Metrics for Hyperbolic arc-(co)secant

analyze3.0ms (0%)

Memory

3.2MiB live, 3.2MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample1.0s (13.3%)

Memory

-2.8MiB live, 1 213.4MiB allocated

Samples

783.0ms	8 256×	0	valid
2.0ms	27×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 526.0ms

ival-div: 121.0ms (23% of total)

ival-sub: 117.0ms (22.2% of total)

ival-log: 105.0ms (20% of total)

ival-mult: 74.0ms (14.1% of total)

ival-sqrt: 59.0ms (11.2% of total)

ival-add: 35.0ms (6.7% of total)

ival-true: 6.0ms (1.1% of total)

exact: 5.0ms (1% of total)

ival-assert: 4.0ms (0.8% of total)

Bogosity

preprocess642.0ms (8.2%)

Memory

35.0MiB live, 789.0MiB 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))

explain136.0ms (1.7%)

Memory

-32.3MiB live, 238.4MiB 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

55.0ms

512×

valid

Compiler

Compiled 136 to 40 computations (70.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 39.0ms

ival-add: 14.0ms (36% of total)

ival-div: 7.0ms (18% of total)

ival-log: 6.0ms (15.4% of total)

ival-mult: 4.0ms (10.3% of total)

ival-sqrt: 4.0ms (10.3% of total)

ival-sub: 3.0ms (7.7% of total)

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

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

exact: 0.0ms (0% of total)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.7MiB live, 1.7MiB 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)

simplify678.0ms (8.7%)

Memory

17.2MiB live, 482.7MiB 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)

localize92.0ms (1.2%)

Memory

-24.4MiB live, 51.8MiB allocated

Localize:

Found 4 expressions of interest:

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

Samples

81.0ms

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 (31.2% of total)

ival-log: 3.0ms (23.4% of total)

ival-sqrt: 2.0ms (15.6% of total)

ival-add: 1.0ms (7.8% of total)

ival-mult: 1.0ms (7.8% of total)

ival-sub: 1.0ms (7.8% of total)

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

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

exact: 0.0ms (0% of total)

series6.0ms (0.1%)

Memory

10.2MiB live, 10.2MiB allocated

Counts

6 → 72

Calls

Call 1

Inputs
#<alt (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))>
#<alt (log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))>
#<alt (/.f64 #s(literal 1 binary64) 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 (/ 2 x)>
#<alt (/ (+ 2 (* -1/2 (pow x 2))) x)>
#<alt (/ (+ 2 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) x)>
#<alt (/ (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) x)>
#<alt (sqrt -1)>
#<alt (+ (sqrt -1) (/ 1 x))>
#<alt (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (/ 1 x)))>
#<alt (- (+ (sqrt -1) (+ (/ 1 x) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))>
#<alt (* -1 (sqrt -1))>
#<alt (+ (* -1 (sqrt -1)) (/ 1 x))>
#<alt (+ (* -1 (sqrt -1)) (* -1 (/ (- (* 1/2 (/ 1 (* x (sqrt -1)))) 1) x)))>
#<alt (+ (* -1 (sqrt -1)) (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (sqrt -1)))) x)) 1) 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) (- (* -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 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 (* -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

18 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)))
1.0ms	x	@	inf	(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
0.0ms	x	@	0	(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))

rewrite289.0ms (3.7%)

Memory

10.4MiB live, 262.9MiB 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	45
0	16	45
1	69	45
2	624	41
3	7596	41
0	8354	41

Stop Event

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

Counts

6 → 334

Calls

Call 1

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

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

simplify651.0ms (8.4%)

Memory

5.2MiB live, 556.9MiB allocated

Algorithm

1×	egg-herbie

Rules

17 138×	`lower-fma.f64`
17 138×	`lower-fma.f32`
3 282×	`lower-*.f64`
3 282×	`lower-*.f32`
2 100×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	155	803
1	409	778
2	1098	758
3	3202	745
4	7969	745
0	8467	716

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

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

eval64.0ms (0.8%)

Memory: -14.1MiB live, 99.8MiB allocated
Compiler: Compiled 10 477 to 1 330 computations (87.3% saved)

prune45.0ms (0.6%)

Memory

-12.5MiB live, 109.2MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

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

Accuracy

100.0%

Counts

407 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(log.f64 (/.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) x))
▶	100.0%	(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x))
▶	99.5%	(log.f64 (/.f64 #s(literal 2 binary64) x))
▶	0.0%	(log.f64 (sqrt.f64 #s(literal -1 binary64)))

Compiler

Compiled 31 to 23 computations (25.8% saved)

simplify283.0ms (3.6%)

Memory

5.7MiB live, 521.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

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

Rules

10 628×	`lower-fma.f32`
10 626×	`lower-fma.f64`
2 680×	`lower-*.f32`
2 676×	`lower-*.f64`
2 456×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	89
0	34	89
1	46	89
2	53	89
3	61	89
4	76	89
5	96	89
6	139	89
7	341	89
8	626	89
9	1223	89
10	2273	89
11	3338	89
12	4436	87
13	6067	87
0	8236	85

Stop Event

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

Calls

Call 1

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

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

localize139.0ms (1.8%)

Memory

-3.7MiB live, 155.5MiB allocated

Localize:

Found 12 expressions of interest:

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

Samples

94.0ms

256×

invalid

Compiler

Compiled 94 to 22 computations (76.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 82.0ms

ival-sub: 34.0ms (41.5% of total)

ival-sqrt: 25.0ms (30.5% of total)

ival-log: 10.0ms (12.2% of total)

ival-div: 5.0ms (6.1% of total)

ival-mult: 5.0ms (6.1% of total)

ival-add: 2.0ms (2.4% of total)

exact: 1.0ms (1.2% of total)

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

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

series555.0ms (7.1%)

Memory

9.3MiB live, 127.6MiB allocated

Counts

13 → 132

Calls

Call 1

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

Outputs
#<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) (- (* -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 (/ 2 x)>
#<alt (/ (+ 2 (* -1/2 (pow x 2))) x)>
#<alt (/ (+ 2 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) x)>
#<alt (/ (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) x)>
#<alt (sqrt -1)>
#<alt (+ (sqrt -1) (/ 1 x))>
#<alt (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (/ 1 x)))>
#<alt (- (+ (sqrt -1) (+ (/ 1 x) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))>
#<alt (* -1 (sqrt -1))>
#<alt (+ (* -1 (sqrt -1)) (/ 1 x))>
#<alt (+ (* -1 (sqrt -1)) (* -1 (/ (- (* 1/2 (/ 1 (* x (sqrt -1)))) 1) x)))>
#<alt (+ (* -1 (sqrt -1)) (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (sqrt -1)))) x)) 1) x)))>
#<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 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 (/ 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 (+ (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 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 (* -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 (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

33 calls:

Time	Variable		Point	Expression
463.0ms	x	@	inf	(log (/ (+ 1 (sqrt (- 1 (* x x)))) x))
42.0ms	x	@	0	(log (/ 2 x))
26.0ms	x	@	inf	(log (/ 2 x))
17.0ms	x	@	-inf	(log (/ 2 x))
0.0ms	x	@	inf	(log (/ (+ (* x (* x -1/2)) 2) x))

rewrite399.0ms (5.1%)

Memory

12.3MiB live, 616.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 416×	`lower-fma.f32`
5 414×	`lower-fma.f64`
3 510×	`lower-*.f32`
3 506×	`lower-*.f64`
2 924×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	76
0	34	76
1	111	76
2	692	76
3	6805	76
0	9186	75

Stop Event

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

Counts

13 → 759

Calls

Call 1

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

Outputs
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(+.f64 (log.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64))) (log.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64))))
(*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal -1 binary64)))
(*.f64 (log.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal -1 binary64))))
(sqrt.f64 #s(literal -1 binary64))
(pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))
(pow.f64 #s(literal 1 binary64) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.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 (neg.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64)))) #s(literal 0 binary64))
(+.f64 (log.f64 #s(literal 2 binary64)) (neg.f64 (log.f64 x)))
(+.f64 #s(literal 0 binary64) (neg.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64)))))
(+.f64 (log.f64 #s(literal -2 binary64)) (neg.f64 (log.f64 (neg.f64 x))))
(+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -2 binary64) x)))
(+.f64 (neg.f64 (log.f64 x)) (log.f64 #s(literal 2 binary64)))
(+.f64 (neg.f64 (log.f64 (neg.f64 x))) (log.f64 #s(literal -2 binary64)))
(+.f64 (log.f64 (pow.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal -1/2 binary64))) (log.f64 (pow.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal -1/2 binary64))))
(-.f64 (log.f64 #s(literal 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 (neg.f64 x)))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (*.f64 x #s(literal -1/2 binary64))))
(-.f64 (neg.f64 (log.f64 x)) (log.f64 #s(literal 1/2 binary64)))
(-.f64 (/.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)) (fma.f64 (log.f64 x) (log.f64 (.f64 #s(literal 2 binary64) x)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (log.f64 x) #s(literal 3 binary64)) (fma.f64 (log.f64 x) (log.f64 (.f64 #s(literal 2 binary64) x)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))))
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(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) #s(literal 8 binary64)) (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/64 binary64) (.f64 (fma.f64 x x #s(literal 4 binary64)) (.f64 (fma.f64 x x #s(literal 4 binary64)) (fma.f64 x x #s(literal 4 binary64)))))) (fma.f64 (fma.f64 x x #s(literal 4 binary64)) (-.f64 (fma.f64 x x #s(literal 4 binary64)) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/4 binary64))))) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x))))) #s(literal 1/16 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) #s(literal 8 binary64)) (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal -1 binary64)) #s(literal 4 binary64)) (-.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/4 binary64)))) (fma.f64 x x #s(literal 4 binary64))))) (-.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/4 binary64)))) (fma.f64 x x #s(literal 4 binary64))))
(.f64 (/.f64 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/4 binary64))) #s(literal -4 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)) #s(literal -8 binary64))) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/4 binary64))) (fma.f64 x (neg.f64 x) #s(literal 4 binary64))))
(-.f64 #s(literal 0 binary64) (*.f64 x #s(literal 1/2 binary64)))
(neg.f64 (*.f64 x #s(literal 1/2 binary64)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) x))
(/.f64 x #s(literal -2 binary64))
(/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 #s(literal 2 binary64) x)))
(/.f64 (neg.f64 x) #s(literal 2 binary64))
(.f64 #s(literal -1 binary64) (.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) x)
(*.f64 (neg.f64 x) #s(literal 1/2 binary64))
(+.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64)))
(+.f64 #s(literal 0 binary64) (*.f64 x x))
(+.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))
(+.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)))) (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))))
(+.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))) (/.f64 (.f64 x (.f64 x (*.f64 x x))) (fma.f64 x x #s(literal 1 binary64))))
(exp.f64 (log.f64 (*.f64 x x)))
(-.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(-.f64 #s(literal 0 binary64) (neg.f64 (*.f64 x x)))
(-.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1 binary64))) (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x x)))) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (.f64 x x))) (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x x))) (-.f64 #s(literal 2 binary64) (*.f64 x x))))
(fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) (neg.f64 (.f64 x x)) #s(literal 1 binary64)) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)))) #s(literal 1 binary64))
(fma.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1 binary64))
(fma.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) (neg.f64 (.f64 x x)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64))
(fma.f64 (+.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))) #s(literal 1 binary64))
(fma.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1 binary64))
(fma.f64 (.f64 (neg.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)) #s(literal 1 binary64))
(neg.f64 (neg.f64 (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 2 binary64) (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 x x))))))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x x))))) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1 binary64)))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 x x)))) (-.f64 #s(literal 2 binary64) (*.f64 x x)))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x x))))) #s(literal 1 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1 binary64)))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 x x)))) #s(literal 1 binary64)) (-.f64 #s(literal 2 binary64) (.f64 x x)))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x x)))))) (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 x x))))) (neg.f64 (-.f64 #s(literal 2 binary64) (*.f64 x x))))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) (-.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(.f64 #s(literal -1 binary64) (neg.f64 (.f64 x x)))
(.f64 #s(literal 2 binary64) (.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(*.f64 x x)
(.f64 #s(literal 1 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(.f64 (.f64 x #s(literal -1/2 binary64)) (neg.f64 (*.f64 #s(literal 2 binary64) x)))
(.f64 (.f64 x (*.f64 x #s(literal -1/2 binary64))) #s(literal -2 binary64))
(*.f64 (neg.f64 x) (neg.f64 x))
(.f64 #s(literal -2 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64))))
(.f64 (.f64 x #s(literal 1/2 binary64)) (*.f64 #s(literal 2 binary64) x))
(.f64 (neg.f64 (.f64 x x)) #s(literal -1 binary64))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x x))))) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 1 binary64))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (.f64 x x))))
(.f64 (.f64 (*.f64 x x) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))

simplify445.0ms (5.7%)

Memory

-12.4MiB live, 579.2MiB allocated

Algorithm

1×	egg-herbie

Rules

15 700×	`lower-fma.f64`
15 700×	`lower-fma.f32`
3 714×	`lower-+.f64`
3 714×	`lower-+.f32`
3 370×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	228	1244
1	626	1187
2	1717	1152
3	4905	1136
0	8398	1084

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 132

Calls

Call 1

Inputs
(+ (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) (- (* -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)))
(/ 2 x)
(/ (+ 2 (* -1/2 (pow x 2))) x)
(/ (+ 2 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) x)
(/ (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2))) x)
(sqrt -1)
(+ (sqrt -1) (/ 1 x))
(+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (/ 1 x)))
(- (+ (sqrt -1) (+ (/ 1 x) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))
(* -1 (sqrt -1))
(+ (* -1 (sqrt -1)) (/ 1 x))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* 1/2 (/ 1 (* x (sqrt -1)))) 1) x)))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (sqrt -1)))) x)) 1) x)))
2
(+ 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)))))
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)))))))
(/ 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))))))
(+ (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))))
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))
(* -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)
(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)))
(-.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)
(+ (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 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 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.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 (log.f64 (neg.f64 (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))))) (/.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 -1/6 binary64) (.f64 x (.f64 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 (.f64 x x) (.f64 x x)))))) x))
(/ 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 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2))) x)
(/.f64 (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal -1/8 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) x)
(/ (+ 2 (* (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 x (*.f64 x #s(literal -1/16 binary64)) #s(literal -1/8 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) x)
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 x))
(+.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (/ 1 x)))
(+.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64))))))
(- (+ (sqrt -1) (+ (/ 1 x) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))
(+.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64))) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64))))) (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (.f64 x x) (.f64 x x))))))
(* -1 (sqrt -1))
(neg.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (sqrt -1)) (/ 1 x))
(-.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* 1/2 (/ 1 (* x (sqrt -1)))) 1) x)))
(-.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64))))) x) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (sqrt -1)) (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (sqrt -1)))) x)) 1) x)))
(-.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64))))) (fma.f64 x #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) #s(literal 1 binary64)) x) (sqrt.f64 #s(literal -1 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 (* (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 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 x (*.f64 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 (.f64 x x) (.f64 x x))))) (/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64))))))
(* -1 (* x (sqrt -1)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* x (- (sqrt -1) (/ 1 x))))
(-.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* x (+ (sqrt -1) (* -1 (/ (- 1 (* 1/2 (/ 1 (* x (sqrt -1))))) x)))))
(+.f64 #s(literal 1 binary64) (-.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 (/ (+ 1 (* -1 (/ (- (* 1/2 (/ 1 (sqrt -1))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x))) x)))))
(-.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64))))) (fma.f64 x #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) #s(literal 1 binary64)) (*.f64 x (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 x (*.f64 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 (.f64 x 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 (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 (.f64 x x) (.f64 x x)))))) (/.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(* -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 -1/2 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 (.f64 x 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 (neg.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 (.f64 x x) (.f64 x x)))))) (/.f64 #s(literal -1/2 binary64) (.f64 x (sqrt.f64 #s(literal -1 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))
(.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))))
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))))
(* x (- (* 2 (/ 1 (pow x 2))) 1/2))
(.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))))
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))))
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 2 binary64) (.f64 x 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 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 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 #s(literal -1/2 binary64)) (log.f64 x))
(- (+ (log -1/2) (* -1 (log (/ 1 x)))) (* 4 (/ 1 (pow x 2))))
(+.f64 (log.f64 #s(literal -1/2 binary64)) (+.f64 (log.f64 x) (/.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 #s(literal -1/2 binary64)) (-.f64 (log.f64 x) (/.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 (/.f64 (+.f64 #s(literal -8 binary64) (/.f64 #s(literal -64/3 binary64) (.f64 x x))) (.f64 (.f64 x x) (.f64 x x))) (+.f64 (log.f64 #s(literal -1/2 binary64)) (/.f64 #s(literal -4 binary64) (*.f64 x x)))))
(+ (log 1/2) (* -1 (log (/ -1 x))))
(+.f64 (log.f64 #s(literal 1/2 binary64)) (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 (log.f64 (neg.f64 x)) (/.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 (/.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)) (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 (/.f64 (+.f64 #s(literal -8 binary64) (/.f64 #s(literal -64/3 binary64) (.f64 x x))) (.f64 (.f64 x x) (.f64 x x))) (+.f64 (log.f64 #s(literal 1/2 binary64)) (log.f64 (neg.f64 x)))) (/.f64 #s(literal -4 binary64) (*.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 (* -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))
(* -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))
(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)

eval165.0ms (2.1%)

Memory: 40.2MiB live, 195.6MiB allocated
Compiler: Compiled 20 339 to 2 698 computations (86.7% saved)

prune324.0ms (4.2%)

Memory

-190.2MiB live, 181.4MiB allocated

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	889	2	891
Fresh	0	0	0
Picked	2	2	4
Done	0	0	0
Total	891	4	895

Accuracy

100.0%

Counts

895 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	0.0%	(*.f64 (log.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64))
▶	99.5%	(neg.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))
✓	100.0%	(log.f64 (/.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) x))
✓	100.0%	(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x))

Compiler

Compiled 33 to 25 computations (24.2% saved)

simplify5.0ms (0.1%)

Memory

8.9MiB live, 8.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

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

12×	`lower-*.f32`
8×	`lower-*.f64`
8×	`lower-+.f64`
8×	`lower-+.f32`
6×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	22
0	13	22
1	18	22
2	20	22
3	22	22
4	24	22
5	28	22
6	33	22
0	33	22

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

localize31.0ms (0.4%)

Memory

-29.1MiB live, 52.2MiB allocated

Localize:

Found 5 expressions of interest:

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

17.0ms

256×

invalid

Compiler

Compiled 24 to 10 computations (58.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-log: 5.0ms (51.8% of total)

ival-mult: 3.0ms (31.1% of total)

ival-neg: 1.0ms (10.4% of total)

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

exact: 0.0ms (0% of total)

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

series47.0ms (0.6%)

Memory

27.9MiB live, 65.1MiB allocated

Counts

5 → 36

Calls

Call 1

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

Outputs
#<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 (+ (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 (* 1/2 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
29.0ms	x	@	-inf	(neg (log (* x 1/2)))
12.0ms	x	@	0	(neg (log (* x 1/2)))
5.0ms	x	@	inf	(neg (log (* x 1/2)))
0.0ms	x	@	0	(log (* x 1/2))
0.0ms	x	@	-inf	(log (* x 1/2))

rewrite218.0ms (2.8%)

Memory

10.8MiB live, 242.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

2 296×	`lower-fma.f64`
2 296×	`lower-fma.f32`
2 124×	`lower-*.f32`
2 120×	`lower-*.f64`
1 196×	`lower-pow.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	18
0	13	19
1	24	17
2	77	17
3	500	17
4	4580	17
0	9357	17

Stop Event

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

Counts

5 → 510

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

simplify18.0ms (0.2%)

Memory

-4.6MiB live, 31.0MiB 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	78	180
3	118	180
4	189	180
5	252	180
6	275	180
7	283	180
0	283	180

Stop Event

1×	iter limit
1×	saturated

Counts

36 → 36

Calls

Call 1

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

eval84.0ms (1.1%)

Memory: 8.0MiB live, 138.4MiB allocated
Compiler: Compiled 8 945 to 1 049 computations (88.3% saved)

prune111.0ms (1.4%)

Memory

-12.3MiB live, 102.4MiB allocated

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	545	1	546
Fresh	0	0	0
Picked	1	1	2
Done	0	2	2
Total	546	4	550

Accuracy

100.0%

Counts

550 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	(neg.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))
✓	100.0%	(log.f64 (/.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) 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 33 to 24 computations (27.3% saved)

simplify4.0ms (0.1%)

Memory

5.4MiB live, 5.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Rules

4×	`lower-*.f32`
2×	`*-commutative`
2×	`lower-*.f64`
2×	`lift-*.f64`
2×	`lift-log.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	9
0	6	9
1	7	9
0	7	9

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize35.0ms (0.5%)

Memory

-23.0MiB live, 19.6MiB allocated

Localize:

Found 2 expressions of interest:

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

Samples

29.0ms

256×

valid

Compiler

Compiled 11 to 6 computations (45.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-mult: 21.0ms (85.7% of total)

ival-log: 3.0ms (12.2% of total)

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

exact: 0.0ms (0% of total)

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

series0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Counts

2 → 24

Calls

Call 1

Inputs
#<alt (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 (* 1/2 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

6 calls:

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

rewrite363.0ms (4.7%)

Memory

33.8MiB live, 423.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

7 112×	`lower-fma.f64`
7 112×	`lower-fma.f32`
4 162×	`lower-*.f32`
4 160×	`lower-*.f64`
4 134×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7
0	6	7
1	10	7
2	24	7
3	136	7
4	1253	7
0	8779	7

Stop Event

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

Counts

2 → 192

Calls

Call 1

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

simplify16.0ms (0.2%)

Memory

-17.4MiB live, 20.8MiB 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: 1 (0.0ms)

Iter	Nodes	Cost
0	18	108
1	29	104
2	37	104
3	63	104
4	90	104
5	126	104
6	172	104
7	205	104
8	250	104
9	265	104
10	273	104
0	273	104

Stop Event

1×	iter limit
1×	saturated

Counts

24 → 24

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))))
(* 1/2 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)))
(* 1/2 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)

eval35.0ms (0.4%)

Memory: -11.3MiB live, 46.4MiB allocated
Compiler: Compiled 6 477 to 491 computations (92.4% saved)

prune41.0ms (0.5%)

Memory

11.9MiB live, 50.3MiB allocated

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	216	0	216
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	216	4	220

Accuracy

100.0%

Counts

220 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	(neg.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))
✓	100.0%	(log.f64 (/.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) 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 87 to 53 computations (39.1% saved)

regimes13.0ms (0.2%)

Memory

-19.2MiB live, 17.9MiB allocated

Counts

8 → 1

Calls

Call 1

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

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

Calls

3 calls:

6.0ms

3.0ms

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

3.0ms

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

Results

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

Compiler

Compiled 29 to 18 computations (37.9% saved)

regimes8.0ms (0.1%)

Memory

13.1MiB live, 13.1MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

3.0ms

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

3.0ms

(+.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
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)

regimes7.0ms (0.1%)

Memory

8.6MiB live, 8.6MiB allocated

Counts

5 → 1

Calls

Call 1

Inputs
(log.f64 (*.f64 x #s(literal 1/2 binary64)))
(*.f64 (log.f64 #s(literal -1 binary64)) #s(literal 1/2 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
99.5%	1	`x`
99.5%	1	`(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))`
99.5%	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)

regimes5.0ms (0.1%)

Memory

9.8MiB live, 9.8MiB 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 (log.f64 #s(literal -1 binary64)) #s(literal 1/2 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)

simplify26.0ms (0.3%)

Memory

-29.7MiB live, 8.7MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	29
1	32	29
2	40	29
3	45	29
4	47	29

Stop Event

1×

saturated

Calls

Call 1

Inputs
(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
(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)))

soundness740.0ms (9.5%)

Memory

10.6MiB live, 401.8MiB allocated

Rules

17 138×	`lower-fma.f64`
17 138×	`lower-fma.f32`
5 416×	`lower-fma.f32`
5 414×	`lower-fma.f64`
4 520×	`lower-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	155	803
1	409	778
2	1098	758
3	3202	745
4	7969	745
0	8467	716
0	9	45
0	16	45
1	69	45
2	624	41
3	7596	41
0	8354	41
0	19	76
0	34	76
1	111	76
2	692	76
3	6805	76
0	9186	75
0	8	18
0	13	19
1	24	17
2	77	17
3	500	17
4	4580	17
0	9357	17

Stop Event

1×	done
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

Compiler

Compiled 74 to 51 computations (31.1% saved)

preprocess35.0ms (0.5%)

Memory: 11.4MiB live, 49.7MiB allocated
Compiler: Compiled 88 to 54 computations (38.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	21	192
1	54	184
2	78	180
3	118	180
4	189	180
5	252	180
6	275	180
7	283	180
0	283	180

Iter	Nodes	Cost
0	18	108
1	29	104
2	37	104
3	63	104
4	90	104
5	126	104
6	172	104
7	205	104
8	250	104
9	265	104
10	273	104
0	273	104

Iter	Nodes	Cost
0	21	192
1	54	184
2	78	180
3	118	180
4	189	180
5	252	180
6	275	180
7	283	180
0	283	180

Iter	Nodes	Cost
0	18	108
1	29	104
2	37	104
3	63	104
4	90	104
5	126	104
6	172	104
7	205	104
8	250	104
9	265	104
10	273	104
0	273	104

analyze3.0ms (0%)

sample1.0s (13.3%)

preprocess642.0ms (8.2%)

explain136.0ms (1.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify678.0ms (8.7%)

localize92.0ms (1.2%)

series6.0ms (0.1%)

rewrite289.0ms (3.7%)

simplify651.0ms (8.4%)

eval64.0ms (0.8%)

prune45.0ms (0.6%)

simplify283.0ms (3.6%)

localize139.0ms (1.8%)

series555.0ms (7.1%)

rewrite399.0ms (5.1%)

simplify445.0ms (5.7%)

eval165.0ms (2.1%)

prune324.0ms (4.2%)

simplify5.0ms (0.1%)

localize31.0ms (0.4%)

series47.0ms (0.6%)

rewrite218.0ms (2.8%)

simplify18.0ms (0.2%)

eval84.0ms (1.1%)

prune111.0ms (1.4%)

simplify4.0ms (0.1%)

localize35.0ms (0.5%)

series0.0ms (0%)

rewrite363.0ms (4.7%)

simplify16.0ms (0.2%)

eval35.0ms (0.4%)

prune41.0ms (0.5%)

regimes13.0ms (0.2%)

regimes8.0ms (0.1%)

regimes7.0ms (0.1%)

regimes5.0ms (0.1%)

simplify26.0ms (0.3%)

soundness740.0ms (9.5%)

preprocess35.0ms (0.5%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	21	192
1	54	184
2	78	180
3	118	180
4	189	180
5	252	180
6	275	180
7	283	180
0	283	180

Iter	Nodes	Cost
0	18	108
1	29	104
2	37	104
3	63	104
4	90	104
5	126	104
6	172	104
7	205	104
8	250	104
9	265	104
10	273	104
0	273	104