Metrics for Hyperbolic arc-(co)secant

analyze3.0ms (0%)

Memory

2.9MiB live, 2.9MiB 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)

sample833.0ms (10.3%)

Memory

11.2MiB live, 861.6MiB allocated

Samples

585.0ms	8 256×	0	valid
1.0ms	22×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 431.0ms

ival-div: 125.0ms (29% of total)

ival-log: 106.0ms (24.6% of total)

ival-sqrt: 58.0ms (13.5% of total)

ival-mult: 49.0ms (11.4% of total)

ival-sub: 42.0ms (9.8% of total)

ival-add: 36.0ms (8.4% of total)

ival-true: 6.0ms (1.4% of total)

exact: 5.0ms (1.2% of total)

ival-assert: 4.0ms (0.9% of total)

Bogosity

preprocess635.0ms (7.8%)

Memory

9.9MiB live, 640.2MiB 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))

explain144.0ms (1.8%)

Memory

13.6MiB live, 243.7MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
256	-	256	(1.4229892014158905e-13)	`(-.f64 #s(literal 1 binary64) (*.f64 x x))`
256	-	256	(1.4229892014158905e-13)	`(*.f64 x x)`
256	-	256	(1.4229892014158905e-13)	`(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))`
256	-	256	(1.4229892014158905e-13)	`(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))`
256	-	256	(1.4229892014158905e-13)	`(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)`
256	-	256	(1.4229892014158905e-13)	`(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))`
0	-	0	-	`#s(literal 1 binary64)`
0	-	0	-	`(/.f64 #s(literal 1 binary64) x)`
0	-	0	-	`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

46.0ms

512×

valid

Compiler

Compiled 189 to 49 computations (74.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 30.0ms

ival-div: 7.0ms (23.6% of total)

ival-sub: 6.0ms (20.2% of total)

ival-log: 6.0ms (20.2% of total)

ival-sqrt: 4.0ms (13.5% of total)

ival-mult: 3.0ms (10.1% of total)

ival-add: 2.0ms (6.7% 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)

simplify741.0ms (9.1%)

Memory

31.5MiB live, 546.0MiB 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)

localize34.0ms (0.4%)

Memory

-15.0MiB live, 62.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	5.3%	(-.f64 #s(literal 1 binary64) (*.f64 x x))
✓	accuracy	5.3%	(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))
✓	accuracy	4.2%	(*.f64 x x)
✓	accuracy	4.2%	(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))

Samples

22.0ms

256×

valid

Compiler

Compiled 107 to 20 computations (81.3% saved)

Precisions

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

ival-div: 4.0ms (30% of total)

ival-log: 3.0ms (22.5% of total)

ival-mult: 2.0ms (15% of total)

ival-sqrt: 2.0ms (15% of total)

ival-add: 1.0ms (7.5% of total)

ival-sub: 1.0ms (7.5% of total)

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

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

exact: 0.0ms (0% of total)

series17.0ms (0.2%)

Memory

-16.1MiB live, 24.7MiB 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 (*.f64 x x)>
#<alt (-.f64 #s(literal 1 binary64) (*.f64 x x))>

Outputs
#<alt (/ 2 x)>
#<alt (/ (+ 2 (* -1/2 (pow x 3))) x)>
#<alt (/ (+ 2 (* (pow x 3) (- (* -1/8 (pow x 3)) 1/2))) x)>
#<alt (/ (+ 2 (* (pow x 3) (- (* (pow x 3) (- (* -1/16 (pow x 3)) 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 (* x (sqrt -1))>
#<alt (* -1 (* x (- (* -1 (sqrt -1)) (/ 1 (pow x 2)))))>
#<alt (* -1 (* x (+ (* -1 (sqrt -1)) (* -1 (/ (+ 1 (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))) (pow x 2))))))>
#<alt (* -1 (* x (- (+ (* -1 (sqrt -1)) (* 1/8 (/ 1 (* (pow x 8) (pow (sqrt -1) 3))))) (+ (* 1/2 (/ 1 (* (pow x 4) (sqrt -1)))) (/ 1 (pow x 2))))))>
#<alt (+ (log 2) (* -1 (log x)))>
#<alt (+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 3))))>
#<alt (+ (log 2) (+ (* -1 (log x)) (* (pow x 3) (- (* -3/32 (pow x 3)) 1/4))))>
#<alt (+ (log 2) (+ (* -1 (log x)) (* (pow x 3) (- (* (pow x 3) (- (* -5/96 (pow x 3)) 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))) (* -1 (log (/ -1 x))))>
#<alt (+ (log (* -1 (sqrt -1))) (+ (* -1 (log (/ -1 x))) (/ 1 (* (pow x 2) (sqrt -1)))))>
#<alt (- (+ (log (* -1 (sqrt -1))) (+ (* -1 (log (/ -1 x))) (/ 1 (* (pow x 2) (sqrt -1))))) (/ 1/6 (* (pow x 6) (pow (sqrt -1) 3))))>
#<alt (- (+ (log (* -1 (sqrt -1))) (+ (* -1 (log (/ -1 x))) (+ (/ 1 (* (pow x 2) (sqrt -1))) (* 3/40 (/ 1 (* (pow x 10) (pow (sqrt -1) 5))))))) (* 1/6 (/ 1 (* (pow x 6) (pow (sqrt -1) 3)))))>
#<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 3))) x)>
#<alt (/ (+ 1 (* (pow x 3) (- (* -1/8 (pow x 3)) 1/2))) x)>
#<alt (/ (+ 1 (* (pow x 3) (- (* (pow x 3) (- (* -1/16 (pow x 3)) 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 (* (sqrt x) (pow (sqrt -1) 2))>
#<alt (* -1 (* x (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/2 (sqrt (/ 1 (pow x 7)))))))>
#<alt (* -1 (* x (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1/2 (sqrt (/ 1 (pow x 7)))) (* 1/8 (* (sqrt (/ 1 (pow x 13))) (/ 1 (pow (sqrt -1) 2))))))))>
#<alt (* -1 (* x (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1/2 (sqrt (/ 1 (pow x 7)))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 19))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 (pow x 13))) (/ 1 (pow (sqrt -1) 2)))))))))>
#<alt x>
#<alt x>
#<alt x>
#<alt 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 1>
#<alt (+ 1 (* -1 (pow x 2)))>
#<alt (+ 1 (* -1 (pow x 2)))>
#<alt (+ 1 (* -1 (pow x 2)))>
#<alt (* -1 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1))>
#<alt (* -1 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1))>

Calls

18 calls:

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

Compiler

Compiled 176 to 126 computations (28.4% saved)

rewrite266.0ms (3.3%)

Memory

6.7MiB live, 406.5MiB 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	44
0	16	44
1	69	44
2	624	40
3	7596	40
0	8354	40

Stop Event

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

Counts

6 → 378

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

simplify743.0ms (9.2%)

Memory

-126.6MiB live, 628.1MiB allocated

Algorithm

1×	egg-herbie

Rules

14 748×	`lower-fma.f64`
14 748×	`lower-fma.f32`
4 060×	`lower-+.f64`
4 060×	`lower-+.f32`
3 664×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	196	757
1	468	696
2	1437	680
3	4150	676
0	8354	652

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 68

Calls

Call 1

Inputs
(/ 2 x)
(/ (+ 2 (* -1/2 (pow x 3))) x)
(/ (+ 2 (* (pow x 3) (- (* -1/8 (pow x 3)) 1/2))) x)
(/ (+ 2 (* (pow x 3) (- (* (pow x 3) (- (* -1/16 (pow x 3)) 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)))))
(* x (sqrt -1))
(* -1 (* x (- (* -1 (sqrt -1)) (/ 1 (pow x 2)))))
(* -1 (* x (+ (* -1 (sqrt -1)) (* -1 (/ (+ 1 (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))) (pow x 2))))))
(* -1 (* x (- (+ (* -1 (sqrt -1)) (* 1/8 (/ 1 (* (pow x 8) (pow (sqrt -1) 3))))) (+ (* 1/2 (/ 1 (* (pow x 4) (sqrt -1)))) (/ 1 (pow x 2))))))
(+ (log 2) (* -1 (log x)))
(+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 3))))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 3) (- (* -3/32 (pow x 3)) 1/4))))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 3) (- (* (pow x 3) (- (* -5/96 (pow x 3)) 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))) (* -1 (log (/ -1 x))))
(+ (log (* -1 (sqrt -1))) (+ (* -1 (log (/ -1 x))) (/ 1 (* (pow x 2) (sqrt -1)))))
(- (+ (log (* -1 (sqrt -1))) (+ (* -1 (log (/ -1 x))) (/ 1 (* (pow x 2) (sqrt -1))))) (/ 1/6 (* (pow x 6) (pow (sqrt -1) 3))))
(- (+ (log (* -1 (sqrt -1))) (+ (* -1 (log (/ -1 x))) (+ (/ 1 (* (pow x 2) (sqrt -1))) (* 3/40 (/ 1 (* (pow x 10) (pow (sqrt -1) 5))))))) (* 1/6 (/ 1 (* (pow x 6) (pow (sqrt -1) 3)))))
(/ 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 3))) x)
(/ (+ 1 (* (pow x 3) (- (* -1/8 (pow x 3)) 1/2))) x)
(/ (+ 1 (* (pow x 3) (- (* (pow x 3) (- (* -1/16 (pow x 3)) 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)))))
(* (sqrt x) (pow (sqrt -1) 2))
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/2 (sqrt (/ 1 (pow x 7)))))))
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1/2 (sqrt (/ 1 (pow x 7)))) (* 1/8 (* (sqrt (/ 1 (pow x 13))) (/ 1 (pow (sqrt -1) 2))))))))
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1/2 (sqrt (/ 1 (pow x 7)))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 19))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 (pow x 13))) (/ 1 (pow (sqrt -1) 2)))))))))
x
x
x
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)
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))

Outputs
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (+ 2 (* -1/2 (pow x 3))) x)
(/.f64 (fma.f64 x (.f64 x (.f64 x #s(literal -1/2 binary64))) #s(literal 2 binary64)) x)
(/ (+ 2 (* (pow x 3) (- (* -1/8 (pow x 3)) 1/2))) x)
(/.f64 (fma.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64)))) #s(literal 2 binary64)) x)
(/ (+ 2 (* (pow x 3) (- (* (pow x 3) (- (* -1/16 (pow x 3)) 1/8)) 1/2))) x)
(/.f64 (fma.f64 x (.f64 (fma.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal -1/8 binary64)) #s(literal -1/2 binary64)) (.f64 x x)) #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 (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) x)) (/.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 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) x) (+.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 (.f64 x x)) x))))))
(* x (sqrt -1))
(*.f64 x (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* x (- (* -1 (sqrt -1)) (/ 1 (pow x 2)))))
(fma.f64 x (sqrt.f64 #s(literal -1 binary64)) (/.f64 x (*.f64 x x)))
(* -1 (* x (+ (* -1 (sqrt -1)) (* -1 (/ (+ 1 (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))) (pow x 2))))))
(fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64)))))) x) (*.f64 x (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* x (- (+ (* -1 (sqrt -1)) (* 1/8 (/ 1 (* (pow x 8) (pow (sqrt -1) 3))))) (+ (* 1/2 (/ 1 (* (pow x 4) (sqrt -1)))) (/ 1 (pow x 2))))))
(fma.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (.f64 x (.f64 x x)) x))) (+.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 8 binary64)))))) (/.f64 x (.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 3))))
(-.f64 (fma.f64 x (.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 3) (- (* -3/32 (pow x 3)) 1/4))))
(fma.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 (.f64 x x) #s(literal -3/32 binary64)) #s(literal -1/4 binary64)) (-.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x)))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 3) (- (* (pow x 3) (- (* -5/96 (pow x 3)) 3/32)) 1/4))))
(-.f64 (fma.f64 (.f64 x (.f64 x x)) (fma.f64 (.f64 x (.f64 x x)) (fma.f64 (.f64 x (.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 x (.f64 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 x (.f64 x (*.f64 x (sqrt.f64 #s(literal -1 binary64)))))))))
(+ (log (* -1 (sqrt -1))) (* -1 (log (/ -1 x))))
(-.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (log.f64 (/.f64 #s(literal -1 binary64) x)))
(+ (log (* -1 (sqrt -1))) (+ (* -1 (log (/ -1 x))) (/ 1 (* (pow x 2) (sqrt -1)))))
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64))))) (-.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (log.f64 (/.f64 #s(literal -1 binary64) x))))
(- (+ (log (* -1 (sqrt -1))) (+ (* -1 (log (/ -1 x))) (/ 1 (* (pow x 2) (sqrt -1))))) (/ 1/6 (* (pow x 6) (pow (sqrt -1) 3))))
(+.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64))))) (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal -1/6 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))))))
(- (+ (log (* -1 (sqrt -1))) (+ (* -1 (log (/ -1 x))) (+ (/ 1 (* (pow x 2) (sqrt -1))) (* 3/40 (/ 1 (* (pow x 10) (pow (sqrt -1) 5))))))) (* 1/6 (/ 1 (* (pow x 6) (pow (sqrt -1) 3)))))
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64))))) (+.f64 (+.f64 (-.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) (log.f64 (/.f64 #s(literal -1 binary64) x))) (/.f64 #s(literal 3/40 binary64) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) (pow.f64 x #s(literal 10 binary64))))) (/.f64 #s(literal 1/6 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x 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 3))) x)
(/.f64 (fma.f64 x (.f64 x (.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)) x)
(/ (+ 1 (* (pow x 3) (- (* -1/8 (pow x 3)) 1/2))) x)
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)
(/ (+ 1 (* (pow x 3) (- (* (pow x 3) (- (* -1/16 (pow x 3)) 1/8)) 1/2))) x)
(/.f64 (fma.f64 x (.f64 (fma.f64 (.f64 x (.f64 x x)) (fma.f64 x (.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal -1/8 binary64)) #s(literal -1/2 binary64)) (.f64 x x)) #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 x (.f64 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 #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 (.f64 x x)) x)))))
(- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (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)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (.f64 x (.f64 x x)) x))))))
(* (sqrt x) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 x))
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/2 (sqrt (/ 1 (pow x 7)))))))
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1/2 (sqrt (/ 1 (pow x 7)))) (* 1/8 (* (sqrt (/ 1 (pow x 13))) (/ 1 (pow (sqrt -1) 2))))))))
(neg.f64 (*.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 13 binary64)))) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* x (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1/2 (sqrt (/ 1 (pow x 7)))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 19))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 (pow x 13))) (/ 1 (pow (sqrt -1) 2)))))))))
(.f64 x (-.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 13 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 19 binary64)))) (/.f64 #s(literal -1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
x
x
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)
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(+ 1 (* -1 (pow x 2)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* -1 (pow x 2))
(*.f64 x (neg.f64 x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* -1 (pow x 2))
(*.f64 x (neg.f64 x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 x x))

eval70.0ms (0.9%)

Memory: 0.5MiB live, 154.7MiB allocated
Compiler: Compiled 12 396 to 1 653 computations (86.7% saved)

prune48.0ms (0.6%)

Memory

4.6MiB live, 125.8MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	442	4	446
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	443	4	447

Accuracy

100.0%

Counts

447 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.1%	(log.f64 (/.f64 (fma.f64 x (.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))
▶	99.1%	(log.f64 (/.f64 #s(literal 2 binary64) x))
▶	0.0%	(log.f64 (sqrt.f64 #s(literal -1 binary64)))

Compiler

Compiled 33 to 24 computations (27.3% saved)

simplify338.0ms (4.2%)

Memory

-30.3MiB live, 368.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

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

9 152×	`lower-fma.f32`
9 150×	`lower-fma.f64`
2 580×	`lower-/.f32`
2 574×	`lower-/.f64`
2 528×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	100
0	36	100
1	50	100
2	62	97
3	73	97
4	88	97
5	108	97
6	151	97
7	364	97
8	651	97
9	1285	97
10	2525	97
11	3638	97
12	4969	97
13	6872	97
0	8477	94

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

localize118.0ms (1.5%)

Memory

22.1MiB live, 139.5MiB allocated

Localize:

Found 12 expressions of interest:

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

43.0ms

256×

invalid

Compiler

Compiled 206 to 43 computations (79.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 30.0ms

ival-log: 10.0ms (33.8% of total)

ival-mult: 6.0ms (20.3% of total)

ival-div: 5.0ms (16.9% of total)

ival-sqrt: 4.0ms (13.5% of total)

ival-add: 3.0ms (10.1% of total)

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

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

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

exact: 0.0ms (0% of total)

series132.0ms (1.6%)

Memory

15.2MiB live, 170.7MiB allocated

Counts

14 → 144

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

Outputs
#<alt (* -1 (log x))>
#<alt (* -1 (log x))>
#<alt (* -1 (log x))>
#<alt (* -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 (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 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 (+ (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 x)) (pow (sqrt -1) 2)))) (* -1 (log (/ -1 x))))>
#<alt (+ (log (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (sqrt (/ 1 (pow x 3))) (* -1 (log (/ -1 x)))))>
#<alt (+ (log (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1 (log (/ -1 x))) (* 1/720 (/ (+ (* -360 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 240 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow x 6))))))>
#<alt (+ (log (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1 (log (/ -1 x))) (+ (* 1/3628800 (/ (+ (* -1814400 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 4)))) (+ (* 453600 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 4)))) (+ (* 725760 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 4)))) (* 907200 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 4))))))) (pow x 10))) (* 1/720 (/ (+ (* -360 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 240 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow x 6)))))))>
#<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 (* (sqrt x) (pow (sqrt -1) 2))>
#<alt (* -1 (* x (- (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (/ 1 (pow x 2)))))>
#<alt (* -1 (* x (- (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/2 (sqrt (/ 1 (pow x 7))))) (/ 1 (pow x 2)))))>
#<alt (* -1 (* x (- (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1/2 (sqrt (/ 1 (pow x 7)))) (* 1/8 (* (sqrt (/ 1 (pow x 13))) (/ 1 (pow (sqrt -1) 2)))))) (/ 1 (pow x 2)))))>
#<alt 2>
#<alt (+ 2 (* -1/2 (pow x 2)))>
#<alt (+ 2 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))>
#<alt (+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))>
#<alt (* x (sqrt -1))>
#<alt (* x (+ (sqrt -1) (/ 1 x)))>
#<alt (* x (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (/ 1 x))))>
#<alt (* x (- (+ (sqrt -1) (+ (/ 1 x) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))>
#<alt (* -1 (* x (sqrt -1)))>
#<alt (* -1 (* x (- (sqrt -1) (/ 1 x))))>
#<alt (* -1 (* x (+ (sqrt -1) (* -1 (/ (- 1 (* 1/2 (/ 1 (* x (sqrt -1))))) x)))))>
#<alt (* -1 (* x (+ (sqrt -1) (* -1 (/ (+ 1 (* -1 (/ (- (* 1/2 (/ 1 (sqrt -1))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x))) x)))))>
#<alt 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 3))) x)>
#<alt (/ (+ 2 (* -1/2 (pow x 3))) x)>
#<alt (/ (+ 2 (* -1/2 (pow x 3))) x)>
#<alt (* -1/2 (pow x 3))>
#<alt (* (pow x 3) (- (* 2 (/ 1 (pow x 4))) 1/2))>
#<alt (* (pow x 3) (- (* 2 (/ 1 (pow x 4))) 1/2))>
#<alt (* (pow x 3) (- (* 2 (/ 1 (pow x 4))) 1/2))>
#<alt (* -1/2 (pow x 4))>
#<alt (* (pow x 4) (- (* 2 (/ 1 (pow x 5))) 1/2))>
#<alt (* (pow x 4) (- (* 2 (/ 1 (pow x 5))) 1/2))>
#<alt (* (pow x 4) (- (* 2 (/ 1 (pow x 5))) 1/2))>
#<alt (+ (log 2) (* -1 (log x)))>
#<alt (+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 3))))>
#<alt (+ (log 2) (+ (* -1 (log x)) (* (pow x 3) (- (* -1/32 (pow x 3)) 1/4))))>
#<alt (+ (log 2) (+ (* -1 (log x)) (* (pow x 3) (- (* (pow x 3) (- (* -1/192 (pow x 3)) 1/32)) 1/4))))>
#<alt (+ (log -1/2) (* -3 (log (/ 1 x))))>
#<alt (- (+ (log -1/2) (* -3 (log (/ 1 x)))) (* 4 (/ 1 (pow x 4))))>
#<alt (+ (log -1/2) (+ (* -3 (log (/ 1 x))) (* -1 (/ (+ 4 (* 8 (/ 1 (pow x 4)))) (pow x 4)))))>
#<alt (- (+ (log -1/2) (+ (* -3 (log (/ 1 x))) (* -1 (/ (+ 8 (* 64/3 (/ 1 (pow x 4)))) (pow x 8))))) (* 4 (/ 1 (pow x 4))))>
#<alt (+ (log -1/2) (* -4 (log (/ -1 x))))>
#<alt (- (+ (log -1/2) (* -4 (log (/ -1 x)))) (* 4 (/ 1 (pow x 5))))>
#<alt (+ (log -1/2) (+ (* -4 (log (/ -1 x))) (* -1 (/ (+ 4 (* 8 (/ 1 (pow x 5)))) (pow x 5)))))>
#<alt (+ (log -1/2) (+ (* -4 (log (/ -1 x))) (* -1 (/ (+ 4 (+ (* 8 (/ 1 (pow x 5))) (/ 64/3 (pow x 10)))) (pow x 5)))))>
#<alt 2>
#<alt (+ 2 (* -1/2 (pow x 3)))>
#<alt (+ 2 (* -1/2 (pow x 3)))>
#<alt (+ 2 (* -1/2 (pow x 3)))>
#<alt (* -1/2 (pow x 4))>
#<alt (* (pow x 4) (- (* 2 (/ 1 (pow x 4))) 1/2))>
#<alt (* (pow x 4) (- (* 2 (/ 1 (pow x 4))) 1/2))>
#<alt (* (pow x 4) (- (* 2 (/ 1 (pow x 4))) 1/2))>
#<alt (* 1/2 (pow x 4))>
#<alt (* (pow x 4) (+ 1/2 (* 2 (/ 1 (pow x 4)))))>
#<alt (* (pow x 4) (+ 1/2 (* 2 (/ 1 (pow x 4)))))>
#<alt (* (pow x 4) (+ 1/2 (* 2 (/ 1 (pow x 4)))))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (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 x>
#<alt x>
#<alt x>
#<alt 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 (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>

Calls

36 calls:

Time	Variable		Point	Expression
36.0ms	x	@	-inf	(log (/ (+ (* x (* x (* x -1/2))) 2) x))
34.0ms	x	@	-inf	(log (/ 2 x))
25.0ms	x	@	0	(log (/ 2 x))
18.0ms	x	@	inf	(log (/ 2 x))
3.0ms	x	@	-inf	(log (/ (+ 1 (sqrt (- 1 (* x x)))) x))

Compiler

Compiled 313 to 248 computations (20.8% saved)

rewrite394.0ms (4.9%)

Memory

-12.6MiB live, 655.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 160×	`lower-fma.f32`
5 158×	`lower-fma.f64`
3 734×	`lower-*.f32`
3 728×	`lower-*.f64`
2 946×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	87
0	36	87
1	115	87
2	698	84
3	6832	84
0	9300	80

Stop Event

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

Counts

14 → 731

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

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)))))
(-.f64 (/.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (log.f64 (.f64 #s(literal 2 binary64) x))) (/.f64 (pow.f64 (log.f64 x) #s(literal 2 binary64)) (log.f64 (.f64 #s(literal 2 binary64) x))))
(fma.f64 #s(literal -1 binary64) (log.f64 x) (log.f64 #s(literal 2 binary64)))
(fma.f64 #s(literal -1 binary64) (log.f64 (*.f64 x #s(literal 1/2 binary64))) #s(literal 0 binary64))
(fma.f64 (-.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (log.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 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)))) #s(literal 0 binary64))
(fma.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) x)) (neg.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))))) (/.f64 #s(literal 1 binary64) (log.f64 (.f64 #s(literal 2 binary64) x))) #s(literal 0 binary64))
(neg.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (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 #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (log.f64 x) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (log.f64 (.f64 #s(literal 2 binary64) x)) (.f64 (log.f64 (.f64 #s(literal 2 binary64) x)) (neg.f64 (log.f64 (.f64 x #s(literal 1/2 binary64)))))))
(/.f64 (-.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)) (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))))
(/.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) x)) (neg.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))))) (log.f64 (.f64 #s(literal 2 binary64) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (log.f64 x) #s(literal 3 binary64)))) (neg.f64 (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 (neg.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) x)) (neg.f64 (log.f64 (.f64 x #s(literal 1/2 binary64)))))) (neg.f64 (log.f64 (.f64 #s(literal 2 binary64) x))))
(/.f64 (+.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (neg.f64 (log.f64 x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (-.f64 (.f64 (neg.f64 (log.f64 x)) (neg.f64 (log.f64 x))) (.f64 (log.f64 #s(literal 2 binary64)) (neg.f64 (log.f64 x))))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) (log.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 #s(literal 0 binary64) (log.f64 (*.f64 x #s(literal 1/2 binary64)))))))
(/.f64 (-.f64 (pow.f64 (log.f64 #s(literal -2 binary64)) #s(literal 3 binary64)) (pow.f64 (log.f64 (neg.f64 x)) #s(literal 3 binary64))) (fma.f64 (log.f64 #s(literal -2 binary64)) (log.f64 #s(literal -2 binary64)) (fma.f64 (log.f64 (neg.f64 x)) (log.f64 (neg.f64 x)) (*.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (neg.f64 x))))))
(/.f64 (-.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 (neg.f64 (log.f64 x)) (neg.f64 (log.f64 x)))) (log.f64 (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) (log.f64 (.f64 x #s(literal 1/2 binary64))))) (log.f64 (.f64 x #s(literal 1/2 binary64))))
(/.f64 (-.f64 (.f64 (log.f64 #s(literal -2 binary64)) (log.f64 #s(literal -2 binary64))) (.f64 (log.f64 (neg.f64 x)) (log.f64 (neg.f64 x)))) (log.f64 (*.f64 #s(literal -2 binary64) (neg.f64 x))))
(.f64 #s(literal -1 binary64) (log.f64 (.f64 x #s(literal 1/2 binary64))))
(.f64 (-.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (log.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 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 (.f64 (log.f64 (.f64 #s(literal 2 binary64) x)) (neg.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))))) (/.f64 #s(literal 1 binary64) (log.f64 (*.f64 #s(literal 2 binary64) x))))
(exp.f64 (.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -2 binary64) x))
(neg.f64 (/.f64 #s(literal -2 binary64) x))
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)))
(neg.f64 (/.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/2 binary64))))
(/.f64 #s(literal -1 binary64) (*.f64 x #s(literal -1/2 binary64)))
(/.f64 #s(literal 2 binary64) x)
(/.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(/.f64 #s(literal -2 binary64) (neg.f64 x))
(/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
(pow.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -2 binary64) x))
(*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
(*.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -2 binary64))
(.f64 (pow.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))
(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x))
(+.f64 (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) x)) #s(literal 0 binary64))
(+.f64 (log1p.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (neg.f64 (log.f64 x)))
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(/.f64 (.f64 (+.f64 (pow.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/2 binary64)))) #s(literal 9 binary64)) #s(literal 512 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (neg.f64 x)) #s(literal 4 binary64)))) (-.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))) #s(literal 64 binary64)) (.f64 (.f64 x (.f64 x (neg.f64 x))) (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))) #s(literal -64 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (neg.f64 x)) #s(literal 4 binary64)))) (fma.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))) #s(literal -8 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))) #s(literal -64 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/2 binary64) #s(literal 2 binary64)))) (fma.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)) #s(literal 16 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) #s(literal 1/4 binary64)) #s(literal -16 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/2 binary64) #s(literal 2 binary64)))) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 (.f64 x x) #s(literal 1/4 binary64))) #s(literal 4 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (.f64 x #s(literal -1/2 binary64))) #s(literal 2 binary64))) #s(literal -1 binary64))
(.f64 #s(literal -1 binary64) (fma.f64 (.f64 x (*.f64 x x)) #s(literal 1/2 binary64) #s(literal -2 binary64)))
(.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (*.f64 x #s(literal -1/2 binary64))) #s(literal 2 binary64)))
(.f64 (fma.f64 x (.f64 x (*.f64 x #s(literal -1/2 binary64))) #s(literal 2 binary64)) #s(literal 1 binary64))
(.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))) #s(literal 8 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (neg.f64 x)) #s(literal 4 binary64))))
(.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))) #s(literal 8 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/4 binary64))) (neg.f64 x)) #s(literal 4 binary64))) #s(literal 1 binary64)))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 (.f64 x x) #s(literal 1/4 binary64))) #s(literal -4 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/2 binary64) #s(literal 2 binary64))))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 (.f64 x x) #s(literal 1/4 binary64))) #s(literal -4 binary64)) (.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 x (*.f64 x x)) #s(literal 1/2 binary64) #s(literal 2 binary64))) #s(literal 1 binary64)))
(.f64 (neg.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))) #s(literal 8 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (neg.f64 x)) #s(literal 4 binary64)))))
(.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 (.f64 x x) #s(literal 1/4 binary64))) #s(literal -4 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/2 binary64) #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (neg.f64 x)) #s(literal 4 binary64))) (fma.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))) #s(literal 8 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/2 binary64) #s(literal 2 binary64))) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 (.f64 x x) #s(literal 1/4 binary64))) #s(literal -4 binary64)))
(.f64 (-.f64 #s(literal 4 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x x) #s(literal 1/4 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (.f64 x (.f64 x (.f64 x #s(literal -1/2 binary64)))))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 (.f64 x x) #s(literal 1/4 binary64))) #s(literal -4 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 (.f64 x x) #s(literal 1/4 binary64))) #s(literal -4 binary64))) (fma.f64 x (.f64 x (*.f64 x #s(literal -1/2 binary64))) #s(literal 2 binary64)))
(.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (.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 (.f64 x x)) #s(literal -1/8 binary64))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))) (.f64 (fma.f64 x (.f64 x x) #s(literal 4 binary64)) (.f64 (fma.f64 x (.f64 x x) #s(literal 4 binary64)) (fma.f64 x (.f64 x x) #s(literal 4 binary64)))))) (fma.f64 (fma.f64 x (.f64 x x) #s(literal 4 binary64)) (-.f64 (fma.f64 x (.f64 x x) #s(literal 4 binary64)) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x x) #s(literal 1/4 binary64)))) (.f64 (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (*.f64 x x) #s(literal 1/4 binary64)))))
(.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (.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) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (neg.f64 x)) #s(literal 4 binary64)) (-.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (fma.f64 x (.f64 x x) #s(literal 4 binary64))))) (-.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (fma.f64 x (*.f64 x x) #s(literal 4 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 (.f64 x x) #s(literal 1/4 binary64))) #s(literal -4 binary64)) (fma.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))) #s(literal -8 binary64))) (fma.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (fma.f64 x (.f64 x (neg.f64 x)) #s(literal 4 binary64))))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64))))
(.f64 (.f64 x x) #s(literal -1/2 binary64))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal -1/2 binary64)) x)
(.f64 (.f64 x (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(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 x x)
(.f64 #s(literal 1 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(-.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))

simplify509.0ms (6.3%)

Memory

17.9MiB live, 623.7MiB allocated

Algorithm

1×	egg-herbie

Rules

15 078×	`lower-fma.f64`
15 078×	`lower-fma.f32`
4 650×	`lower-*.f64`
4 650×	`lower-*.f32`
3 370×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	298	1455
1	737	1351
2	2101	1261
3	6024	1239
0	8540	1179

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 136

Calls

Call 1

Inputs
(* -1 (log x))
(* -1 (log x))
(* -1 (log x))
(* -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)))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 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 x)) (pow (sqrt -1) 2)))) (* -1 (log (/ -1 x))))
(+ (log (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (sqrt (/ 1 (pow x 3))) (* -1 (log (/ -1 x)))))
(+ (log (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1 (log (/ -1 x))) (* 1/720 (/ (+ (* -360 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 240 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow x 6))))))
(+ (log (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1 (log (/ -1 x))) (+ (* 1/3628800 (/ (+ (* -1814400 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 4)))) (+ (* 453600 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 4)))) (+ (* 725760 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 4)))) (* 907200 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 4))))))) (pow x 10))) (* 1/720 (/ (+ (* -360 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 240 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow x 6)))))))
(/ 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)))))
(* (sqrt x) (pow (sqrt -1) 2))
(* -1 (* x (- (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (/ 1 (pow x 2)))))
(* -1 (* x (- (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/2 (sqrt (/ 1 (pow x 7))))) (/ 1 (pow x 2)))))
(* -1 (* x (- (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1/2 (sqrt (/ 1 (pow x 7)))) (* 1/8 (* (sqrt (/ 1 (pow x 13))) (/ 1 (pow (sqrt -1) 2)))))) (/ 1 (pow x 2)))))
2
(+ 2 (* -1/2 (pow x 2)))
(+ 2 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 2 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(* x (sqrt -1))
(* x (+ (sqrt -1) (/ 1 x)))
(* x (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (/ 1 x))))
(* x (- (+ (sqrt -1) (+ (/ 1 x) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (* x (sqrt -1)))
(* -1 (* x (- (sqrt -1) (/ 1 x))))
(* -1 (* x (+ (sqrt -1) (* -1 (/ (- 1 (* 1/2 (/ 1 (* x (sqrt -1))))) x)))))
(* -1 (* x (+ (sqrt -1) (* -1 (/ (+ 1 (* -1 (/ (- (* 1/2 (/ 1 (sqrt -1))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt -1) 3))))) x))) x)))))
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 3))) x)
(/ (+ 2 (* -1/2 (pow x 3))) x)
(/ (+ 2 (* -1/2 (pow x 3))) x)
(* -1/2 (pow x 3))
(* (pow x 3) (- (* 2 (/ 1 (pow x 4))) 1/2))
(* (pow x 3) (- (* 2 (/ 1 (pow x 4))) 1/2))
(* (pow x 3) (- (* 2 (/ 1 (pow x 4))) 1/2))
(* -1/2 (pow x 4))
(* (pow x 4) (- (* 2 (/ 1 (pow x 5))) 1/2))
(* (pow x 4) (- (* 2 (/ 1 (pow x 5))) 1/2))
(* (pow x 4) (- (* 2 (/ 1 (pow x 5))) 1/2))
(+ (log 2) (* -1 (log x)))
(+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 3))))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 3) (- (* -1/32 (pow x 3)) 1/4))))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 3) (- (* (pow x 3) (- (* -1/192 (pow x 3)) 1/32)) 1/4))))
(+ (log -1/2) (* -3 (log (/ 1 x))))
(- (+ (log -1/2) (* -3 (log (/ 1 x)))) (* 4 (/ 1 (pow x 4))))
(+ (log -1/2) (+ (* -3 (log (/ 1 x))) (* -1 (/ (+ 4 (* 8 (/ 1 (pow x 4)))) (pow x 4)))))
(- (+ (log -1/2) (+ (* -3 (log (/ 1 x))) (* -1 (/ (+ 8 (* 64/3 (/ 1 (pow x 4)))) (pow x 8))))) (* 4 (/ 1 (pow x 4))))
(+ (log -1/2) (* -4 (log (/ -1 x))))
(- (+ (log -1/2) (* -4 (log (/ -1 x)))) (* 4 (/ 1 (pow x 5))))
(+ (log -1/2) (+ (* -4 (log (/ -1 x))) (* -1 (/ (+ 4 (* 8 (/ 1 (pow x 5)))) (pow x 5)))))
(+ (log -1/2) (+ (* -4 (log (/ -1 x))) (* -1 (/ (+ 4 (+ (* 8 (/ 1 (pow x 5))) (/ 64/3 (pow x 10)))) (pow x 5)))))
2
(+ 2 (* -1/2 (pow x 3)))
(+ 2 (* -1/2 (pow x 3)))
(+ 2 (* -1/2 (pow x 3)))
(* -1/2 (pow x 4))
(* (pow x 4) (- (* 2 (/ 1 (pow x 4))) 1/2))
(* (pow x 4) (- (* 2 (/ 1 (pow x 4))) 1/2))
(* (pow x 4) (- (* 2 (/ 1 (pow x 4))) 1/2))
(* 1/2 (pow x 4))
(* (pow x 4) (+ 1/2 (* 2 (/ 1 (pow x 4)))))
(* (pow x 4) (+ 1/2 (* 2 (/ 1 (pow x 4)))))
(* (pow x 4) (+ 1/2 (* 2 (/ 1 (pow x 4)))))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (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)
x
x
x
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)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
x
x
x
x
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)

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

eval122.0ms (1.5%)

Memory: -19.5MiB live, 264.3MiB allocated
Compiler: Compiled 22 336 to 2 557 computations (88.6% saved)

prune154.0ms (1.9%)

Memory

-11.0MiB live, 228.6MiB allocated

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	864	3	867
Fresh	0	0	0
Picked	3	1	4
Done	0	0	0
Total	867	4	871

Accuracy

100.0%

Counts

871 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.1%	(neg.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))
▶	31.5%	(neg.f64 (log.f64 x))
▶	99.5%	(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 32 to 23 computations (28.1% saved)

simplify7.0ms (0.1%)

Memory

5.8MiB live, 5.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	49
0	23	49
1	35	49
2	40	49
3	43	49
4	47	49
5	54	49
6	61	49
0	61	49

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

Outputs
(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)
(neg.f64 (log.f64 x))
(log.f64 x)
x
(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)

localize60.0ms (0.7%)

Memory

31.8MiB live, 68.5MiB allocated

Localize:

Found 9 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(log.f64 (*.f64 x #s(literal 1/2 binary64)))
✓	accuracy	5.2%	(*.f64 x #s(literal 1/2 binary64))
✓	accuracy	5.2%	(neg.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))
✓	accuracy	1.5%	(neg.f64 (log.f64 x))
✓	accuracy	1.5%	(log.f64 x)
✓	accuracy	14.4%	(log.f64 (/.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) x))
✓	accuracy	2.3%	(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
✓	accuracy	2.3%	(*.f64 x #s(literal -1/2 binary64))
✓	accuracy	1.1%	(/.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) x)

Samples

29.0ms

256×

valid

Compiler

Compiled 104 to 29 computations (72.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-log: 9.0ms (45.8% of total)

ival-mult: 5.0ms (25.4% of total)

ival-div: 2.0ms (10.2% of total)

ival-neg: 2.0ms (10.2% of total)

ival-add: 1.0ms (5.1% of total)

exact: 1.0ms (5.1% of total)

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

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

series141.0ms (1.7%)

Memory

-22.9MiB live, 169.0MiB allocated

Counts

9 → 108

Calls

Call 1

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

Outputs
#<alt (+ (log 2) (* -1 (log x)))>
#<alt (+ (log 2) (+ (* -1 (log x)) (* -1/4 x)))>
#<alt (+ (log 2) (+ (* -1 (log x)) (* x (- (* -1/32 x) 1/4))))>
#<alt (+ (log 2) (+ (* -1 (log x)) (* x (- (* x (- (* -1/192 x) 1/32)) 1/4))))>
#<alt (log -1/2)>
#<alt (- (log -1/2) (* 4 (/ 1 x)))>
#<alt (+ (log -1/2) (* -1 (/ (+ 4 (* 8 (/ 1 x))) x)))>
#<alt (- (+ (log -1/2) (* -1 (/ (+ 8 (* 64/3 (/ 1 x))) (pow x 2)))) (* 4 (/ 1 x)))>
#<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 x)>
#<alt (/ (+ 2 (* -1/2 x)) x)>
#<alt (/ (+ 2 (* -1/2 x)) x)>
#<alt (/ (+ 2 (* -1/2 x)) x)>
#<alt -1/2>
#<alt (- (* 2 (/ 1 x)) 1/2)>
#<alt (- (* 2 (/ 1 x)) 1/2)>
#<alt (- (* 2 (/ 1 x)) 1/2)>
#<alt (* -1/2 x)>
#<alt (* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))>
#<alt (* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))>
#<alt (* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))>
#<alt 2>
#<alt (+ 2 (* -1/2 x))>
#<alt (+ 2 (* -1/2 x))>
#<alt (+ 2 (* -1/2 x))>
#<alt (* -1/2 x)>
#<alt (* x (- (* 2 (/ 1 x)) 1/2))>
#<alt (* x (- (* 2 (/ 1 x)) 1/2))>
#<alt (* x (- (* 2 (/ 1 x)) 1/2))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 2 (/ 1 x))))>
#<alt (* x (+ 1/2 (* 2 (/ 1 x))))>
#<alt (* x (+ 1/2 (* 2 (/ 1 x))))>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 (log x))>
#<alt (* -1 (log x))>
#<alt (* -1 (log x))>
#<alt (* -1 (log x))>
#<alt (log (/ 1 x))>
#<alt (log (/ 1 x))>
#<alt (log (/ 1 x))>
#<alt (log (/ 1 x))>
#<alt (log (/ -1 x))>
#<alt (log (/ -1 x))>
#<alt (log (/ -1 x))>
#<alt (log (/ -1 x))>
#<alt (log x)>
#<alt (log x)>
#<alt (log x)>
#<alt (log x)>
#<alt (* -1 (log (/ 1 x)))>
#<alt (* -1 (log (/ 1 x)))>
#<alt (* -1 (log (/ 1 x)))>
#<alt (* -1 (log (/ 1 x)))>
#<alt (* -1 (log (/ -1 x)))>
#<alt (* -1 (log (/ -1 x)))>
#<alt (* -1 (log (/ -1 x)))>
#<alt (* -1 (log (/ -1 x)))>
#<alt (* -1 (+ (log 1/2) (log x)))>
#<alt (* -1 (+ (log 1/2) (log x)))>
#<alt (* -1 (+ (log 1/2) (log x)))>
#<alt (* -1 (+ (log 1/2) (log x)))>
#<alt (log (/ 1 x))>
#<alt (log (/ 1 x))>
#<alt (log (/ 1 x))>
#<alt (log (/ 1 x))>
#<alt (log (/ -1 x))>
#<alt (log (/ -1 x))>
#<alt (log (/ -1 x))>
#<alt (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 (* -1 (log (/ 1 x)))>
#<alt (* -1 (log (/ 1 x)))>
#<alt (* -1 (log (/ 1 x)))>
#<alt (* -1 (log (/ 1 x)))>
#<alt (* -1 (log (/ -1 x)))>
#<alt (* -1 (log (/ -1 x)))>
#<alt (* -1 (log (/ -1 x)))>
#<alt (* -1 (log (/ -1 x)))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>

Calls

27 calls:

Time	Variable		Point	Expression
33.0ms	x	@	inf	(log x)
29.0ms	x	@	0	(neg (log (* x 1/2)))
10.0ms	x	@	-inf	(log (* x 1/2))
8.0ms	x	@	0	(log (* x 1/2))
7.0ms	x	@	-inf	(neg (log x))

Compiler

Compiled 189 to 147 computations (22.2% saved)

rewrite362.0ms (4.5%)

Memory

29.2MiB live, 546.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

3 982×	`lower-*.f32`
3 978×	`lower-*.f64`
3 312×	`lower-fma.f32`
3 310×	`lower-fma.f64`
3 298×	`lower-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	43
0	23	43
1	65	42
2	335	42
3	3012	42
0	8379	42

Stop Event

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

Counts

9 → 706

Calls

Call 1

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

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

simplify286.0ms (3.5%)

Memory

-29.2MiB live, 416.7MiB allocated

Algorithm

1×	egg-herbie

Rules

7 430×	`lower-fma.f64`
7 430×	`lower-fma.f32`
2 360×	`lower--.f64`
2 360×	`lower--.f32`
2 074×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	90	515
1	227	503
2	474	497
3	1037	488
4	2416	456
5	5493	455
6	7310	454
0	8029	436

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 100

Calls

Call 1

Inputs
(+ (log 2) (* -1 (log x)))
(+ (log 2) (+ (* -1 (log x)) (* -1/4 x)))
(+ (log 2) (+ (* -1 (log x)) (* x (- (* -1/32 x) 1/4))))
(+ (log 2) (+ (* -1 (log x)) (* x (- (* x (- (* -1/192 x) 1/32)) 1/4))))
(log -1/2)
(- (log -1/2) (* 4 (/ 1 x)))
(+ (log -1/2) (* -1 (/ (+ 4 (* 8 (/ 1 x))) x)))
(- (+ (log -1/2) (* -1 (/ (+ 8 (* 64/3 (/ 1 x))) (pow x 2)))) (* 4 (/ 1 x)))
(+ (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 x)
(/ (+ 2 (* -1/2 x)) x)
(/ (+ 2 (* -1/2 x)) x)
(/ (+ 2 (* -1/2 x)) x)
-1/2
(- (* 2 (/ 1 x)) 1/2)
(- (* 2 (/ 1 x)) 1/2)
(- (* 2 (/ 1 x)) 1/2)
(* -1/2 x)
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
(* -1 (* x (- 1/2 (* 2 (/ 1 (pow x 2))))))
2
(+ 2 (* -1/2 x))
(+ 2 (* -1/2 x))
(+ 2 (* -1/2 x))
(* -1/2 x)
(* x (- (* 2 (/ 1 x)) 1/2))
(* x (- (* 2 (/ 1 x)) 1/2))
(* x (- (* 2 (/ 1 x)) 1/2))
(* 1/2 x)
(* x (+ 1/2 (* 2 (/ 1 x))))
(* x (+ 1/2 (* 2 (/ 1 x))))
(* x (+ 1/2 (* 2 (/ 1 x))))
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
x
x
x
x
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 (log x))
(* -1 (log x))
(* -1 (log x))
(* -1 (log x))
(log (/ 1 x))
(log (/ 1 x))
(log (/ 1 x))
(log (/ 1 x))
(log (/ -1 x))
(log (/ -1 x))
(log (/ -1 x))
(log (/ -1 x))
(log x)
(log x)
(log x)
(log x)
(* -1 (log (/ 1 x)))
(* -1 (log (/ 1 x)))
(* -1 (log (/ 1 x)))
(* -1 (log (/ 1 x)))
(* -1 (log (/ -1 x)))
(* -1 (log (/ -1 x)))
(* -1 (log (/ -1 x)))
(* -1 (log (/ -1 x)))
(* -1 (+ (log 1/2) (log x)))
(* -1 (+ (log 1/2) (log x)))
(* -1 (+ (log 1/2) (log x)))
(* -1 (+ (log 1/2) (log x)))
(log (/ 1 x))
(log (/ 1 x))
(log (/ 1 x))
(log (/ 1 x))
(log (/ -1 x))
(log (/ -1 x))
(log (/ -1 x))
(log (/ -1 x))
(+ (log 1/2) (log x))
(+ (log 1/2) (log x))
(+ (log 1/2) (log x))
(+ (log 1/2) (log x))
(* -1 (log (/ 1 x)))
(* -1 (log (/ 1 x)))
(* -1 (log (/ 1 x)))
(* -1 (log (/ 1 x)))
(* -1 (log (/ -1 x)))
(* -1 (log (/ -1 x)))
(* -1 (log (/ -1 x)))
(* -1 (log (/ -1 x)))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
x
x
x
x
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)

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

eval106.0ms (1.3%)

Memory: 30.3MiB live, 289.3MiB allocated
Compiler: Compiled 24 959 to 2 279 computations (90.9% saved)

prune92.0ms (1.1%)

Memory

-22.0MiB live, 274.4MiB allocated

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	804	2	806
Fresh	0	0	0
Picked	1	2	3
Done	0	1	1
Total	805	5	810

Accuracy

100.0%

Counts

810 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.1%	(neg.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))
✓	31.5%	(neg.f64 (log.f64 x))
▶	99.5%	(log.f64 (fma.f64 x #s(literal -1/2 binary64) (/.f64 #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))
▶	0.0%	(log.f64 #s(literal -1/2 binary64))

Compiler

Compiled 33 to 25 computations (24.2% saved)

simplify4.0ms (0.1%)

Memory

10.0MiB live, 10.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

4×	`lower-*.f64`
4×	`lower-+.f64`
4×	`lower-fma.f32`
4×	`lower-*.f32`
4×	`lift-log.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	22
0	12	22
1	14	22
0	14	22

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize57.0ms (0.7%)

Memory

-17.4MiB live, 21.8MiB allocated

Localize:

Found 4 expressions of interest:

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

Samples

48.0ms

256×

invalid

Compiler

Compiled 49 to 17 computations (65.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 41.0ms

ival-log: 35.0ms (85.2% of total)

ival-div: 2.0ms (4.9% of total)

ival-mult: 2.0ms (4.9% of total)

ival-add: 1.0ms (2.4% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Counts

4 → 36

Calls

Call 1

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

Outputs
#<alt (+ (log 2) (* -1 (log x)))>
#<alt (+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 2))))>
#<alt (+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* -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 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 (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 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)>

Calls

9 calls:

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

Compiler

Compiled 75 to 60 computations (20% saved)

rewrite230.0ms (2.8%)

Memory

10.7MiB live, 162.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

3 324×	`lower-fma.f32`
3 322×	`lower-fma.f64`
1 982×	`lower-*.f64`
1 982×	`lower-*.f32`
1 530×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	18
0	12	18
1	36	18
2	268	18
0	4004	18

Stop Event

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

Counts

4 → 117

Calls

Call 1

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

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

simplify290.0ms (3.6%)

Memory

2.4MiB live, 574.7MiB allocated

Algorithm

1×	egg-herbie

Rules

9 612×	`lower-fma.f64`
9 612×	`lower-fma.f32`
2 500×	`lower-*.f64`
2 500×	`lower-*.f32`
1 916×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	322
1	192	302
2	474	302
3	1198	302
4	3009	290
5	5277	286
6	7721	286
0	8105	271

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

Calls

Call 1

Inputs
(+ (log 2) (* -1 (log x)))
(+ (log 2) (+ (* -1 (log x)) (* -1/4 (pow x 2))))
(+ (log 2) (+ (* -1 (log x)) (* (pow x 2) (- (* -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 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))))))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)

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

eval18.0ms (0.2%)

Memory: 7.6MiB live, 46.7MiB allocated
Compiler: Compiled 3 599 to 470 computations (86.9% saved)

prune18.0ms (0.2%)

Memory

8.5MiB live, 47.0MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	153	5	158

Accuracy

100.0%

Counts

158 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.1%	(neg.f64 (log.f64 (*.f64 x #s(literal 1/2 binary64))))
✓	31.5%	(neg.f64 (log.f64 x))
✓	99.5%	(log.f64 (fma.f64 x #s(literal -1/2 binary64) (/.f64 #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))
✓	0.0%	(log.f64 #s(literal -1/2 binary64))

Compiler

Compiled 102 to 61 computations (40.2% saved)

regimes14.0ms (0.2%)

Memory

-15.1MiB live, 25.3MiB allocated

Counts

10 → 1

Calls

Call 1

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

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

4.0ms

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

3.0ms

Results

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

Compiler

Compiled 29 to 18 computations (37.9% saved)

regimes10.0ms (0.1%)

Memory

18.2MiB live, 18.2MiB allocated

Counts

8 → 1

Calls

Call 1

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

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

Calls

3 calls:

3.0ms

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

3.0ms

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

3.0ms

Results

Accuracy	Segments	Branch
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)

regimes10.0ms (0.1%)

Memory

-23.5MiB live, 14.2MiB allocated

Counts

5 → 1

Calls

Call 1

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

5.0ms

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

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

Results

Accuracy	Segments	Branch
99.1%	1	`x`
99.1%	1	`(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))`
99.1%	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

9.6MiB live, 9.6MiB allocated

Counts

2 → 1

Calls

Call 1

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

Outputs
(neg.f64 (log.f64 x))

Calls

3 calls:

2.0ms

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

2.0ms

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

2.0ms

Results

Accuracy	Segments	Branch
31.5%	1	`x`
31.5%	1	`(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))`
31.5%	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)

regimes4.0ms (0.1%)

Memory

9.6MiB live, 9.6MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

1.0ms

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

1.0ms

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

1.0ms

Results

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

Compiler

Compiled 29 to 18 computations (37.9% saved)

simplify9.0ms (0.1%)

Memory

-26.6MiB live, 11.7MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	28
1	35	28
2	45	28
3	51	28
4	53	28

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

soundness953.0ms (11.7%)

Memory

-2.6MiB live, 525.0MiB allocated

Rules

15 078×	`lower-fma.f64`
15 078×	`lower-fma.f32`
14 748×	`lower-fma.f64`
14 748×	`lower-fma.f32`
7 430×	`lower-fma.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	298	1455
1	737	1351
2	2101	1261
3	6024	1239
0	8540	1179
0	20	87
0	36	87
1	115	87
2	698	84
3	6832	84
0	9300	80
0	90	515
1	227	503
2	474	497
3	1037	488
4	2416	456
5	5493	455
6	7310	454
0	8029	436
0	9	44
0	16	44
1	69	44
2	624	40
3	7596	40
0	8354	40
0	196	757
1	468	696
2	1437	680
3	4150	676
0	8354	652

Stop Event

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

Compiler

Compiled 116 to 83 computations (28.4% saved)

preprocess131.0ms (1.6%)

Memory: 1.0MiB live, 81.8MiB allocated
Compiler: Compiled 86 to 58 computations (32.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze3.0ms (0%)

sample833.0ms (10.3%)

preprocess635.0ms (7.8%)

explain144.0ms (1.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify741.0ms (9.1%)

localize34.0ms (0.4%)

series17.0ms (0.2%)

rewrite266.0ms (3.3%)

simplify743.0ms (9.2%)

eval70.0ms (0.9%)

prune48.0ms (0.6%)

simplify338.0ms (4.2%)

localize118.0ms (1.5%)

series132.0ms (1.6%)

rewrite394.0ms (4.9%)

simplify509.0ms (6.3%)

eval122.0ms (1.5%)

prune154.0ms (1.9%)

simplify7.0ms (0.1%)

localize60.0ms (0.7%)

series141.0ms (1.7%)

rewrite362.0ms (4.5%)

simplify286.0ms (3.5%)

eval106.0ms (1.3%)

prune92.0ms (1.1%)

simplify4.0ms (0.1%)

localize57.0ms (0.7%)

series3.0ms (0%)

rewrite230.0ms (2.8%)

simplify290.0ms (3.6%)

eval18.0ms (0.2%)

prune18.0ms (0.2%)

regimes14.0ms (0.2%)

regimes10.0ms (0.1%)

regimes10.0ms (0.1%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

simplify9.0ms (0.1%)

soundness953.0ms (11.7%)

preprocess131.0ms (1.6%)

end0.0ms (0%)

Profiling