Metrics for Hyperbolic arc-cosine

analyze98.0ms (1.3%)

Memory

27.4MiB live, 110.6MiB 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%	100%	0%	0%	0%	0%	3
16.7%	12.5%	62.5%	0%	0%	25%	0%	4
30%	18.7%	43.7%	0%	0%	37.5%	0%	5
38.9%	21.9%	34.4%	0%	0%	43.7%	0%	6
44.1%	23.4%	29.7%	0%	0%	46.9%	0%	7
47%	24.2%	27.3%	0%	0%	48.4%	0%	8
48.5%	24.6%	26.2%	0%	0%	49.2%	0%	9
49.2%	24.8%	25.6%	0%	0%	49.6%	0%	10
49.6%	24.9%	25.3%	0%	0%	49.8%	0%	11
49.8%	24.9%	25.1%	0%	0%	49.9%	0%	12

Compiler

Compiled 11 to 9 computations (18.2% saved)

sample3.5s (47.2%)

Memory

0.7MiB live, 3 805.9MiB allocated

Samples

1.6s	7 117×	1	invalid
1.1s	8 256×	0	valid
81.0ms	1 097×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 2.0s

ival-sqrt: 472.0ms (24% of total)

ival-log: 410.0ms (20.8% of total)

ival-mult: 326.0ms (16.5% of total)

adjust: 284.0ms (14.4% of total)

ival-add: 234.0ms (11.9% of total)

ival-sub: 213.0ms (10.8% of total)

exact: 13.0ms (0.7% of total)

ival-true: 12.0ms (0.6% of total)

ival-assert: 6.0ms (0.3% of total)

Bogosity

preprocess779.0ms (10.4%)

Memory

-12.7MiB live, 1 085.4MiB allocated

Algorithm

1×	egg-herbie

Rules

29 894×	`accelerator-lowering-fma.f32`
29 894×	`accelerator-lowering-fma.f64`
4 210×	`-lowering-.f32`
4 210×	`-lowering-.f64`
2 884×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	27	19
2	59	19
3	130	19
4	295	19
5	579	19
6	1088	19
7	1677	19
8	3021	19
9	4118	19
10	5059	19
11	5487	19
12	5727	19
13	5799	19
14	5883	19
15	6475	19
16	7565	19
17	7621	19
18	7719	19
19	7753	19
20	7769	19
0	7	9
1	16	9
2	20	9
3	35	9
4	66	9
5	127	9
6	287	9
7	567	9
8	2049	9
9	3153	9
10	4418	9
11	5102	9
12	5404	9
13	5589	9
14	5691	9
15	6010	9
16	6556	9
17	7667	9
0	8087	8

Stop Event

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

Calls

Call 1

Inputs
(log (+ x (sqrt (- (* x x) 1))))

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

explain99.0ms (1.3%)

Memory

14.1MiB live, 251.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
122	-	-	`(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))`
0	-	-	`(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))`
0	-	-	`(*.f64 x x)`
0	-	-	`(-.f64 (*.f64 x x) #s(literal 1 binary64))`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))`	oflow-rescue	122	0
↳	`(-.f64 (*.f64 x x) #s(literal 1 binary64))`	overflow	122
↳	`(*.f64 x x)`	overflow	122

Confusion

	Predicted +	Predicted -
+	122	0
-	0	134

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	122	0	0
-	0	0	134

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	134
1	122

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

35.0ms

512×

valid

Compiler

Compiled 90 to 32 computations (64.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-log: 6.0ms (29.1% of total)

ival-mult: 4.0ms (19.4% of total)

ival-sqrt: 4.0ms (19.4% of total)

ival-sub: 3.0ms (14.5% of total)

ival-add: 3.0ms (14.5% of total)

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

exact: 0.0ms (0% of total)

ival-assert: 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

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.8%	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))

Compiler

Compiled 10 to 7 computations (30% saved)

simplify573.0ms (7.7%)

Memory

4.7MiB live, 918.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

29 894×	`accelerator-lowering-fma.f32`
29 894×	`accelerator-lowering-fma.f64`
4 210×	`-lowering-.f32`
4 210×	`-lowering-.f64`
2 884×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	33
1	16	33
2	20	33
3	35	33
4	66	33
5	127	33
6	287	33
7	567	33
8	2049	33
9	3153	33
10	4418	33
11	5102	33
12	5404	33
13	5589	33
14	5691	33
15	6010	33
16	6556	33
17	7667	33
0	8087	29

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(log (+ x (sqrt (- (* x x) 1))))
(+ x (sqrt (- (* x x) 1)))
x
(sqrt (- (* x x) 1))
(- (* x x) 1)
(* x x)
1

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

localize31.0ms (0.4%)

Memory

-8.3MiB live, 65.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
✓	accuracy	100.0%	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))
✓	accuracy	55.6%	(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))

Samples

18.0ms

256×

valid

Compiler

Compiled 35 to 9 computations (74.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-add: 3.0ms (25.7% of total)

ival-log: 3.0ms (25.7% of total)

ival-mult: 2.0ms (17.1% of total)

ival-sqrt: 2.0ms (17.1% of total)

ival-sub: 1.0ms (8.6% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Memory

13.4MiB live, 13.4MiB allocated

Counts

5 → 60

Calls

Call 1

Inputs
#<alt (- (* x x) 1)>
#<alt (log (+ x (sqrt (- (* x x) 1))))>
#<alt (+ x (sqrt (- (* x x) 1)))>
#<alt (sqrt (- (* x x) 1))>
#<alt (* x x)>

Outputs
#<alt -1>
#<alt (- (pow x 2) 1)>
#<alt (- (pow x 2) 1)>
#<alt (- (pow x 2) 1)>
#<alt (pow x 2)>
#<alt (* (pow x 2) (- 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- 1 (/ 1 (pow x 2))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (- 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- 1 (/ 1 (pow x 2))))>
#<alt (log (sqrt -1))>
#<alt (+ (log (sqrt -1)) (/ x (sqrt -1)))>
#<alt (+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))>
#<alt (+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))>
#<alt (+ (log 2) (* -1 (log (/ 1 x))))>
#<alt (- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))>
#<alt (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))>
#<alt (- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))>
#<alt (+ (log -1/2) (log (/ -1 x)))>
#<alt (+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))>
#<alt (+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))>
#<alt (+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))>
#<alt (sqrt -1)>
#<alt (+ x (sqrt -1))>
#<alt (+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))>
#<alt (+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))>
#<alt (* 2 x)>
#<alt (* x (- 2 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))>
#<alt (* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (/ 1/2 x)>
#<alt (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)>
#<alt (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))>
#<alt (* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))>
#<alt (sqrt -1)>
#<alt (+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))>
#<alt (+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))>
#<alt (+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))>
#<alt x>
#<alt (* x (- 1 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))>
#<alt (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))>
#<alt (* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>

Calls

15 calls:

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

rewrite329.0ms (4.4%)

Memory

1.4MiB live, 539.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 994×	`accelerator-lowering-fma.f32`
4 994×	`accelerator-lowering-fma.f64`
3 230×	`-lowering-.f32`
3 230×	`-lowering-.f64`
2 612×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	31
1	44	31
2	317	31
3	3621	31
0	8641	27

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 328

Calls

Call 1

Inputs
(- (* x x) 1)
(log (+ x (sqrt (- (* x x) 1))))
(+ x (sqrt (- (* x x) 1)))
(sqrt (- (* x x) 1))
(* x x)

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

simplify302.0ms (4.1%)

Memory

20.8MiB live, 366.9MiB allocated

Algorithm

1×	egg-herbie

Rules

10 204×	`accelerator-lowering-fma.f32`
10 204×	`accelerator-lowering-fma.f64`
3 650×	`-lowering-.f32`
3 650×	`-lowering-.f64`
2 854×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	150	595
1	411	569
2	1143	562
3	3327	524
4	7966	524
0	8526	495

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

Inputs
-1
(- (pow x 2) 1)
(- (pow x 2) 1)
(- (pow x 2) 1)
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(log (sqrt -1))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(+ (log 2) (* -1 (log (/ 1 x))))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(+ (log -1/2) (log (/ -1 x)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(sqrt -1)
(+ x (sqrt -1))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(* 2 x)
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(sqrt -1)
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
x
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(* -1 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))
(* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

Outputs
-1
#s(literal -1 binary64)
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(log (sqrt -1))
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f64 (log.f64 (sqrt.f64 #s(literal -1 binary64))) (/.f64 x (sqrt.f64 #s(literal -1 binary64))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal 1 binary64)) (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(fma.f64 x (fma.f64 x (.f64 x (/.f64 (.f64 (.f64 x x) #s(literal 3/40 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal -1 binary64)))) (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+.f64 (log.f64 #s(literal 2 binary64)) (+.f64 (log.f64 x) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(+.f64 (log.f64 #s(literal 2 binary64)) (+.f64 (log.f64 x) (/.f64 (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal -3/32 binary64) (.f64 x x))) (.f64 x x))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(+.f64 (log.f64 #s(literal 2 binary64)) (+.f64 (log.f64 x) (+.f64 (/.f64 (+.f64 #s(literal -3/32 binary64) (/.f64 #s(literal -5/96 binary64) (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))))
(+ (log -1/2) (log (/ -1 x)))
(+.f64 (log.f64 #s(literal -1/2 binary64)) (neg.f64 (log.f64 (neg.f64 x))))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (+.f64 (log.f64 #s(literal -1/2 binary64)) (neg.f64 (log.f64 (neg.f64 x)))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+.f64 (+.f64 (neg.f64 (log.f64 (neg.f64 x))) (/.f64 #s(literal 3/32 binary64) (.f64 x (.f64 x (.f64 x x))))) (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (log.f64 #s(literal -1/2 binary64))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(+.f64 (+.f64 (log.f64 #s(literal -1/2 binary64)) (neg.f64 (log.f64 (neg.f64 x)))) (+.f64 (/.f64 #s(literal 3/32 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (/.f64 #s(literal 5/96 binary64) (pow.f64 x #s(literal 6 binary64))))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ x (sqrt -1))
(+.f64 x (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(fma.f64 x (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(fma.f64 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (fma.f64 x (*.f64 x #s(literal 1/8 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 x #s(literal 2 binary64) (/.f64 #s(literal -1/2 binary64) x))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(fma.f64 x #s(literal 2 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 x x))) x))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal -1/2 binary64) x))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 x x))) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x x))) (.f64 x x))) x)
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal -1/16 binary64) (/.f64 #s(literal -5/128 binary64) (.f64 x x))) (.f64 x (.f64 x (*.f64 x x)))))) x)
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(fma.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (fma.f64 x (.f64 x #s(literal 1/8 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f64 x (fma.f64 x (/.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/16 binary64)) (.f64 x x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (fma.f64 x (.f64 x #s(literal 1/8 binary64)) #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal -1 binary64)))
x
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(+.f64 x (/.f64 #s(literal -1/2 binary64) x))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(-.f64 x (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 x x))) x))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(+.f64 (/.f64 #s(literal -1/2 binary64) x) (fma.f64 x (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) x))
(* -1 x)
(neg.f64 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))
(-.f64 (/.f64 #s(literal 1/2 binary64) x) x)
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))
(-.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 x x))) x) x)
(* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))))
(-.f64 (/.f64 #s(literal 1/2 binary64) x) (fma.f64 x (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) (.f64 x x))) (.f64 x (.f64 x (.f64 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)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

eval58.0ms (0.8%)

Memory: -35.1MiB live, 82.4MiB allocated
Compiler: Compiled 10 792 to 1 570 computations (85.5% saved)

prune42.0ms (0.6%)

Memory

37.0MiB live, 74.3MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	385	3	388
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	386	3	389

Accuracy

100.0%

Counts

389 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(log.f64 (fma.f64 x #s(literal 2 binary64) (/.f64 #s(literal -1/2 binary64) x)))
▶	53.8%	(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))
▶	99.0%	(log.f64 (+.f64 x x))

Compiler

Compiled 22 to 15 computations (31.8% saved)

simplify752.0ms (10.1%)

Memory

-111.9MiB live, 638.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

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

Rules

26 840×	`accelerator-lowering-fma.f32`
26 840×	`accelerator-lowering-fma.f64`
4 030×	`-lowering-.f32`
4 030×	`-lowering-.f64`
2 948×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	59
1	24	59
2	34	59
3	51	59
4	80	59
5	141	59
6	308	59
7	592	59
8	2147	59
9	3312	59
10	4676	59
11	5443	59
12	5823	59
13	5985	59
14	6093	59
15	6437	59
16	6990	59
17	7960	59
0	8045	53

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize47.0ms (0.6%)

Memory

-4.3MiB live, 72.7MiB allocated

Localize:

Found 9 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 x #s(literal 2 binary64) (/.f64 #s(literal -1/2 binary64) x))
✓	accuracy	100.0%	(/.f64 #s(literal -1/2 binary64) x)
✓	accuracy	100.0%	(log.f64 (fma.f64 x #s(literal 2 binary64) (/.f64 #s(literal -1/2 binary64) x)))
✓	accuracy	100.0%	(fma.f64 x x #s(literal -1 binary64))
✓	accuracy	100.0%	(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))
✓	accuracy	100.0%	(+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x)
✓	accuracy	55.6%	(sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))
✓	accuracy	100.0%	(+.f64 x x)
✓	accuracy	100.0%	(log.f64 (+.f64 x x))

Samples

30.0ms

256×

valid

Compiler

Compiled 55 to 17 computations (69.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-log: 9.0ms (42.8% of total)

ival-add: 5.0ms (23.8% of total)

ival-mult: 3.0ms (14.3% of total)

ival-div: 2.0ms (9.5% of total)

ival-sqrt: 2.0ms (9.5% of total)

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

exact: 0.0ms (0% of total)

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

series60.0ms (0.8%)

Memory

-0.9MiB live, 51.3MiB allocated

Counts

9 → 108

Calls

Call 1

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

Outputs
#<alt (+ (log 2) (log x))>
#<alt (+ (log 2) (log x))>
#<alt (+ (log 2) (log x))>
#<alt (+ (log 2) (log x))>
#<alt (+ (log 2) (* -1 (log (/ 1 x))))>
#<alt (+ (log 2) (* -1 (log (/ 1 x))))>
#<alt (+ (log 2) (* -1 (log (/ 1 x))))>
#<alt (+ (log 2) (* -1 (log (/ 1 x))))>
#<alt (+ (log -2) (* -1 (log (/ -1 x))))>
#<alt (+ (log -2) (* -1 (log (/ -1 x))))>
#<alt (+ (log -2) (* -1 (log (/ -1 x))))>
#<alt (+ (log -2) (* -1 (log (/ -1 x))))>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (log (sqrt -1))>
#<alt (+ (log (sqrt -1)) (/ x (sqrt -1)))>
#<alt (+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))>
#<alt (+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))>
#<alt (+ (log 2) (* -1 (log (/ 1 x))))>
#<alt (- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))>
#<alt (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))>
#<alt (- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))>
#<alt (+ (log -1/2) (log (/ -1 x)))>
#<alt (+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))>
#<alt (+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))>
#<alt (+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))>
#<alt (sqrt -1)>
#<alt (+ x (sqrt -1))>
#<alt (+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))>
#<alt (+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))>
#<alt (* 2 x)>
#<alt (* x (- 2 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))>
#<alt (* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (/ 1/2 x)>
#<alt (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)>
#<alt (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))>
#<alt (* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))>
#<alt (sqrt -1)>
#<alt (+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))>
#<alt (+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))>
#<alt (+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))>
#<alt x>
#<alt (* x (- 1 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))>
#<alt (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))>
#<alt (* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt -1>
#<alt (- (pow x 2) 1)>
#<alt (- (pow x 2) 1)>
#<alt (- (pow x 2) 1)>
#<alt (pow x 2)>
#<alt (* (pow x 2) (- 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- 1 (/ 1 (pow x 2))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (- 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- 1 (/ 1 (pow x 2))))>
#<alt (+ (log -1/2) (* -1 (log x)))>
#<alt (+ (log -1/2) (+ (* -4 (pow x 2)) (* -1 (log x))))>
#<alt (+ (log -1/2) (+ (* -1 (log x)) (* (pow x 2) (- (* -8 (pow x 2)) 4))))>
#<alt (+ (log -1/2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -64/3 (pow x 2)) 8)) 4))))>
#<alt (+ (log 2) (* -1 (log (/ 1 x))))>
#<alt (- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))>
#<alt (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 1/32 (/ 1 (pow x 2)))) (pow x 2)))))>
#<alt (- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/32 (* 1/192 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))>
#<alt (+ (log -2) (* -1 (log (/ -1 x))))>
#<alt (- (+ (log -2) (* -1 (log (/ -1 x)))) (* 1/4 (/ 1 (pow x 2))))>
#<alt (+ (log -2) (+ (* -1 (log (/ -1 x))) (* -1 (/ (+ 1/4 (* 1/32 (/ 1 (pow x 2)))) (pow x 2)))))>
#<alt (- (+ (log -2) (+ (* -1 (log (/ -1 x))) (* -1 (/ (+ 1/32 (* 1/192 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))>
#<alt (/ -1/2 x)>
#<alt (/ (- (* 2 (pow x 2)) 1/2) x)>
#<alt (/ (- (* 2 (pow x 2)) 1/2) x)>
#<alt (/ (- (* 2 (pow x 2)) 1/2) x)>
#<alt (* 2 x)>
#<alt (* x (- 2 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* x (- 2 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* x (- 2 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 2)))>
#<alt (* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 2)))>
#<alt (* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 2)))>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>
#<alt (/ -1/2 x)>

Calls

27 calls:

Time	Variable		Point	Expression
31.0ms	x	@	0	(log (+ x x))
19.0ms	x	@	-inf	(log (+ x x))
6.0ms	x	@	inf	(log (+ x x))
0.0ms	x	@	0	(log (+ (* x 2) (/ -1/2 x)))
0.0ms	x	@	-inf	(log (+ (* x 2) (/ -1/2 x)))

rewrite66.0ms (0.9%)

Memory

-13.1MiB live, 61.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

760×	`accelerator-lowering-fma.f32`
760×	`accelerator-lowering-fma.f64`
350×	`-lowering-.f32`
350×	`-lowering-.f64`
320×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	45
1	76	45
0	806	41

Stop Event

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

Counts

9 → 237

Calls

Call 1

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

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

simplify315.0ms (4.2%)

Memory

10.8MiB live, 475.9MiB allocated

Algorithm

1×	egg-herbie

Rules

11 472×	`accelerator-lowering-fma.f32`
11 472×	`accelerator-lowering-fma.f64`
4 284×	`-lowering-.f32`
4 284×	`-lowering-.f64`
3 792×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	205	985
1	556	939
2	1521	932
3	4376	877
0	8279	833

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 108

Calls

Call 1

Inputs
(+ (log 2) (log x))
(+ (log 2) (log x))
(+ (log 2) (log x))
(+ (log 2) (log x))
(+ (log 2) (* -1 (log (/ 1 x))))
(+ (log 2) (* -1 (log (/ 1 x))))
(+ (log 2) (* -1 (log (/ 1 x))))
(+ (log 2) (* -1 (log (/ 1 x))))
(+ (log -2) (* -1 (log (/ -1 x))))
(+ (log -2) (* -1 (log (/ -1 x))))
(+ (log -2) (* -1 (log (/ -1 x))))
(+ (log -2) (* -1 (log (/ -1 x))))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(log (sqrt -1))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(+ (log 2) (* -1 (log (/ 1 x))))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(+ (log -1/2) (log (/ -1 x)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(sqrt -1)
(+ x (sqrt -1))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(* 2 x)
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(sqrt -1)
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
x
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(* -1 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))
(* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))))
-1
(- (pow x 2) 1)
(- (pow x 2) 1)
(- (pow x 2) 1)
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(+ (log -1/2) (* -1 (log x)))
(+ (log -1/2) (+ (* -4 (pow x 2)) (* -1 (log x))))
(+ (log -1/2) (+ (* -1 (log x)) (* (pow x 2) (- (* -8 (pow x 2)) 4))))
(+ (log -1/2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -64/3 (pow x 2)) 8)) 4))))
(+ (log 2) (* -1 (log (/ 1 x))))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 1/32 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/32 (* 1/192 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(+ (log -2) (* -1 (log (/ -1 x))))
(- (+ (log -2) (* -1 (log (/ -1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+ (log -2) (+ (* -1 (log (/ -1 x))) (* -1 (/ (+ 1/4 (* 1/32 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log -2) (+ (* -1 (log (/ -1 x))) (* -1 (/ (+ 1/32 (* 1/192 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(/ -1/2 x)
(/ (- (* 2 (pow x 2)) 1/2) x)
(/ (- (* 2 (pow x 2)) 1/2) x)
(/ (- (* 2 (pow x 2)) 1/2) x)
(* 2 x)
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(* 2 x)
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 2)))
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 2)))
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 2)))
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)

Outputs
(+ (log 2) (log x))
(+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (log x))
(+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (log x))
(+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (log x))
(+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(+ (log -2) (* -1 (log (/ -1 x))))
(-.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))
(+ (log -2) (* -1 (log (/ -1 x))))
(-.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))
(+ (log -2) (* -1 (log (/ -1 x))))
(-.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))
(+ (log -2) (* -1 (log (/ -1 x))))
(-.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (/.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)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(log (sqrt -1))
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f64 (log.f64 (sqrt.f64 #s(literal -1 binary64))) (/.f64 x (sqrt.f64 #s(literal -1 binary64))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal 1 binary64)) (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(fma.f64 x (fma.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 x (.f64 x #s(literal -1/6 binary64)) #s(literal -1 binary64)) (.f64 (.f64 x x) (/.f64 (.f64 (*.f64 x x) #s(literal 3/40 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))))) (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+.f64 (log.f64 #s(literal 2 binary64)) (+.f64 (log.f64 x) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(+.f64 (log.f64 #s(literal 2 binary64)) (+.f64 (log.f64 x) (/.f64 (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal -3/32 binary64) (.f64 x x))) (.f64 x x))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(+.f64 (log.f64 #s(literal 2 binary64)) (+.f64 (/.f64 (+.f64 #s(literal -3/32 binary64) (/.f64 #s(literal -5/96 binary64) (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (log.f64 x) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))))
(+ (log -1/2) (log (/ -1 x)))
(+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal -1/2 binary64)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (log.f64 #s(literal -1/2 binary64))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+.f64 (log.f64 #s(literal -1/2 binary64)) (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (/.f64 #s(literal 3/32 binary64) (.f64 x (.f64 x (.f64 x x)))))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (+.f64 (/.f64 #s(literal 3/32 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (+.f64 (log.f64 #s(literal -1/2 binary64)) (/.f64 #s(literal 5/96 binary64) (pow.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal 1/4 binary64) (.f64 x x)))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ x (sqrt -1))
(+.f64 x (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(fma.f64 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(fma.f64 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64)))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2 binary64) x (/.f64 #s(literal -1/2 binary64) x))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(fma.f64 #s(literal 2 binary64) x (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 x x))) x))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal -1/2 binary64) x))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x x))) (.f64 x x))) x)
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) (/.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 5/128 binary64) (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))) x)
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(fma.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (/.f64 (.f64 x (.f64 x #s(literal 1/16 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal -1 binary64)))
x
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(+.f64 x (/.f64 #s(literal -1/2 binary64) x))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(+.f64 x (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 x x))) x))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 x (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (+.f64 x (/.f64 #s(literal -1/2 binary64) x)))
(* -1 x)
(neg.f64 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))
(-.f64 (/.f64 #s(literal 1/2 binary64) x) x)
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))
(-.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x) x)
(* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))))
(fma.f64 x (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (-.f64 (/.f64 #s(literal 1/2 binary64) x) x))
-1
#s(literal -1 binary64)
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(+ (log -1/2) (* -1 (log x)))
(-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 x))
(+ (log -1/2) (+ (* -4 (pow x 2)) (* -1 (log x))))
(-.f64 (fma.f64 x (*.f64 x #s(literal -4 binary64)) (log.f64 #s(literal -1/2 binary64))) (log.f64 x))
(+ (log -1/2) (+ (* -1 (log x)) (* (pow x 2) (- (* -8 (pow x 2)) 4))))
(fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -8 binary64)) #s(literal -4 binary64))) (-.f64 (log.f64 #s(literal -1/2 binary64)) (log.f64 x)))
(+ (log -1/2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -64/3 (pow x 2)) 8)) 4))))
(-.f64 (fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -64/3 binary64)) #s(literal -8 binary64))) #s(literal -4 binary64)) (log.f64 #s(literal -1/2 binary64))) (log.f64 x))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+.f64 (log.f64 #s(literal 2 binary64)) (+.f64 (log.f64 x) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 1/32 (/ 1 (pow x 2)))) (pow x 2)))))
(+.f64 (log.f64 #s(literal 2 binary64)) (+.f64 (log.f64 x) (/.f64 (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal -1/32 binary64) (.f64 x x))) (.f64 x x))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/32 (* 1/192 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(+.f64 (+.f64 (log.f64 #s(literal 2 binary64)) (log.f64 x)) (+.f64 (/.f64 (-.f64 #s(literal -1/32 binary64) (/.f64 #s(literal 1/192 binary64) (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))))
(+ (log -2) (* -1 (log (/ -1 x))))
(-.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))
(- (+ (log -2) (* -1 (log (/ -1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+.f64 (log.f64 #s(literal -2 binary64)) (-.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) (log.f64 (/.f64 #s(literal -1 binary64) x))))
(+ (log -2) (+ (* -1 (log (/ -1 x))) (* -1 (/ (+ 1/4 (* 1/32 (/ 1 (pow x 2)))) (pow x 2)))))
(+.f64 (log.f64 #s(literal -2 binary64)) (-.f64 (/.f64 (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal -1/32 binary64) (.f64 x x))) (.f64 x x)) (log.f64 (/.f64 #s(literal -1 binary64) x))))
(- (+ (log -2) (+ (* -1 (log (/ -1 x))) (* -1 (/ (+ 1/32 (* 1/192 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(+.f64 (-.f64 (log.f64 #s(literal -2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x))) (+.f64 (/.f64 (-.f64 #s(literal -1/32 binary64) (/.f64 #s(literal 1/192 binary64) (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/4 binary64) (*.f64 x x))))
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ (- (* 2 (pow x 2)) 1/2) x)
(fma.f64 #s(literal 2 binary64) x (/.f64 #s(literal -1/2 binary64) x))
(/ (- (* 2 (pow x 2)) 1/2) x)
(fma.f64 #s(literal 2 binary64) x (/.f64 #s(literal -1/2 binary64) x))
(/ (- (* 2 (pow x 2)) 1/2) x)
(fma.f64 #s(literal 2 binary64) x (/.f64 #s(literal -1/2 binary64) x))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2 binary64) x (/.f64 #s(literal -1/2 binary64) x))
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2 binary64) x (/.f64 #s(literal -1/2 binary64) x))
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2 binary64) x (/.f64 #s(literal -1/2 binary64) x))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 2)))
(fma.f64 #s(literal 2 binary64) x (/.f64 #s(literal -1/2 binary64) x))
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 2)))
(fma.f64 #s(literal 2 binary64) x (/.f64 #s(literal -1/2 binary64) x))
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 2)))
(fma.f64 #s(literal 2 binary64) x (/.f64 #s(literal -1/2 binary64) x))
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)

eval45.0ms (0.6%)

Memory: -9.3MiB live, 69.7MiB allocated
Compiler: Compiled 4 482 to 685 computations (84.7% saved)

prune23.0ms (0.3%)

Memory

11.8MiB live, 49.4MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	345	0	345
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	345	3	348

Accuracy

100.0%

Counts

348 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(log.f64 (fma.f64 x #s(literal 2 binary64) (/.f64 #s(literal -1/2 binary64) x)))
✓	53.8%	(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))
✓	99.0%	(log.f64 (+.f64 x x))

Compiler

Compiled 51 to 34 computations (33.3% saved)

regimes6.0ms (0.1%)

Memory

12.6MiB live, 12.6MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

2.0ms	x
2.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))
2.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	1	`(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))`
99.6%	1	`(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))`

Compiler

Compiled 21 to 14 computations (33.3% saved)

regimes4.0ms (0.1%)

Memory

9.6MiB live, 9.5MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(log.f64 (+.f64 x x))

Outputs
(log.f64 (+.f64 x x))

Calls

3 calls:

1.0ms	x
1.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
1.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))

Results

Accuracy	Segments	Branch
99.0%	1	`x`
99.0%	1	`(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))`
99.0%	1	`(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))`

Compiler

Compiled 21 to 14 computations (33.3% saved)

simplify9.0ms (0.1%)

Memory

-19.5MiB live, 17.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness202.0ms (2.7%)

Memory

-3.7MiB live, 150.9MiB allocated

Rules

10 204×	`accelerator-lowering-fma.f32`
10 204×	`accelerator-lowering-fma.f64`
3 650×	`-lowering-.f32`
3 650×	`-lowering-.f64`
2 854×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	150	595
1	411	569
2	1143	562
3	3327	524
4	7966	524
0	8526	495

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 25 to 17 computations (32% saved)

preprocess88.0ms (1.2%)

Memory: 12.4MiB live, 51.9MiB allocated
Compiler: Compiled 44 to 30 computations (31.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze98.0ms (1.3%)

sample3.5s (47.2%)

preprocess779.0ms (10.4%)

explain99.0ms (1.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify573.0ms (7.7%)

localize31.0ms (0.4%)

series5.0ms (0.1%)

rewrite329.0ms (4.4%)

simplify302.0ms (4.1%)

eval58.0ms (0.8%)

prune42.0ms (0.6%)

simplify752.0ms (10.1%)

localize47.0ms (0.6%)

series60.0ms (0.8%)

rewrite66.0ms (0.9%)

simplify315.0ms (4.2%)

eval45.0ms (0.6%)

prune23.0ms (0.3%)

regimes6.0ms (0.1%)

regimes4.0ms (0.1%)

simplify9.0ms (0.1%)

soundness202.0ms (2.7%)

preprocess88.0ms (1.2%)

end0.0ms (0%)

Profiling