #s(literal 3 binary64)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64))))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (log.f64 (*.f64 x #s(literal 1/2 binary64))))
(pow.f64 (exp.f64 (+.f64 (pow.f64 (log.f64 x) #s(literal 3 binary64)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) (log.f64 x) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))))
(pow.f64 (exp.f64 (+.f64 (pow.f64 (log.f64 x) #s(literal 3 binary64)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) (log.f64 x) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64))))))
(pow.f64 (exp.f64 (+.f64 (pow.f64 (log.f64 x) #s(literal 3 binary64)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) (log.f64 x) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))) #s(literal -1 binary64)))
(pow.f64 (exp.f64 (fma.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) (log.f64 x) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))) (.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) (log.f64 x) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64))))))
(pow.f64 (exp.f64 (fma.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) (log.f64 x) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))) (/.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) (fma.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) (log.f64 x) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))))
(pow.f64 (exp.f64 (/.f64 #s(literal 1 binary64) (log.f64 (.f64 x #s(literal 1/2 binary64))))) (pow.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(pow.f64 (exp.f64 (pow.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal -2 binary64))) (pow.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3 binary64)))
(pow.f64 (exp.f64 (/.f64 (pow.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (log.f64 (.f64 x #s(literal 1/2 binary64)))))
(pow.f64 (exp.f64 (/.f64 (pow.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64)) (+.f64 (pow.f64 (log.f64 x) #s(literal 3 binary64)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64))))) (fma.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) (log.f64 x) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64))))
(pow.f64 (exp.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) (log.f64 x) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64))))) (+.f64 (pow.f64 (log.f64 x) #s(literal 3 binary64)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64))))
(pow.f64 (exp.f64 (pow.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3/2 binary64))) (pow.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal -1/2 binary64)))
(pow.f64 (exp.f64 (/.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) (+.f64 (pow.f64 (log.f64 x) #s(literal 3 binary64)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64))))) (/.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) (log.f64 x) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64))))))
(pow.f64 (exp.f64 (pow.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/2 binary64))) (pow.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1/2 binary64)))
(pow.f64 (exp.f64 (/.f64 (pow.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3 binary64)) (+.f64 (pow.f64 (log.f64 x) #s(literal 6 binary64)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 6 binary64))))) (pow.f64 (fma.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) (log.f64 x) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64))) #s(literal 2 binary64)))
(pow.f64 (exp.f64 (/.f64 (pow.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3 binary64)) (.f64 (+.f64 (pow.f64 (log.f64 x) #s(literal 3 binary64)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64))) (pow.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64))))) (+.f64 (pow.f64 (log.f64 x) #s(literal 3 binary64)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64))))
(pow.f64 (exp.f64 (pow.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal -3 binary64))) (pow.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 4 binary64)))
(pow.f64 (exp.f64 (/.f64 (pow.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3 binary64)) (.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) (+.f64 (pow.f64 (log.f64 x) #s(literal 3 binary64)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)))))) (fma.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) (log.f64 x) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64))))
(pow.f64 (exp.f64 (/.f64 (pow.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3 binary64)))) (log.f64 (*.f64 x #s(literal 1/2 binary64))))
(pow.f64 (exp.f64 (/.f64 (+.f64 (pow.f64 (log.f64 x) #s(literal 3 binary64)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64))) (+.f64 (pow.f64 (log.f64 x) #s(literal 6 binary64)) (pow.f64 (.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) (log.f64 #s(literal 1/2 binary64))) #s(literal 3 binary64))))) (fma.f64 (.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) (log.f64 #s(literal 1/2 binary64))) (-.f64 (.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) (log.f64 #s(literal 1/2 binary64))) (pow.f64 (log.f64 x) #s(literal 2 binary64))) (pow.f64 (log.f64 x) #s(literal 4 binary64))))
(pow.f64 (exp.f64 (/.f64 (+.f64 (pow.f64 (log.f64 x) #s(literal 3 binary64)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64))) (pow.f64 (fma.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) (log.f64 x) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64))) #s(literal 2 binary64)))) (fma.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) (log.f64 x) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64))))
(*.f64 x #s(literal 1/2 binary64))
(*.f64 x #s(literal 2 binary64))
(*.f64 x (exp.f64 (+.f64 (log.f64 #s(literal 2 binary64)) #s(literal 0 binary64))))
(*.f64 #s(literal 1/2 binary64) x)
(.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))
(.f64 #s(literal -1 binary64) (.f64 x #s(literal -1/2 binary64)))
(.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 2 binary64) x)
(*.f64 #s(literal -1/2 binary64) (neg.f64 x))
(*.f64 #s(literal -1/2 binary64) (/.f64 x #s(literal -1 binary64)))
(*.f64 #s(literal -2 binary64) (neg.f64 x))
(*.f64 (neg.f64 x) #s(literal -1/2 binary64))
(*.f64 (neg.f64 x) #s(literal -2 binary64))
(.f64 (pow.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) (pow.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (/.f64 (pow.f64 (log.f64 x) #s(literal 2 binary64)) (log.f64 (.f64 x #s(literal 1/2 binary64))))) (pow.f64 (exp.f64 #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (log.f64 (*.f64 x #s(literal 1/2 binary64)))))))
(*.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (log.f64 #s(literal 2 binary64)))) x)
(.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (log.f64 #s(literal -1 binary64)))) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (.f64 x #s(literal -1/2 binary64)))))
(*.f64 (exp.f64 (+.f64 (log.f64 #s(literal 2 binary64)) #s(literal 0 binary64))) x)
(.f64 (exp.f64 (-.f64 #s(literal 0 binary64) (/.f64 (pow.f64 (log.f64 x) #s(literal 2 binary64)) (log.f64 (.f64 x #s(literal 1/2 binary64)))))) (exp.f64 (/.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (log.f64 (*.f64 x #s(literal 1/2 binary64))))))
(.f64 (exp.f64 (/.f64 (pow.f64 (log.f64 x) #s(literal 2 binary64)) (log.f64 (.f64 x #s(literal 1/2 binary64))))) (exp.f64 (neg.f64 (/.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (log.f64 (*.f64 x #s(literal 1/2 binary64)))))))
(*.f64 (exp.f64 (-.f64 #s(literal 0 binary64) (log.f64 #s(literal 2 binary64)))) x)
(.f64 (exp.f64 (-.f64 #s(literal 0 binary64) (log.f64 #s(literal -1 binary64)))) (.f64 x #s(literal -1/2 binary64)))

simplify15.0ms (0.2%)

Memory

15.5MiB live, 15.5MiB allocated

Algorithm

1×	egg-herbie

Rules

160×	`lower-fma.f64`
160×	`lower-fma.f32`
100×	`lower-*.f64`
100×	`lower-*.f32`
64×	`lower-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	192
1	54	184
2	79	180
3	119	180
4	190	180
5	254	180
6	280	180
7	288	180
0	288	180

Stop Event

1×	iter limit
1×	saturated

Counts

36 → 36

Calls

Call 1

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

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

eval89.0ms (1.1%)

Memory: -5.4MiB live, 111.3MiB allocated
Compiler: Compiled 8 933 to 1 048 computations (88.3% saved)

prune71.0ms (0.9%)

Memory

-4.2MiB live, 114.2MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	542	1	543
Fresh	0	0	0
Picked	0	1	1
Done	1	4	5
Total	543	6	549

Accuracy

100.0%

Counts

549 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(neg.f64 (log.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))))
✓	98.8%	(neg.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))
✓	99.2%	(log.f64 (/.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) x))
✓	54.1%	(log.f64 (/.f64 (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x) (.f64 x x)))
✓	100.0%	(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x))
	1.5%	(log.f64 (*.f64 x #s(literal 1/2 binary64)))

Compiler

Compiled 175 to 85 computations (51.4% saved)

regimes13.0ms (0.2%)

Memory

18.3MiB live, 18.3MiB allocated

Counts

13 → 1

Calls

Call 1

Inputs
(log.f64 (*.f64 x #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal -1 binary64)))
(neg.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(log.f64 (/.f64 #s(literal 2 binary64) x))
(log.f64 (/.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) x))
(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)))
(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x))
(neg.f64 (log.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))))
(log.f64 (/.f64 (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x) (.f64 x x)))
(neg.f64 (log.f64 (/.f64 (.f64 x x) (fma.f64 x (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) x))))
(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
(+.f64 (neg.f64 (log.f64 x)) (log1p.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))

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

Calls

3 calls:

4.0ms

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

4.0ms

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

4.0ms

Results

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

Compiler

Compiled 29 to 18 computations (37.9% saved)

regimes9.0ms (0.1%)

Memory

13.8MiB live, 13.8MiB allocated

Counts

8 → 1

Calls

Call 1

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

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

Calls

3 calls:

3.0ms

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

3.0ms

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

3.0ms

Results

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

Compiler

Compiled 29 to 18 computations (37.9% saved)

regimes14.0ms (0.2%)

Memory

-35.4MiB live, 18.2MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

3 calls:

7.0ms

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

3.0ms

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

3.0ms

Results

Accuracy	Segments	Branch
99.2%	1	`x`
99.2%	1	`(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))`
99.2%	1	`(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))`

Compiler

Compiled 29 to 18 computations (37.9% saved)

regimes7.0ms (0.1%)

Memory

13.5MiB live, 13.5MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

3 calls:

2.0ms

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

2.0ms

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

2.0ms

Results

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

Compiler

Compiled 29 to 18 computations (37.9% saved)

regimes5.0ms (0.1%)

Memory

7.5MiB live, 7.5MiB allocated

Accuracy

Total -1.0b remaining (-1.6%)

Threshold costs -1b (-1.6%)

Counts

2 → 1

Calls

Call 1

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

Outputs
(log.f64 (*.f64 x #s(literal 1/2 binary64)))

Calls

3 calls:

2.0ms

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

2.0ms

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

1.0ms

Results

Accuracy	Segments	Branch
1.5%	1	`x`
1.5%	1	`(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))`
1.5%	1	`(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))`

Compiler

Compiled 29 to 18 computations (37.9% saved)

simplify6.0ms (0.1%)

Memory

6.5MiB live, 6.5MiB allocated

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
12×	`+-commutative_binary64`
10×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	41
1	37	41
2	47	41
3	53	41
4	55	41

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness848.0ms (10.6%)

Memory

-17.7MiB live, 532.4MiB allocated

Rules

18 210×	`lower-fma.f64`
18 210×	`lower-fma.f32`
13 898×	`lower-fma.f64`
13 898×	`lower-fma.f32`
8 584×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	30
0	16	30
1	69	30
2	624	28
3	7596	28
0	8354	28
0	21	92
0	40	87
1	132	82
0	975	82
0	228	1462
1	658	1391
2	1766	1344
3	5138	1320
0	8341	1280
0	5	12
0	8	11
1	19	11
2	72	11
3	498	11
4	4576	11
0	9349	11
0	24	90
0	44	90
1	149	89
2	958	89
0	8626	87
0	127	618
1	328	598
2	901	582
3	2639	570
4	7140	570
0	8341	547

Stop Event

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

Compiler

Compiled 164 to 101 computations (38.4% saved)

preprocess82.0ms (1%)

Memory: 8.7MiB live, 95.3MiB allocated
Compiler: Compiled 112 to 60 computations (46.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	21	192
1	54	184
2	79	180
3	119	180
4	190	180
5	254	180
6	280	180
7	288	180
0	288	180

Iter	Nodes	Cost
0	21	192
1	54	184
2	79	180
3	119	180
4	190	180
5	254	180
6	280	180
7	288	180
0	288	180

analyze4.0ms (0%)

sample1.3s (15.7%)

preprocess940.0ms (11.7%)

explain134.0ms (1.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify592.0ms (7.4%)

localize33.0ms (0.4%)

series5.0ms (0.1%)

rewrite269.0ms (3.4%)

simplify357.0ms (4.4%)

eval27.0ms (0.3%)

prune45.0ms (0.6%)

simplify323.0ms (4%)

localize100.0ms (1.3%)

series137.0ms (1.7%)

rewrite73.0ms (0.9%)

simplify445.0ms (5.6%)

eval44.0ms (0.5%)

prune36.0ms (0.4%)

simplify242.0ms (3%)

localize130.0ms (1.6%)

series22.0ms (0.3%)

rewrite372.0ms (4.6%)

simplify705.0ms (8.8%)

eval181.0ms (2.3%)

prune105.0ms (1.3%)

simplify5.0ms (0.1%)

localize41.0ms (0.5%)

series50.0ms (0.6%)

rewrite188.0ms (2.3%)

simplify15.0ms (0.2%)

eval89.0ms (1.1%)

prune71.0ms (0.9%)

regimes13.0ms (0.2%)

regimes9.0ms (0.1%)

regimes14.0ms (0.2%)

regimes7.0ms (0.1%)

regimes5.0ms (0.1%)

simplify6.0ms (0.1%)

soundness848.0ms (10.6%)

preprocess82.0ms (1%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	21	192
1	54	184
2	79	180
3	119	180
4	190	180
5	254	180
6	280	180
7	288	180
0	288	180