Metrics for Rust f32::acosh

analyze0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	25%	75%	0%	0%	0%	0
100%	25%	0%	75%	0%	0%	0%	1

Compiler

Compiled 6 to 5 computations (16.7% saved)

sample418.0ms (5.9%)

Memory

15.1MiB live, 582.0MiB allocated

Samples

309.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 186.0ms

ival-acosh: 130.0ms (70% of total)

ival->=: 47.0ms (25.3% of total)

exact: 5.0ms (2.7% of total)

ival-assert: 3.0ms (1.6% of total)

Bogosity

preprocess1.2s (17.5%)

Memory

-12.6MiB live, 699.6MiB 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	4	7
1	10	7
2	14	7
3	17	7
4	21	7
5	28	7
6	35	7
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×	saturated

Calls

Call 1

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

Outputs
(log (+ x (sqrt (- (* x x) 1))))
(log.f32 (+.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))

explain220.0ms (3.1%)

Memory

14.0MiB live, 172.7MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
146	-	-	`(sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))`
3	-	-	`(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))`
0	-	-	`(-.f32 (*.f32 x x) #s(literal 1 binary32))`
0	-	-	`(*.f32 x x)`
0	-	-	`#s(literal 1 binary32)`
0	-	-	`(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f32`	`(sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))`	oflow-rescue	146	0
↳	`(*.f32 x x)`	overflow	146
↳	`(-.f32 (*.f32 x x) #s(literal 1 binary32))`	overflow	146
`log.f32`	`(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))`	oflow-rescue	3	0
↳	`(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))`	overflow	3
↳	`(*.f32 x x)`	overflow	146
↳	`(-.f32 (*.f32 x x) #s(literal 1 binary32))`	overflow	146

Confusion

	Predicted +	Predicted -
+	146	0
-	0	110

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	146	0	0
-	0	0	110

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	110
1	143
2	3

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

140.0ms

512×

valid

Compiler

Compiled 90 to 32 computations (64.4% saved)

Precisions

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

ival-sub: 27.0ms (44.6% of total)

ival-add: 21.0ms (34.7% of total)

ival-log: 5.0ms (8.3% of total)

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

ival-sqrt: 3.0ms (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

1.9MiB live, 1.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	46.6%	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))

Compiler

Compiled 10 to 7 computations (30% saved)

simplify652.0ms (9.3%)

Memory

-5.6MiB live, 888.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))
✓	cost-diff	0	(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))
✓	cost-diff	0	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))
✓	cost-diff	64	(-.f32 (*.f32 x x) #s(literal 1 binary32))

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.f32 (+.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))
(+ x (sqrt (- (* x x) 1)))
(+.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))
x
(sqrt (- (* x x) 1))
(sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))
(- (* x x) 1)
(fma.f32 x x #s(literal -1 binary32))
(* x x)
(*.f32 x x)
1
#s(literal 1 binary32)

localize75.0ms (1.1%)

Memory

-30.2MiB live, 46.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(-.f32 (*.f32 x x) #s(literal 1 binary32))
✓	accuracy	99.9%	(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))
✓	accuracy	98.9%	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))
✓	accuracy	50.6%	(sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))

Samples

29.0ms

256×

valid

Compiler

Compiled 35 to 9 computations (74.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 23.0ms

ival-sqrt: 16.0ms (68.6% of total)

ival-log: 2.0ms (8.6% of total)

ival-mult: 2.0ms (8.6% of total)

ival-sub: 1.0ms (4.3% of total)

ival-add: 1.0ms (4.3% 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

7.7MiB live, 7.7MiB allocated

Counts

4 → 48

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))>

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))))))>

Calls

12 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)

rewrite413.0ms (5.9%)

Memory

-5.5MiB live, 629.4MiB 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	28
1	44	28
2	317	28
3	3621	28
0	8641	24

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 320

Calls

Call 1

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

Outputs
(neg.f32 (-.f32 #s(literal 1 binary32) (*.f32 x x)))
(exp.f32 (log.f32 (fma.f32 x x #s(literal -1 binary32))))
(exp.f32 (*.f32 (neg.f32 (log.f32 (fma.f32 x x #s(literal -1 binary32)))) #s(literal -1 binary32)))
(+.f32 (*.f32 x x) #s(literal -1 binary32))
(+.f32 #s(literal -1 binary32) (*.f32 x x))
(+.f32 (+.f32 x #s(literal -1 binary32)) (*.f32 x (+.f32 x #s(literal -1 binary32))))
(+.f32 (/.f32 (.f32 (.f32 x x) (.f32 x (.f32 x (.f32 x x)))) (fma.f32 x x (fma.f32 x (.f32 x (.f32 x x)) #s(literal 1 binary32)))) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x (fma.f32 x (.f32 x (*.f32 x x)) #s(literal 1 binary32))))))
(+.f32 (.f32 (.f32 x (*.f32 x x)) (/.f32 x (fma.f32 x x #s(literal 1 binary32)))) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal 1 binary32)))))
(+.f32 (.f32 (+.f32 x #s(literal 1 binary32)) x) (.f32 (+.f32 x #s(literal 1 binary32)) #s(literal -1 binary32)))
(+.f32 (.f32 (+.f32 x #s(literal -1 binary32)) x) (.f32 (+.f32 x #s(literal -1 binary32)) #s(literal 1 binary32)))
(+.f32 (.f32 (+.f32 x #s(literal -1 binary32)) #s(literal 1 binary32)) (.f32 (+.f32 x #s(literal -1 binary32)) x))
(+.f32 (.f32 x (+.f32 x #s(literal 1 binary32))) (.f32 #s(literal -1 binary32) (+.f32 x #s(literal 1 binary32))))
(+.f32 (*.f32 x (+.f32 x #s(literal -1 binary32))) (+.f32 x #s(literal -1 binary32)))
(fabs.f32 (fma.f32 x x #s(literal -1 binary32)))
(pow.f32 (fma.f32 x x #s(literal -1 binary32)) #s(literal 1 binary32))
(pow.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) #s(literal 2 binary32))
(pow.f32 (*.f32 (fma.f32 x x #s(literal -1 binary32)) (fma.f32 x x #s(literal -1 binary32))) #s(literal 1/2 binary32))
(pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal -1 binary32))) #s(literal -1 binary32))
(pow.f32 (sqrt.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) #s(literal 4 binary32))
(pow.f32 (.f32 (.f32 (fma.f32 x x #s(literal -1 binary32)) (fma.f32 x x #s(literal -1 binary32))) (*.f32 (fma.f32 x x #s(literal -1 binary32)) (fma.f32 x x #s(literal -1 binary32)))) #s(literal 1/4 binary32))
(pow.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal -1 binary32))) #s(literal 1 binary32)) #s(literal -1 binary32))
(pow.f32 (/.f32 (fma.f32 x (.f32 x (.f32 x x)) (-.f32 #s(literal 1 binary32) (.f32 x (.f32 x #s(literal -1 binary32))))) (fma.f32 (.f32 x (.f32 x x)) (.f32 x (.f32 x x)) #s(literal -1 binary32))) #s(literal -1 binary32))
(pow.f32 (exp.f32 #s(literal 1/2 binary32)) (*.f32 #s(literal 2 binary32) (log.f32 (fma.f32 x x #s(literal -1 binary32)))))
(pow.f32 (exp.f32 #s(literal 2 binary32)) (*.f32 #s(literal 1/2 binary32) (log.f32 (fma.f32 x x #s(literal -1 binary32)))))
(pow.f32 (exp.f32 #s(literal 1 binary32)) (log.f32 (fma.f32 x x #s(literal -1 binary32))))
(fma.f32 x x #s(literal -1 binary32))
(fma.f32 x (+.f32 x #s(literal 1 binary32)) (*.f32 #s(literal -1 binary32) (+.f32 x #s(literal 1 binary32))))
(fma.f32 x (+.f32 x #s(literal -1 binary32)) (+.f32 x #s(literal -1 binary32)))
(fma.f32 x (/.f32 (.f32 x (.f32 x x)) (fma.f32 x x #s(literal 1 binary32))) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal 1 binary32)))))
(fma.f32 (*.f32 x x) #s(literal 1 binary32) #s(literal -1 binary32))
(fma.f32 (.f32 x x) (/.f32 (.f32 x x) (fma.f32 x x #s(literal 1 binary32))) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal 1 binary32)))))
(fma.f32 (.f32 x x) (/.f32 (.f32 x (.f32 x (.f32 x x))) (fma.f32 x x (fma.f32 x (.f32 x (.f32 x x)) #s(literal 1 binary32)))) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x (fma.f32 x (.f32 x (.f32 x x)) #s(literal 1 binary32))))))
(fma.f32 #s(literal 1 binary32) (*.f32 x x) #s(literal -1 binary32))
(fma.f32 #s(literal 1 binary32) (+.f32 x #s(literal -1 binary32)) (*.f32 x (+.f32 x #s(literal -1 binary32))))
(fma.f32 (fma.f32 x x #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (+.f32 x #s(literal 1 binary32))) (*.f32 x (+.f32 x #s(literal -1 binary32))))
(fma.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (/.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (+.f32 x #s(literal 1 binary32))) (*.f32 x (+.f32 x #s(literal -1 binary32))))
(fma.f32 (.f32 x (.f32 x x)) (/.f32 x (fma.f32 x x #s(literal 1 binary32))) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal 1 binary32)))))
(fma.f32 (.f32 x (.f32 x x)) (/.f32 (.f32 x (.f32 x x)) (fma.f32 x x (fma.f32 x (.f32 x (.f32 x x)) #s(literal 1 binary32)))) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x (fma.f32 x (.f32 x (.f32 x x)) #s(literal 1 binary32))))))
(fma.f32 (.f32 (.f32 x x) (.f32 x (.f32 x (.f32 x x)))) (/.f32 #s(literal 1 binary32) (fma.f32 x x (fma.f32 x (.f32 x (.f32 x x)) #s(literal 1 binary32)))) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x (fma.f32 x (.f32 x (*.f32 x x)) #s(literal 1 binary32))))))
(fma.f32 (fma.f32 (.f32 x (.f32 x x)) (.f32 x (.f32 x x)) #s(literal -1 binary32)) (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x (fma.f32 x (.f32 x (.f32 x x)) #s(literal 1 binary32)))) (+.f32 x #s(literal 1 binary32))) (*.f32 x (+.f32 x #s(literal -1 binary32))))
(fma.f32 (.f32 x (.f32 x (*.f32 x x))) (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal 1 binary32))) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal 1 binary32)))))
(fma.f32 (.f32 x (.f32 x (.f32 x x))) (/.f32 (.f32 x x) (fma.f32 x x (fma.f32 x (.f32 x (.f32 x x)) #s(literal 1 binary32)))) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x (fma.f32 x (.f32 x (.f32 x x)) #s(literal 1 binary32))))))
(fma.f32 (fma.f32 (.f32 x x) (.f32 x x) #s(literal -1 binary32)) (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal 1 binary32))) (+.f32 x #s(literal 1 binary32))) (*.f32 x (+.f32 x #s(literal -1 binary32))))
(fma.f32 (+.f32 x #s(literal 1 binary32)) x (*.f32 (+.f32 x #s(literal 1 binary32)) #s(literal -1 binary32)))
(fma.f32 (+.f32 x #s(literal 1 binary32)) (/.f32 (+.f32 x #s(literal -1 binary32)) (+.f32 x #s(literal 1 binary32))) (*.f32 x (+.f32 x #s(literal -1 binary32))))
(fma.f32 (+.f32 x #s(literal -1 binary32)) x (*.f32 (+.f32 x #s(literal -1 binary32)) #s(literal 1 binary32)))
(fma.f32 (+.f32 x #s(literal -1 binary32)) #s(literal 1 binary32) (*.f32 (+.f32 x #s(literal -1 binary32)) x))
(fma.f32 (+.f32 x #s(literal -1 binary32)) (/.f32 (+.f32 x #s(literal 1 binary32)) (+.f32 x #s(literal 1 binary32))) (*.f32 x (+.f32 x #s(literal -1 binary32))))
(fma.f32 (sqrt.f32 (+.f32 x #s(literal -1 binary32))) (sqrt.f32 (+.f32 x #s(literal -1 binary32))) (*.f32 x (+.f32 x #s(literal -1 binary32))))
(fma.f32 (fma.f32 x (.f32 x x) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 x x #s(literal 1 binary32)) x)) (.f32 x (+.f32 x #s(literal -1 binary32))))
(fma.f32 (/.f32 x (fma.f32 x x #s(literal 1 binary32))) (/.f32 (.f32 x (.f32 x x)) #s(literal 1 binary32)) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal 1 binary32)))))
(fma.f32 (/.f32 (.f32 x x) (fma.f32 x x #s(literal 1 binary32))) (/.f32 (.f32 x x) #s(literal 1 binary32)) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal 1 binary32)))))
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(/.f32 (.f32 (fma.f32 x x (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x (-.f32 #s(literal 1 binary32) (.f32 x x)))) (*.f32 (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (fma.f32 x x (fma.f32 x x #s(literal -1 binary32)))))
(/.f32 (-.f32 (.f32 (.f32 x x) (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))) (.f32 (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (fma.f32 x x #s(literal -1 binary32)))) (.f32 (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))))
(/.f32 (.f32 (fma.f32 (.f32 x (.f32 x x)) (.f32 (.f32 x x) (.f32 x (.f32 x (.f32 x x)))) (.f32 (.f32 (fma.f32 x x #s(literal -1 binary32)) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (.f32 (fma.f32 x x #s(literal -1 binary32)) (.f32 (fma.f32 x x #s(literal -1 binary32)) (fma.f32 x x #s(literal -1 binary32)))))) #s(literal 1 binary32)) (.f32 (fma.f32 (.f32 (fma.f32 x x #s(literal -1 binary32)) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (-.f32 (.f32 (fma.f32 x x #s(literal -1 binary32)) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (.f32 x (.f32 x x))) (.f32 (.f32 x x) (.f32 x (.f32 x (.f32 x x))))) (fma.f32 x (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (fma.f32 x x #s(literal -1 binary32)))))
(/.f32 (.f32 (-.f32 (.f32 (.f32 x x) (.f32 x (.f32 x (.f32 x x)))) (.f32 (fma.f32 x x #s(literal -1 binary32)) (.f32 (fma.f32 x x #s(literal -1 binary32)) (fma.f32 x x #s(literal -1 binary32))))) #s(literal 1 binary32)) (.f32 (-.f32 (.f32 x (.f32 x x)) (.f32 (fma.f32 x x #s(literal -1 binary32)) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))) (fma.f32 x (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (fma.f32 x x #s(literal -1 binary32)))))
(/.f32 (.f32 (-.f32 (.f32 (.f32 x x) (.f32 x (.f32 x (.f32 x x)))) (.f32 (fma.f32 x x #s(literal -1 binary32)) (.f32 (fma.f32 x x #s(literal -1 binary32)) (fma.f32 x x #s(literal -1 binary32))))) #s(literal 1 binary32)) (.f32 (fma.f32 x (.f32 x (.f32 x x)) (.f32 (fma.f32 x x #s(literal -1 binary32)) (fma.f32 x x (fma.f32 x x #s(literal -1 binary32))))) (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))))
(/.f32 (.f32 (.f32 (fma.f32 x x (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x (-.f32 #s(literal 1 binary32) (.f32 x x)))) #s(literal 1 binary32)) (.f32 (fma.f32 x x (fma.f32 x x #s(literal -1 binary32))) (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))))
(/.f32 (neg.f32 (neg.f32 (fma.f32 x (.f32 x x) (.f32 (fma.f32 x x #s(literal -1 binary32)) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))))) (neg.f32 (neg.f32 (fma.f32 x (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (fma.f32 x x #s(literal -1 binary32))))))
(/.f32 (neg.f32 (neg.f32 (fma.f32 x x (-.f32 #s(literal 1 binary32) (*.f32 x x))))) (neg.f32 (neg.f32 (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))))
(/.f32 (neg.f32 (fma.f32 x x (-.f32 #s(literal -1 binary32) (*.f32 x x)))) (neg.f32 (-.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)))
(/.f32 (-.f32 (.f32 (.f32 (/.f32 (.f32 x x) (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))) (/.f32 (.f32 x x) (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))) (/.f32 (.f32 x x) (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))) (.f32 (.f32 (/.f32 (fma.f32 x x #s(literal -1 binary32)) (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))) (/.f32 (fma.f32 x x #s(literal -1 binary32)) (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))) (/.f32 (fma.f32 x x #s(literal -1 binary32)) (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))))) (fma.f32 (/.f32 (.f32 x x) (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))) (/.f32 (.f32 x x) (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))) (fma.f32 (/.f32 (fma.f32 x x #s(literal -1 binary32)) (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))) (/.f32 (fma.f32 x x #s(literal -1 binary32)) (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))) (.f32 (/.f32 (*.f32 x x) (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))) (/.f32 (fma.f32 x x #s(literal -1 binary32)) (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))))))
(/.f32 (-.f32 (.f32 (/.f32 (.f32 x x) (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))) (/.f32 (.f32 x x) (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))) (.f32 (/.f32 (fma.f32 x x #s(literal -1 binary32)) (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))) (/.f32 (fma.f32 x x #s(literal -1 binary32)) (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))))) (fma.f32 x (/.f32 x (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))) (/.f32 (fma.f32 x x #s(literal -1 binary32)) (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))))
(/.f32 (.f32 (fma.f32 x (.f32 x x) (*.f32 (fma.f32 x x #s(literal -1 binary32)) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))) #s(literal 1 binary32)) (fma.f32 x (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (fma.f32 x x #s(literal -1 binary32))))
(/.f32 (.f32 (fma.f32 (.f32 x (.f32 x x)) (.f32 (.f32 x x) (.f32 x (.f32 x (.f32 x x)))) (.f32 (.f32 (fma.f32 x x #s(literal -1 binary32)) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (.f32 (fma.f32 x x #s(literal -1 binary32)) (.f32 (fma.f32 x x #s(literal -1 binary32)) (fma.f32 x x #s(literal -1 binary32)))))) (/.f32 #s(literal 1 binary32) (fma.f32 x (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (fma.f32 x x #s(literal -1 binary32))))) (fma.f32 (.f32 (fma.f32 x x #s(literal -1 binary32)) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (-.f32 (.f32 (fma.f32 x x #s(literal -1 binary32)) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (.f32 x (.f32 x x))) (.f32 (.f32 x x) (.f32 x (.f32 x (*.f32 x x))))))
(/.f32 (.f32 (-.f32 (.f32 (.f32 x x) (.f32 x (.f32 x (.f32 x x)))) (.f32 (fma.f32 x x #s(literal -1 binary32)) (.f32 (fma.f32 x x #s(literal -1 binary32)) (fma.f32 x x #s(literal -1 binary32))))) (/.f32 #s(literal 1 binary32) (fma.f32 x (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (fma.f32 x x #s(literal -1 binary32))))) (-.f32 (.f32 x (.f32 x x)) (*.f32 (fma.f32 x x #s(literal -1 binary32)) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))))
(/.f32 (.f32 (-.f32 (.f32 (.f32 x x) (.f32 x (.f32 x (.f32 x x)))) (.f32 (fma.f32 x x #s(literal -1 binary32)) (.f32 (fma.f32 x x #s(literal -1 binary32)) (fma.f32 x x #s(literal -1 binary32))))) (/.f32 #s(literal 1 binary32) (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))) (fma.f32 x (.f32 x (.f32 x x)) (*.f32 (fma.f32 x x #s(literal -1 binary32)) (fma.f32 x x (fma.f32 x x #s(literal -1 binary32))))))
(/.f32 (.f32 (.f32 (fma.f32 x x (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x (-.f32 #s(literal 1 binary32) (*.f32 x x)))) (/.f32 #s(literal 1 binary32) (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))) (fma.f32 x x (fma.f32 x x #s(literal -1 binary32))))
(*.f32 #s(literal 1 binary32) (+.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))
(.f32 (+.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (.f32 (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (/.f32 #s(literal 1 binary32) (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))))
(*.f32 (+.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (/.f32 (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))))
(.f32 (fma.f32 x (.f32 x x) (*.f32 (fma.f32 x x #s(literal -1 binary32)) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))) (/.f32 #s(literal 1 binary32) (fma.f32 x (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (fma.f32 x x #s(literal -1 binary32)))))
(.f32 (fma.f32 x (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (fma.f32 x x #s(literal -1 binary32))) (.f32 (+.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (/.f32 #s(literal 1 binary32) (fma.f32 x (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (fma.f32 x x #s(literal -1 binary32))))))
(*.f32 (fma.f32 x (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (fma.f32 x x #s(literal -1 binary32))) (/.f32 (+.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (fma.f32 x (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (fma.f32 x x #s(literal -1 binary32)))))
(.f32 (fma.f32 x x (-.f32 #s(literal 1 binary32) (.f32 x x))) (/.f32 #s(literal 1 binary32) (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))))
(.f32 (neg.f32 (fma.f32 x (.f32 x x) (*.f32 (fma.f32 x x #s(literal -1 binary32)) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))) (/.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 x (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (fma.f32 x x #s(literal -1 binary32))))))
(.f32 (neg.f32 (fma.f32 x x (-.f32 #s(literal 1 binary32) (.f32 x x)))) (/.f32 #s(literal 1 binary32) (neg.f32 (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))))
(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (fma.f32 x x #s(literal -1 binary32)))) (fma.f32 x (.f32 x x) (*.f32 (fma.f32 x x #s(literal -1 binary32)) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))))
(.f32 (/.f32 #s(literal 1 binary32) (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))) (fma.f32 x x (-.f32 #s(literal 1 binary32) (.f32 x x))))
(.f32 (fma.f32 x x (-.f32 #s(literal -1 binary32) (.f32 x x))) (/.f32 #s(literal 1 binary32) (-.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)))
(.f32 (/.f32 (fma.f32 x x (-.f32 #s(literal 1 binary32) (.f32 x x))) (fma.f32 x x (-.f32 #s(literal 1 binary32) (*.f32 x x)))) (+.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))
(.f32 (/.f32 (fma.f32 x (.f32 x x) (.f32 (fma.f32 x x #s(literal -1 binary32)) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))) (fma.f32 x (.f32 x (.f32 x (.f32 x (.f32 x x)))) (.f32 (+.f32 #s(literal -1 binary32) (.f32 x (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))) (.f32 (fma.f32 x x #s(literal -1 binary32)) (.f32 (-.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x) (-.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)))))) (fma.f32 (+.f32 #s(literal -1 binary32) (.f32 x (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))) (-.f32 (+.f32 #s(literal -1 binary32) (.f32 x (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))) (.f32 x x)) (.f32 x (.f32 x (*.f32 x x)))))
(.f32 (/.f32 (fma.f32 x (.f32 x x) (.f32 (fma.f32 x x #s(literal -1 binary32)) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))) (.f32 (fma.f32 x (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (fma.f32 x x #s(literal -1 binary32))) (-.f32 (.f32 x x) (+.f32 #s(literal -1 binary32) (.f32 x (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))))))) (-.f32 (.f32 x x) (+.f32 #s(literal -1 binary32) (.f32 x (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))))))
(.f32 (/.f32 (fma.f32 x x (-.f32 #s(literal 1 binary32) (.f32 x x))) (-.f32 (.f32 x (.f32 x x)) (*.f32 (fma.f32 x x #s(literal -1 binary32)) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))) (fma.f32 x x (fma.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)))))
(exp.f32 (*.f32 #s(literal 1/2 binary32) (log.f32 (fma.f32 x x #s(literal -1 binary32)))))
(exp.f32 (.f32 (.f32 #s(literal 1/2 binary32) (log.f32 (fma.f32 x x #s(literal -1 binary32)))) #s(literal 1 binary32)))
(exp.f32 (.f32 (.f32 #s(literal 2 binary32) (log.f32 (fma.f32 x x #s(literal -1 binary32)))) #s(literal 1/4 binary32)))
(exp.f32 (.f32 (.f32 (log.f32 (fma.f32 x x #s(literal -1 binary32))) #s(literal 1/4 binary32)) #s(literal 2 binary32)))
(exp.f32 (-.f32 (log.f32 (fma.f32 x x #s(literal -1 binary32))) (*.f32 #s(literal 1/2 binary32) (log.f32 (fma.f32 x x #s(literal -1 binary32))))))
(fabs.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))
(pow.f32 (fma.f32 x x #s(literal -1 binary32)) #s(literal 1/2 binary32))
(pow.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) #s(literal 1 binary32))
(pow.f32 (*.f32 (fma.f32 x x #s(literal -1 binary32)) (fma.f32 x x #s(literal -1 binary32))) #s(literal 1/4 binary32))
(pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal -1 binary32))) #s(literal -1/2 binary32))
(pow.f32 (sqrt.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) #s(literal 2 binary32))
(pow.f32 (.f32 (.f32 (fma.f32 x x #s(literal -1 binary32)) (fma.f32 x x #s(literal -1 binary32))) (*.f32 (fma.f32 x x #s(literal -1 binary32)) (fma.f32 x x #s(literal -1 binary32)))) #s(literal 1/8 binary32))
(pow.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal -1 binary32)))) #s(literal -1 binary32))
(pow.f32 (/.f32 (sqrt.f32 (fma.f32 x x (fma.f32 x (.f32 x (.f32 x x)) #s(literal 1 binary32)))) (sqrt.f32 (fma.f32 (.f32 x (.f32 x x)) (.f32 x (.f32 x x)) #s(literal -1 binary32)))) #s(literal -1 binary32))
(pow.f32 (/.f32 (sqrt.f32 (fma.f32 x x #s(literal 1 binary32))) (sqrt.f32 (fma.f32 (.f32 x x) (.f32 x x) #s(literal -1 binary32)))) #s(literal -1 binary32))
(pow.f32 (exp.f32 #s(literal 1/2 binary32)) (log.f32 (fma.f32 x x #s(literal -1 binary32))))
(/.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal -1 binary32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 x x (fma.f32 x (.f32 x (.f32 x x)) #s(literal 1 binary32)))) (sqrt.f32 (fma.f32 (.f32 x (.f32 x x)) (.f32 x (.f32 x x)) #s(literal -1 binary32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 x x #s(literal 1 binary32))) (sqrt.f32 (fma.f32 (.f32 x x) (.f32 x x) #s(literal -1 binary32)))))
(/.f32 (fma.f32 x x #s(literal -1 binary32)) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))
(/.f32 (sqrt.f32 (fma.f32 (.f32 x (.f32 x x)) (.f32 x (.f32 x x)) #s(literal -1 binary32))) (sqrt.f32 (fma.f32 x x (fma.f32 x (.f32 x (.f32 x x)) #s(literal 1 binary32)))))
(/.f32 (sqrt.f32 (fma.f32 (.f32 x (.f32 x x)) (.f32 x (.f32 x x)) #s(literal -1 binary32))) (sqrt.f32 (fma.f32 x (.f32 x (.f32 x x)) (-.f32 #s(literal 1 binary32) (.f32 x (.f32 x #s(literal -1 binary32)))))))
(/.f32 (sqrt.f32 (fma.f32 (.f32 x x) (.f32 x x) #s(literal -1 binary32))) (sqrt.f32 (fma.f32 x x #s(literal 1 binary32))))
(/.f32 (sqrt.f32 (neg.f32 (fma.f32 (.f32 x (.f32 x x)) (.f32 x (.f32 x x)) #s(literal -1 binary32)))) (sqrt.f32 (neg.f32 (fma.f32 x x (fma.f32 x (.f32 x (.f32 x x)) #s(literal 1 binary32))))))
(/.f32 (sqrt.f32 (neg.f32 (fma.f32 (.f32 x x) (.f32 x x) #s(literal -1 binary32)))) (sqrt.f32 (neg.f32 (fma.f32 x x #s(literal 1 binary32)))))
(/.f32 (neg.f32 (sqrt.f32 (fma.f32 (.f32 x (.f32 x x)) (.f32 x (.f32 x x)) #s(literal -1 binary32)))) (neg.f32 (sqrt.f32 (fma.f32 x x (fma.f32 x (.f32 x (.f32 x x)) #s(literal 1 binary32))))))
(/.f32 (neg.f32 (sqrt.f32 (fma.f32 (.f32 x x) (.f32 x x) #s(literal -1 binary32)))) (neg.f32 (sqrt.f32 (fma.f32 x x #s(literal 1 binary32)))))
(/.f32 (exp.f32 (.f32 #s(literal 1/2 binary32) (log.f32 (fma.f32 (.f32 x (.f32 x x)) (.f32 x (.f32 x x)) #s(literal -1 binary32))))) (exp.f32 (.f32 #s(literal 1/2 binary32) (log1p.f32 (fma.f32 x x (.f32 x (.f32 x (*.f32 x x))))))))
(/.f32 (exp.f32 (.f32 #s(literal 1/2 binary32) (log.f32 (fma.f32 (.f32 x x) (.f32 x x) #s(literal -1 binary32))))) (exp.f32 (.f32 #s(literal 1/2 binary32) (log1p.f32 (*.f32 x x)))))
(sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))
(*.f32 (sqrt.f32 (+.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 x #s(literal -1 binary32))))
(*.f32 (sqrt.f32 (+.f32 x #s(literal -1 binary32))) (sqrt.f32 (+.f32 x #s(literal 1 binary32))))
(.f32 (sqrt.f32 (fma.f32 (.f32 x (.f32 x x)) (.f32 x (.f32 x x)) #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (fma.f32 x x (fma.f32 x (.f32 x (*.f32 x x)) #s(literal 1 binary32))))))
(.f32 (sqrt.f32 (fma.f32 (.f32 x x) (*.f32 x x) #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (fma.f32 x x #s(literal 1 binary32)))))
(*.f32 (sqrt.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (sqrt.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))

simplify371.0ms (5.3%)

Memory

35.6MiB live, 637.0MiB 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	559
1	411	533
2	1143	526
3	3327	488
4	7966	488
0	8526	459

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

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))))))

Outputs
-1
#s(literal -1 binary32)
(- (pow x 2) 1)
(fma.f32 x x #s(literal -1 binary32))
(- (pow x 2) 1)
(fma.f32 x x #s(literal -1 binary32))
(- (pow x 2) 1)
(fma.f32 x x #s(literal -1 binary32))
(pow x 2)
(*.f32 x x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f32 x x #s(literal -1 binary32))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f32 x x #s(literal -1 binary32))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f32 x x #s(literal -1 binary32))
(pow x 2)
(*.f32 x x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f32 x x #s(literal -1 binary32))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f32 x x #s(literal -1 binary32))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f32 x x #s(literal -1 binary32))
(log (sqrt -1))
(log.f32 (sqrt.f32 #s(literal -1 binary32)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f32 (log.f32 (sqrt.f32 #s(literal -1 binary32))) (/.f32 x (sqrt.f32 #s(literal -1 binary32))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (fma.f32 x (*.f32 x #s(literal 1/6 binary32)) #s(literal 1 binary32)) (log.f32 (sqrt.f32 #s(literal -1 binary32))))
(+ (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.f32 x (fma.f32 x (.f32 x (/.f32 (.f32 (.f32 x x) #s(literal 3/40 binary32)) (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 5 binary32)))) (.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 #s(literal -1 binary32))) (fma.f32 x (*.f32 x #s(literal -1/6 binary32)) #s(literal -1 binary32)))) (log.f32 (sqrt.f32 #s(literal -1 binary32))))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+.f32 (log.f32 #s(literal 2 binary32)) (+.f32 (log.f32 x) (/.f32 #s(literal -1/4 binary32) (*.f32 x x))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(+.f32 (log.f32 #s(literal 2 binary32)) (+.f32 (log.f32 x) (/.f32 (+.f32 #s(literal -1/4 binary32) (/.f32 #s(literal -3/32 binary32) (.f32 x x))) (.f32 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))))
(+.f32 (log.f32 #s(literal 2 binary32)) (+.f32 (log.f32 x) (+.f32 (/.f32 (+.f32 #s(literal -3/32 binary32) (/.f32 #s(literal -5/96 binary32) (.f32 x x))) (.f32 x (.f32 x (.f32 x x)))) (/.f32 #s(literal -1/4 binary32) (*.f32 x x)))))
(+ (log -1/2) (log (/ -1 x)))
(+.f32 (log.f32 #s(literal -1/2 binary32)) (neg.f32 (log.f32 (neg.f32 x))))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+.f32 (/.f32 #s(literal 1/4 binary32) (*.f32 x x)) (+.f32 (log.f32 #s(literal -1/2 binary32)) (neg.f32 (log.f32 (neg.f32 x)))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+.f32 (+.f32 (neg.f32 (log.f32 (neg.f32 x))) (/.f32 #s(literal 3/32 binary32) (.f32 x (.f32 x (.f32 x x))))) (+.f32 (/.f32 #s(literal 1/4 binary32) (.f32 x x)) (log.f32 #s(literal -1/2 binary32))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(+.f32 (+.f32 (log.f32 #s(literal -1/2 binary32)) (neg.f32 (log.f32 (neg.f32 x)))) (+.f32 (/.f32 #s(literal 3/32 binary32) (.f32 x (.f32 x (.f32 x x)))) (+.f32 (/.f32 #s(literal 1/4 binary32) (.f32 x x)) (/.f32 #s(literal 5/96 binary32) (pow.f32 x #s(literal 6 binary32))))))
(sqrt -1)
(sqrt.f32 #s(literal -1 binary32))
(+ x (sqrt -1))
(+.f32 x (sqrt.f32 #s(literal -1 binary32)))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(fma.f32 x (fma.f32 x (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32))) #s(literal 1 binary32)) (sqrt.f32 #s(literal -1 binary32)))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(fma.f32 x (fma.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (fma.f32 x (*.f32 x #s(literal 1/8 binary32)) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (sqrt.f32 #s(literal -1 binary32)))
(* 2 x)
(*.f32 x #s(literal 2 binary32))
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(fma.f32 x #s(literal 2 binary32) (/.f32 #s(literal -1/2 binary32) x))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(fma.f32 x #s(literal 2 binary32) (/.f32 (+.f32 #s(literal -1/2 binary32) (/.f32 #s(literal -1/8 binary32) (*.f32 x x))) x))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(fma.f32 x (+.f32 #s(literal 2 binary32) (/.f32 (+.f32 #s(literal -1/8 binary32) (/.f32 #s(literal -1/16 binary32) (.f32 x x))) (.f32 x (.f32 x (.f32 x x))))) (/.f32 #s(literal -1/2 binary32) x))
(/ 1/2 x)
(/.f32 #s(literal 1/2 binary32) x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(/.f32 (-.f32 #s(literal 1/2 binary32) (/.f32 #s(literal -1/8 binary32) (*.f32 x x))) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(/.f32 (+.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 #s(literal 1/8 binary32) (/.f32 #s(literal 1/16 binary32) (.f32 x x))) (.f32 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))
(/.f32 (-.f32 (/.f32 #s(literal 1/8 binary32) (.f32 x x)) (+.f32 #s(literal -1/2 binary32) (/.f32 (+.f32 #s(literal -1/16 binary32) (/.f32 #s(literal -5/128 binary32) (.f32 x x))) (.f32 x (.f32 x (*.f32 x x)))))) x)
(sqrt -1)
(sqrt.f32 #s(literal -1 binary32))
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(fma.f32 x (*.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) #s(literal 1/2 binary32)) (sqrt.f32 #s(literal -1 binary32)))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f32 x (.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (fma.f32 x (.f32 x #s(literal 1/8 binary32)) #s(literal 1/2 binary32))) (sqrt.f32 #s(literal -1 binary32)))
(+ (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.f32 x (fma.f32 x (/.f32 (.f32 (.f32 (.f32 x x) #s(literal 1/16 binary32)) (.f32 x x)) (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 5 binary32))) (.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (fma.f32 x (.f32 x #s(literal 1/8 binary32)) #s(literal 1/2 binary32)))) (sqrt.f32 #s(literal -1 binary32)))
x
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(+.f32 x (/.f32 #s(literal -1/2 binary32) x))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(-.f32 x (/.f32 (-.f32 #s(literal 1/2 binary32) (/.f32 #s(literal -1/8 binary32) (*.f32 x x))) x))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(+.f32 (/.f32 #s(literal -1/2 binary32) x) (fma.f32 x (/.f32 (+.f32 #s(literal -1/8 binary32) (/.f32 #s(literal -1/16 binary32) (.f32 x x))) (.f32 x (.f32 x (.f32 x x)))) x))
(* -1 x)
(neg.f32 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))
(-.f32 (/.f32 #s(literal 1/2 binary32) x) x)
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))
(-.f32 (/.f32 (-.f32 #s(literal 1/2 binary32) (/.f32 #s(literal -1/8 binary32) (*.f32 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.f32 x (/.f32 (+.f32 #s(literal 1/8 binary32) (/.f32 #s(literal 1/16 binary32) (.f32 x x))) (.f32 x (.f32 x (.f32 x x)))) (-.f32 (/.f32 #s(literal 1/2 binary32) x) x))

eval87.0ms (1.2%)

Memory: -20.9MiB live, 96.3MiB allocated
Compiler: Compiled 10 598 to 1 538 computations (85.5% saved)

prune54.0ms (0.8%)

Memory

4.9MiB live, 162.6MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	363	5	368
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	364	5	369

Accuracy

100.0%

Counts

369 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	96.9%	(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))
▶	97.9%	(log.f32 (fma.f32 x #s(literal 2 binary32) (/.f32 #s(literal -1/2 binary32) x)))
▶	46.6%	(log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))
▶	46.6%	(log.f32 (+.f32 x (sqrt.f32 (+.f32 (+.f32 x #s(literal -1 binary32)) (*.f32 x (+.f32 x #s(literal -1 binary32)))))))
▶	96.8%	(log.f32 (+.f32 x x))

Compiler

Compiled 84 to 56 computations (33.3% saved)

simplify486.0ms (6.9%)

Memory

-10.3MiB live, 706.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(log.f32 x)
✓	cost-diff	0	(log.f32 #s(literal 2 binary32))
✓	cost-diff	0	(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))
✓	cost-diff	0	(sqrt.f32 (+.f32 (+.f32 x #s(literal -1 binary32)) (*.f32 x (+.f32 x #s(literal -1 binary32)))))
✓	cost-diff	0	(+.f32 x (sqrt.f32 (+.f32 (+.f32 x #s(literal -1 binary32)) (*.f32 x (+.f32 x #s(literal -1 binary32))))))
✓	cost-diff	0	(log.f32 (+.f32 x (sqrt.f32 (+.f32 (+.f32 x #s(literal -1 binary32)) (*.f32 x (+.f32 x #s(literal -1 binary32)))))))
✓	cost-diff	256	(+.f32 (+.f32 x #s(literal -1 binary32)) (*.f32 x (+.f32 x #s(literal -1 binary32))))
✓	cost-diff	0	(fma.f32 x x #s(literal -1 binary32))
✓	cost-diff	0	(sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))
✓	cost-diff	0	(+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)
✓	cost-diff	0	(log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))
✓	cost-diff	0	(+.f32 x x)
✓	cost-diff	0	(log.f32 (+.f32 x x))
✓	cost-diff	0	(/.f32 #s(literal -1/2 binary32) x)
✓	cost-diff	0	(fma.f32 x #s(literal 2 binary32) (/.f32 #s(literal -1/2 binary32) x))
✓	cost-diff	0	(log.f32 (fma.f32 x #s(literal 2 binary32) (/.f32 #s(literal -1/2 binary32) x)))

Rules

24 096×	`accelerator-lowering-fma.f32`
24 096×	`accelerator-lowering-fma.f64`
3 892×	`-lowering-.f32`
3 892×	`-lowering-.f64`
2 344×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	108
1	45	108
2	81	108
3	158	108
4	487	108
5	1587	108
6	2814	108
7	4868	108
8	6419	108
9	7275	108
10	7607	108
11	7658	108
12	7698	108
0	8188	98

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

Outputs
(log (+ (* x 2) (/ -1/2 x)))
(log.f32 (+.f32 x (+.f32 x (/.f32 #s(literal -1/2 binary32) x))))
(+ (* x 2) (/ -1/2 x))
(+.f32 x (+.f32 x (/.f32 #s(literal -1/2 binary32) x)))
x
2
#s(literal 2 binary32)
(/ -1/2 x)
(/.f32 #s(literal -1/2 binary32) x)
-1/2
#s(literal -1/2 binary32)
(log (+ x x))
(log.f32 (+.f32 x x))
(+ x x)
(+.f32 x x)
x
(log (+ (sqrt (+ (* x x) -1)) x))
(log.f32 (+.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))
(+ (sqrt (+ (* x x) -1)) x)
(+.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))
(sqrt (+ (* x x) -1))
(sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))
(+ (* x x) -1)
(fma.f32 x x #s(literal -1 binary32))
x
-1
#s(literal -1 binary32)
(log (+ x (sqrt (+ (+ x -1) (* x (+ x -1))))))
(log.f32 (+.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))
(+ x (sqrt (+ (+ x -1) (* x (+ x -1)))))
(+.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))
x
(sqrt (+ (+ x -1) (* x (+ x -1))))
(sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))
(+ (+ x -1) (* x (+ x -1)))
(fma.f32 x x #s(literal -1 binary32))
(+ x -1)
(+.f32 x #s(literal -1 binary32))
-1
#s(literal -1 binary32)
(* x (+ x -1))
(fma.f32 x x (neg.f32 x))
(+ (log 2) (log x))
(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))
(log 2)
(log.f32 #s(literal 2 binary32))
2
#s(literal 2 binary32)
(log x)
(log.f32 x)
x

localize113.0ms (1.6%)

Memory

11.4MiB live, 103.7MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(log.f32 x)
✓	accuracy	100.0%	(log.f32 #s(literal 2 binary32))
✓	accuracy	99.0%	(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))
✓	accuracy	99.9%	(+.f32 x (sqrt.f32 (+.f32 (+.f32 x #s(literal -1 binary32)) (*.f32 x (+.f32 x #s(literal -1 binary32))))))
✓	accuracy	99.8%	(+.f32 (+.f32 x #s(literal -1 binary32)) (*.f32 x (+.f32 x #s(literal -1 binary32))))
✓	accuracy	98.9%	(log.f32 (+.f32 x (sqrt.f32 (+.f32 (+.f32 x #s(literal -1 binary32)) (*.f32 x (+.f32 x #s(literal -1 binary32)))))))
✓	accuracy	50.6%	(sqrt.f32 (+.f32 (+.f32 x #s(literal -1 binary32)) (*.f32 x (+.f32 x #s(literal -1 binary32)))))
✓	accuracy	100.0%	(fma.f32 x x #s(literal -1 binary32))
✓	accuracy	99.9%	(+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)
✓	accuracy	98.9%	(log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))
✓	accuracy	50.6%	(sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))
✓	accuracy	100.0%	(+.f32 x x)
✓	accuracy	98.9%	(log.f32 (+.f32 x x))
✓	accuracy	100.0%	(fma.f32 x #s(literal 2 binary32) (/.f32 #s(literal -1/2 binary32) x))
✓	accuracy	100.0%	(/.f32 #s(literal -1/2 binary32) x)
✓	accuracy	98.9%	(log.f32 (fma.f32 x #s(literal 2 binary32) (/.f32 #s(literal -1/2 binary32) x)))

Samples

85.0ms

256×

valid

Compiler

Compiled 120 to 26 computations (78.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 74.0ms

ival-div: 45.0ms (60.6% of total)

ival-log: 13.0ms (17.5% of total)

ival-add: 8.0ms (10.8% of total)

ival-mult: 4.0ms (5.4% of total)

ival-sqrt: 3.0ms (4% of total)

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

exact: 0.0ms (0% of total)

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

series118.0ms (1.7%)

Memory

-12.3MiB live, 214.4MiB allocated

Counts

16 → 180

Calls

Call 1

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

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

Calls

45 calls:

Time	Variable		Point	Expression
28.0ms	x	@	-inf	(+ (log 2) (log x))
28.0ms	x	@	0	(log (+ x x))
23.0ms	x	@	0	(+ (log 2) (log x))
19.0ms	x	@	-inf	(log (+ x x))
6.0ms	x	@	inf	(log (+ x x))

rewrite108.0ms (1.5%)

Memory

5.5MiB live, 199.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

1 172×	`accelerator-lowering-fma.f32`
1 172×	`accelerator-lowering-fma.f64`
606×	`-lowering-.f32`
606×	`-lowering-.f64`
550×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	101
1	140	81
0	1490	73

Stop Event

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

Counts

16 → 430

Calls

Call 1

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

Outputs
(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))
(+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))
(-.f32 (log.f32 (+.f32 (+.f32 x x) (/.f32 #s(literal -1/8 binary32) (.f32 x (.f32 x x))))) (log.f32 (fma.f32 (/.f32 #s(literal -1/2 binary32) x) (-.f32 (/.f32 #s(literal -1/2 binary32) x) (+.f32 x x)) (+.f32 x x))))
(-.f32 (log.f32 (-.f32 (+.f32 x x) (/.f32 #s(literal 1/4 binary32) (*.f32 x x)))) (log.f32 (+.f32 x (-.f32 x (/.f32 #s(literal -1/2 binary32) x)))))
(-.f32 (log.f32 (*.f32 (fma.f32 x x #s(literal 0 binary32)) (+.f32 x x))) (log.f32 (fma.f32 x x #s(literal 0 binary32))))
(-.f32 (log.f32 #s(literal 0 binary32)) (log.f32 #s(literal 0 binary32)))
(-.f32 (/.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32)) (log.f32 (/.f32 #s(literal 2 binary32) x))) (/.f32 (pow.f32 (log.f32 x) #s(literal 2 binary32)) (log.f32 (/.f32 #s(literal 2 binary32) x))))
(/.f32 (+.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 3 binary32)) (pow.f32 (log.f32 x) #s(literal 3 binary32))) (fma.f32 (log.f32 x) (-.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32))))
(/.f32 (+.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 3 binary32)) (pow.f32 (log.f32 x) #s(literal 3 binary32))) (+.f32 (pow.f32 (log.f32 x) #s(literal 2 binary32)) (-.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32)) (*.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x)))))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (log.f32 x) (-.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32))) (+.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 3 binary32)) (pow.f32 (log.f32 x) #s(literal 3 binary32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (log.f32 (/.f32 #s(literal 2 binary32) x)) (*.f32 (log.f32 (+.f32 x x)) (log.f32 (/.f32 #s(literal 2 binary32) x)))))
(/.f32 (*.f32 (log.f32 (+.f32 x x)) (log.f32 (/.f32 #s(literal 2 binary32) x))) (log.f32 (/.f32 #s(literal 2 binary32) x)))
(/.f32 (neg.f32 (+.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 3 binary32)) (pow.f32 (log.f32 x) #s(literal 3 binary32)))) (neg.f32 (fma.f32 (log.f32 x) (-.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32)))))
(/.f32 (neg.f32 (*.f32 (log.f32 (+.f32 x x)) (log.f32 (/.f32 #s(literal 2 binary32) x)))) (neg.f32 (log.f32 (/.f32 #s(literal 2 binary32) x))))
(/.f32 (-.f32 (pow.f32 (log.f32 x) #s(literal 2 binary32)) (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32))) (-.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))))
(*.f32 (+.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 3 binary32)) (pow.f32 (log.f32 x) #s(literal 3 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 (log.f32 x) (-.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32)))))
(.f32 (.f32 (log.f32 (+.f32 x x)) (log.f32 (/.f32 #s(literal 2 binary32) x))) (/.f32 #s(literal 1 binary32) (log.f32 (/.f32 #s(literal 2 binary32) x))))
(log.f32 (+.f32 x x))
(exp.f32 (*.f32 (log.f32 (+.f32 x x)) #s(literal 3 binary32)))
(+.f32 x x)
(+.f32 x (+.f32 x (/.f32 #s(literal -1/2 binary32) x)))
(+.f32 (+.f32 x x) (/.f32 #s(literal -1/2 binary32) x))
(+.f32 (/.f32 #s(literal -1/2 binary32) x) (+.f32 x x))
(+.f32 (.f32 (+.f32 x x) x) (.f32 (+.f32 x x) x))
(+.f32 (.f32 x (+.f32 x x)) (.f32 x (+.f32 x x)))
(+.f32 (+.f32 (/.f32 #s(literal -1/2 binary32) x) x) x)
(pow.f32 (+.f32 x x) #s(literal 2 binary32))
(pow.f32 (+.f32 x x) #s(literal 3 binary32))
(fma.f32 x #s(literal 2 binary32) (/.f32 #s(literal -1/2 binary32) x))
(fma.f32 x (+.f32 x x) (*.f32 x (+.f32 x x)))
(fma.f32 x (*.f32 #s(literal 2 binary32) (+.f32 x x)) (/.f32 #s(literal -1/2 binary32) x))
(fma.f32 #s(literal 2 binary32) x (/.f32 #s(literal -1/2 binary32) x))
(fma.f32 #s(literal 2 binary32) (*.f32 x (+.f32 x x)) (/.f32 #s(literal -1/2 binary32) x))
(fma.f32 (+.f32 x x) x (*.f32 (+.f32 x x) x))
(fma.f32 (+.f32 x x) (+.f32 x x) (/.f32 #s(literal -1/2 binary32) x))
(fma.f32 #s(literal -1/2 binary32) (/.f32 #s(literal 1 binary32) x) (+.f32 x x))
(fma.f32 (*.f32 x x) #s(literal 4 binary32) (/.f32 #s(literal -1/2 binary32) x))
(fma.f32 #s(literal 1/2 binary32) (/.f32 #s(literal 1 binary32) (neg.f32 x)) (+.f32 x x))
(fma.f32 (.f32 x (.f32 x x)) #s(literal 8 binary32) (/.f32 #s(literal -1/2 binary32) x))
(fma.f32 (*.f32 (fma.f32 x x #s(literal 0 binary32)) (+.f32 x x)) (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal 0 binary32))) (/.f32 #s(literal -1/2 binary32) x))
(fma.f32 #s(literal 1 binary32) (/.f32 #s(literal -1/2 binary32) x) (+.f32 x x))
(fma.f32 (+.f32 (+.f32 x x) (/.f32 #s(literal -1/8 binary32) (.f32 x (.f32 x x)))) (/.f32 #s(literal 1 binary32) (fma.f32 (/.f32 #s(literal -1/2 binary32) x) (-.f32 (/.f32 #s(literal -1/2 binary32) x) (+.f32 x x)) (+.f32 x x))) (/.f32 #s(literal -1/2 binary32) x))
(fma.f32 (/.f32 #s(literal 1 binary32) x) #s(literal -1/2 binary32) (+.f32 x x))
(fma.f32 #s(literal 0 binary32) (/.f32 #s(literal 1 binary32) #s(literal 0 binary32)) (/.f32 #s(literal -1/2 binary32) x))
(fma.f32 (-.f32 (+.f32 x x) (/.f32 #s(literal 1/4 binary32) (*.f32 x x))) (/.f32 #s(literal 1 binary32) (+.f32 x (-.f32 x (/.f32 #s(literal -1/2 binary32) x)))) (/.f32 #s(literal -1/2 binary32) x))
(fma.f32 #s(literal 8 binary32) (.f32 x (.f32 x x)) (/.f32 #s(literal -1/2 binary32) x))
(fma.f32 #s(literal 4 binary32) (*.f32 x x) (/.f32 #s(literal -1/2 binary32) x))
(fma.f32 (pow.f32 (+.f32 x x) #s(literal 3/2 binary32)) (pow.f32 (+.f32 x x) #s(literal 3/2 binary32)) (/.f32 #s(literal -1/2 binary32) x))
(fma.f32 (*.f32 (+.f32 x x) x) #s(literal 2 binary32) (/.f32 #s(literal -1/2 binary32) x))
(fma.f32 (*.f32 (+.f32 x x) #s(literal 2 binary32)) x (/.f32 #s(literal -1/2 binary32) x))
(-.f32 (/.f32 (+.f32 x x) (+.f32 x (-.f32 x (/.f32 #s(literal -1/2 binary32) x)))) (/.f32 (/.f32 #s(literal 1/4 binary32) (*.f32 x x)) (+.f32 x (-.f32 x (/.f32 #s(literal -1/2 binary32) x)))))
(-.f32 (/.f32 (.f32 x x) #s(literal 0 binary32)) (/.f32 (.f32 x x) #s(literal 0 binary32)))
(/.f32 (*.f32 (fma.f32 x x #s(literal 0 binary32)) (+.f32 x x)) (fma.f32 x x #s(literal 0 binary32)))
(/.f32 #s(literal 1 binary32) (+.f32 x x))
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(*.f32 (sqrt.f32 (+.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 x #s(literal -1 binary32))))
(*.f32 (pow.f32 (fma.f32 x x #s(literal -1 binary32)) #s(literal 1/4 binary32)) (pow.f32 (fma.f32 x x #s(literal -1 binary32)) #s(literal 1/4 binary32)))
(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))
(+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))
(-.f32 (log.f32 (+.f32 (+.f32 x x) (/.f32 #s(literal -1/8 binary32) (.f32 x (.f32 x x))))) (log.f32 (fma.f32 (/.f32 #s(literal -1/2 binary32) x) (-.f32 (/.f32 #s(literal -1/2 binary32) x) (+.f32 x x)) (+.f32 x x))))
(-.f32 (log.f32 (-.f32 (+.f32 x x) (/.f32 #s(literal 1/4 binary32) (*.f32 x x)))) (log.f32 (+.f32 x (-.f32 x (/.f32 #s(literal -1/2 binary32) x)))))
(-.f32 (log.f32 (*.f32 (fma.f32 x x #s(literal 0 binary32)) (+.f32 x x))) (log.f32 (fma.f32 x x #s(literal 0 binary32))))
(-.f32 (log.f32 #s(literal 0 binary32)) (log.f32 #s(literal 0 binary32)))
(-.f32 (/.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32)) (log.f32 (/.f32 #s(literal 2 binary32) x))) (/.f32 (pow.f32 (log.f32 x) #s(literal 2 binary32)) (log.f32 (/.f32 #s(literal 2 binary32) x))))
(/.f32 (+.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 3 binary32)) (pow.f32 (log.f32 x) #s(literal 3 binary32))) (fma.f32 (log.f32 x) (-.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32))))
(/.f32 (+.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 3 binary32)) (pow.f32 (log.f32 x) #s(literal 3 binary32))) (+.f32 (pow.f32 (log.f32 x) #s(literal 2 binary32)) (-.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32)) (*.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x)))))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 (log.f32 x) (-.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32))) (+.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 3 binary32)) (pow.f32 (log.f32 x) #s(literal 3 binary32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (log.f32 (/.f32 #s(literal 2 binary32) x)) (*.f32 (log.f32 (+.f32 x x)) (log.f32 (/.f32 #s(literal 2 binary32) x)))))
(/.f32 (*.f32 (log.f32 (+.f32 x x)) (log.f32 (/.f32 #s(literal 2 binary32) x))) (log.f32 (/.f32 #s(literal 2 binary32) x)))
(/.f32 (neg.f32 (+.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 3 binary32)) (pow.f32 (log.f32 x) #s(literal 3 binary32)))) (neg.f32 (fma.f32 (log.f32 x) (-.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32)))))
(/.f32 (neg.f32 (*.f32 (log.f32 (+.f32 x x)) (log.f32 (/.f32 #s(literal 2 binary32) x)))) (neg.f32 (log.f32 (/.f32 #s(literal 2 binary32) x))))
(/.f32 (-.f32 (pow.f32 (log.f32 x) #s(literal 2 binary32)) (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32))) (-.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))))
(*.f32 (+.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 3 binary32)) (pow.f32 (log.f32 x) #s(literal 3 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 (log.f32 x) (-.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32)))))
(.f32 (.f32 (log.f32 (+.f32 x x)) (log.f32 (/.f32 #s(literal 2 binary32) x))) (/.f32 #s(literal 1 binary32) (log.f32 (/.f32 #s(literal 2 binary32) x))))
(log.f32 (+.f32 x x))
(log.f32 #s(literal 2 binary32))
(log.f32 x)

simplify472.0ms (6.7%)

Memory

29.9MiB live, 585.2MiB allocated

Algorithm

1×	egg-herbie

Rules

11 484×	`accelerator-lowering-fma.f32`
11 484×	`accelerator-lowering-fma.f64`
4 284×	`-lowering-.f32`
4 284×	`-lowering-.f64`
3 832×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	209	1712
1	565	1596
2	1540	1582
3	4404	1490
0	8332	1417

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

Calls

Call 1

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

Outputs
(+ (log -1/2) (* -1 (log x)))
(-.f32 (log.f32 #s(literal -1/2 binary32)) (log.f32 x))
(+ (log -1/2) (+ (* -4 (pow x 2)) (* -1 (log x))))
(fma.f32 x (*.f32 x #s(literal -4 binary32)) (-.f32 (log.f32 #s(literal -1/2 binary32)) (log.f32 x)))
(+ (log -1/2) (+ (* -1 (log x)) (* (pow x 2) (- (* -8 (pow x 2)) 4))))
(fma.f32 x (.f32 x (fma.f32 x (.f32 x #s(literal -8 binary32)) #s(literal -4 binary32))) (-.f32 (log.f32 #s(literal -1/2 binary32)) (log.f32 x)))
(+ (log -1/2) (+ (* -1 (log x)) (* (pow x 2) (- (* (pow x 2) (- (* -64/3 (pow x 2)) 8)) 4))))
(fma.f32 x (.f32 x (fma.f32 x (.f32 x (fma.f32 (*.f32 x x) #s(literal -64/3 binary32) #s(literal -8 binary32))) #s(literal -4 binary32))) (-.f32 (log.f32 #s(literal -1/2 binary32)) (log.f32 x)))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+.f32 (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x)) (/.f32 #s(literal -1/4 binary32) (*.f32 x x)))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 1/32 (/ 1 (pow x 2)))) (pow x 2)))))
(+.f32 (log.f32 #s(literal 2 binary32)) (+.f32 (log.f32 x) (/.f32 (-.f32 #s(literal -1/4 binary32) (/.f32 #s(literal 1/32 binary32) (.f32 x x))) (.f32 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))))
(+.f32 (log.f32 #s(literal 2 binary32)) (+.f32 (log.f32 x) (+.f32 (/.f32 (-.f32 #s(literal -1/32 binary32) (/.f32 #s(literal 1/192 binary32) (.f32 x x))) (.f32 x (.f32 x (.f32 x x)))) (/.f32 #s(literal -1/4 binary32) (*.f32 x x)))))
(+ (log -2) (* -1 (log (/ -1 x))))
(-.f32 (log.f32 #s(literal -2 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) x)))
(- (+ (log -2) (* -1 (log (/ -1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+.f32 (-.f32 (log.f32 #s(literal -2 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) x))) (/.f32 #s(literal -1/4 binary32) (*.f32 x x)))
(+ (log -2) (+ (* -1 (log (/ -1 x))) (* -1 (/ (+ 1/4 (* 1/32 (/ 1 (pow x 2)))) (pow x 2)))))
(+.f32 (/.f32 (-.f32 #s(literal -1/4 binary32) (/.f32 #s(literal 1/32 binary32) (.f32 x x))) (.f32 x x)) (-.f32 (log.f32 #s(literal -2 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) 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))))
(+.f32 (/.f32 (-.f32 #s(literal -1/32 binary32) (/.f32 #s(literal 1/192 binary32) (.f32 x x))) (.f32 x (.f32 x (.f32 x x)))) (+.f32 (-.f32 (log.f32 #s(literal -2 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) x))) (/.f32 #s(literal -1/4 binary32) (*.f32 x x))))
(/ -1/2 x)
(/.f32 #s(literal -1/2 binary32) x)
(/ (- (* 2 (pow x 2)) 1/2) x)
(fma.f32 x #s(literal 2 binary32) (/.f32 #s(literal -1/2 binary32) x))
(/ (- (* 2 (pow x 2)) 1/2) x)
(fma.f32 x #s(literal 2 binary32) (/.f32 #s(literal -1/2 binary32) x))
(/ (- (* 2 (pow x 2)) 1/2) x)
(fma.f32 x #s(literal 2 binary32) (/.f32 #s(literal -1/2 binary32) x))
(* 2 x)
(*.f32 x #s(literal 2 binary32))
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(fma.f32 x #s(literal 2 binary32) (/.f32 #s(literal -1/2 binary32) x))
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(fma.f32 x #s(literal 2 binary32) (/.f32 #s(literal -1/2 binary32) x))
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(fma.f32 x #s(literal 2 binary32) (/.f32 #s(literal -1/2 binary32) x))
(* 2 x)
(*.f32 x #s(literal 2 binary32))
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 2)))
(fma.f32 x #s(literal 2 binary32) (/.f32 #s(literal -1/2 binary32) x))
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 2)))
(fma.f32 x #s(literal 2 binary32) (/.f32 #s(literal -1/2 binary32) x))
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 2)))
(fma.f32 x #s(literal 2 binary32) (/.f32 #s(literal -1/2 binary32) x))
(/ -1/2 x)
(/.f32 #s(literal -1/2 binary32) x)
(/ -1/2 x)
(/.f32 #s(literal -1/2 binary32) x)
(/ -1/2 x)
(/.f32 #s(literal -1/2 binary32) x)
(/ -1/2 x)
(/.f32 #s(literal -1/2 binary32) x)
(/ -1/2 x)
(/.f32 #s(literal -1/2 binary32) x)
(/ -1/2 x)
(/.f32 #s(literal -1/2 binary32) x)
(/ -1/2 x)
(/.f32 #s(literal -1/2 binary32) x)
(/ -1/2 x)
(/.f32 #s(literal -1/2 binary32) x)
(/ -1/2 x)
(/.f32 #s(literal -1/2 binary32) x)
(/ -1/2 x)
(/.f32 #s(literal -1/2 binary32) x)
(/ -1/2 x)
(/.f32 #s(literal -1/2 binary32) x)
(/ -1/2 x)
(/.f32 #s(literal -1/2 binary32) x)
(+ (log 2) (log x))
(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))
(+ (log 2) (log x))
(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))
(+ (log 2) (log x))
(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))
(+ (log 2) (log x))
(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))
(+ (log -2) (* -1 (log (/ -1 x))))
(-.f32 (log.f32 #s(literal -2 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) x)))
(+ (log -2) (* -1 (log (/ -1 x))))
(-.f32 (log.f32 #s(literal -2 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) x)))
(+ (log -2) (* -1 (log (/ -1 x))))
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(log x)
(log.f32 x)
(* -1 (log (/ 1 x)))
(log.f32 x)
(* -1 (log (/ 1 x)))
(log.f32 x)
(* -1 (log (/ 1 x)))
(log.f32 x)
(* -1 (log (/ 1 x)))
(log.f32 x)
(+ (log -1) (* -1 (log (/ -1 x))))
(-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) x)))
(+ (log -1) (* -1 (log (/ -1 x))))
(-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) x)))
(+ (log -1) (* -1 (log (/ -1 x))))
(-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) x)))
(+ (log -1) (* -1 (log (/ -1 x))))
(-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) x)))

eval153.0ms (2.2%)

Memory: 6.8MiB live, 81.8MiB allocated
Compiler: Compiled 9 412 to 1 127 computations (88% saved)

prune131.0ms (1.9%)

Memory

-24.8MiB live, 94.2MiB allocated

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	609	1	610
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	610	5	615

Accuracy

100.0%

Counts

615 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	96.9%	(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))
✓	97.9%	(log.f32 (fma.f32 x #s(literal 2 binary32) (/.f32 #s(literal -1/2 binary32) x)))
✓	46.6%	(log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))
▶	46.6%	(log.f32 (+.f32 (sqrt.f32 (+.f32 (fma.f32 x (+.f32 x #s(literal -1 binary32)) #s(literal -1 binary32)) x)) x))
✓	96.8%	(log.f32 (+.f32 x x))

Compiler

Compiled 41 to 28 computations (31.7% saved)

simplify786.0ms (11.2%)

Memory

-15.9MiB live, 888.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f32 (+.f32 (fma.f32 x (+.f32 x #s(literal -1 binary32)) #s(literal -1 binary32)) x))
✓	cost-diff	0	(+.f32 (sqrt.f32 (+.f32 (fma.f32 x (+.f32 x #s(literal -1 binary32)) #s(literal -1 binary32)) x)) x)
✓	cost-diff	0	(log.f32 (+.f32 (sqrt.f32 (+.f32 (fma.f32 x (+.f32 x #s(literal -1 binary32)) #s(literal -1 binary32)) x)) x))
✓	cost-diff	192	(+.f32 (fma.f32 x (+.f32 x #s(literal -1 binary32)) #s(literal -1 binary32)) x)

Rules

20 822×	`accelerator-lowering-fma.f32`
20 822×	`accelerator-lowering-fma.f64`
4 842×	`+-lowering-+.f64`
4 842×	`+-lowering-+.f32`
4 532×	`--lowering--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	56
1	21	48
2	44	48
3	90	48
4	167	40
5	284	40
6	986	40
7	2131	40
8	2845	40
9	3078	40
10	3143	40
11	3168	40
12	3169	40
13	3467	40
14	3687	40
15	3717	40
16	3727	40
17	3737	40
18	3737	40
19	3737	40
20	6818	40
21	7128	40
0	8494	35

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

Outputs
(log (+ (sqrt (+ (+ (* x (+ x -1)) -1) x)) x))
(log.f32 (+.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))
(+ (sqrt (+ (+ (* x (+ x -1)) -1) x)) x)
(+.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))
(sqrt (+ (+ (* x (+ x -1)) -1) x))
(sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))
(+ (+ (* x (+ x -1)) -1) x)
(fma.f32 x x #s(literal -1 binary32))
(+ (* x (+ x -1)) -1)
(fma.f32 x x (-.f32 #s(literal -1 binary32) x))
x
(+ x -1)
(+.f32 x #s(literal -1 binary32))
-1
#s(literal -1 binary32)

localize28.0ms (0.4%)

Memory

17.7MiB live, 56.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(+.f32 (sqrt.f32 (+.f32 (fma.f32 x (+.f32 x #s(literal -1 binary32)) #s(literal -1 binary32)) x)) x)
✓	accuracy	99.8%	(+.f32 (fma.f32 x (+.f32 x #s(literal -1 binary32)) #s(literal -1 binary32)) x)
✓	accuracy	98.9%	(log.f32 (+.f32 (sqrt.f32 (+.f32 (fma.f32 x (+.f32 x #s(literal -1 binary32)) #s(literal -1 binary32)) x)) x))
✓	accuracy	50.6%	(sqrt.f32 (+.f32 (fma.f32 x (+.f32 x #s(literal -1 binary32)) #s(literal -1 binary32)) x))

Samples

17.0ms

256×

valid

Compiler

Compiled 53 to 11 computations (79.2% saved)

Precisions

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

ival-add: 5.0ms (47.3% of total)

ival-log: 2.0ms (18.9% of total)

ival-mult: 2.0ms (18.9% of total)

ival-sqrt: 2.0ms (18.9% of total)

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

exact: 0.0ms (0% of total)

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

series1.0ms (0%)

Memory

2.3MiB live, 2.3MiB allocated

Counts

4 → 48

Calls

Call 1

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

Calls

12 calls:

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

rewrite352.0ms (5%)

Memory

6.4MiB live, 517.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 732×	`accelerator-lowering-fma.f32`
5 732×	`accelerator-lowering-fma.f64`
5 104×	`-lowering-.f32`
5 104×	`-lowering-.f64`
4 282×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	44
1	65	36
2	596	28
0	8443	24

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 363

Calls

Call 1

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

Outputs
(neg.f32 (/.f32 (.f32 (fma.f32 x x (.f32 (fma.f32 x (+.f32 x #s(literal -1 binary32)) #s(literal -1 binary32)) (fma.f32 x (+.f32 x #s(literal -1 binary32)) (-.f32 #s(literal -1 binary32) x)))) (fma.f32 x x #s(literal -1 binary32))) (neg.f32 (fma.f32 x (-.f32 x (fma.f32 x (+.f32 x #s(literal -1 binary32)) #s(literal -1 binary32))) (*.f32 (fma.f32 x (+.f32 x #s(literal -1 binary32)) #s(literal -1 binary32)) (fma.f32 x (+.f32 x #s(literal -1 binary32)) #s(literal -1 binary32)))))))
(neg.f32 (/.f32 (*.f32 (fma.f32 x x #s(literal -1 binary32)) (fma.f32 x (+.f32 x #s(literal -1 binary32)) (-.f32 #s(literal -1 binary32) x))) (+.f32 (+.f32 #s(literal 1 binary32) (fma.f32 x (neg.f32 x) x)) x)))
(neg.f32 (/.f32 (neg.f32 (.f32 (fma.f32 x x (.f32 (fma.f32 x (+.f32 x #s(literal -1 binary32)) #s(literal -1 binary32)) (fma.f32 x (+.f32 x #s(literal -1 binary32)) (-.f32 #s(literal -1 binary32) x)))) (fma.f32 x x #s(literal -1 binary32)))) (fma.f32 x (-.f32 x (fma.f32 x (+.f32 x #s(literal -1 binary32)) #s(literal -1 binary32))) (*.f32 (fma.f32 x (+.f32 x #s(literal -1 binary32)) #s(literal -1 binary32)) (fma.f32 x (+.f32 x #s(literal -1 binary32)) #s(literal -1 binary32))))))
(neg.f32 (/.f32 (*.f32 (fma.f32 x x #s(literal -1 binary32)) (+.f32 (+.f32 #s(literal 1 binary32) (fma.f32 x (neg.f32 x) x)) x)) (fma.f32 x (+.f32 x #s(literal -1 binary32)) (-.f32 #s(literal -1 binary32) x))))
(exp.f32 (log.f32 (fma.f32 x x #s(literal -1 binary32))))
(exp.f32 (*.f32 (log.f32 (fma.f32 x x #s(literal -1 binary32))) #s(literal 1 binary32)))
(exp.f32 (.f32 (.f32 #s(literal 1/2 binary32) (log.f32 (fma.f32 x x #s(literal -1 binary32)))) #s(literal 2 binary32)))
(exp.f32 (.f32 (log.f32 (.f32 (fma.f32 x x #s(literal -1 binary32)) (fma.f32 x x #s(literal -1 binary32)))) #s(literal 1/2 binary32)))
(+.f32 x (fma.f32 x (+.f32 x #s(literal -1 binary32)) #s(literal -1 binary32)))
(+.f32 #s(literal -1 binary32) (fma.f32 x (+.f32 x #s(literal -1 binary32)) x))
(+.f32 (+.f32 x #s(literal -1 binary32)) (fma.f32 x x (neg.f32 x)))
(+.f32 (fma.f32 x x (neg.f32 x)) (+.f32 x #s(literal -1 binary32)))
(+.f32 (fma.f32 x (+.f32 x #s(literal -1 binary32)) #s(literal -1 binary32)) x)
(+.f32 (*.f32 x x) #s(literal -1 binary32))
(+.f32 (*.f32 x x) (+.f32 (neg.f32 x) (+.f32 x #s(literal -1 binary32))))
(+.f32 (neg.f32 x) (fma.f32 x x (+.f32 x #s(literal -1 binary32))))
(+.f32 (+.f32 (neg.f32 x) #s(literal -1 binary32)) (fma.f32 x x x))
(+.f32 (+.f32 (neg.f32 x) #s(literal -1 binary32)) (*.f32 (+.f32 x #s(literal 1 binary32)) x))
(+.f32 (/.f32 (.f32 (fma.f32 x (+.f32 x #s(literal -1 binary32)) #s(literal -1 binary32)) (fma.f32 x (+.f32 x #s(literal -1 binary32)) #s(literal -1 binary32))) (fma.f32 x (+.f32 x #s(literal -1 binary32)) (-.f32 #s(literal -1 binary32) x))) (neg.f32 (/.f32 (.f32 x x) (fma.f32 x (+.f32 x #s(literal -1 binary32)) (-.f32 #s(literal -1 binary32) x)))))
(+.f32 (fma.f32 x x x) (+.f32 (neg.f32 x) #s(literal -1 binary32)))
(+.f32 (+.f32 #s(literal -1 binary32) (*.f32 x x)) (+.f32 (neg.f32 x) x))
(+.f32 (fma.f32 x (+.f32 x #s(literal -1 binary32)) x) #s(literal -1 binary32))
(+.f32 (*.f32 (+.f32 x #s(literal 1 binary32)) x) (+.f32 (neg.f32 x) #s(literal -1 binary32)))
(+.f32 (+.f32 x (*.f32 x x)) (+.f32 (neg.f32 x) #s(literal -1 binary32)))
(+.f32 (+.f32 x (+.f32 #s(literal -1 binary32) (*.f32 x x))) (neg.f32 x))
(+.f32 (+.f32 (+.f32 x #s(literal -1 binary32)) (*.f32 x x)) (neg.f32 x))
(+.f32 (+.f32 (+.f32 x #s(literal -1 binary32)) (neg.f32 x)) (*.f32 x x))
(fabs.f32 (fma.f32 x x #s(literal -1 binary32)))
(pow.f32 (fma.f32 x x #s(literal -1 binary32)) #s(literal 1 binary32))
(pow.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) #s(literal 2 binary32))
(pow.f32 (*.f32 (fma.f32 x x #s(literal -1 binary32)) (fma.f32 x x #s(literal -1 binary32))) #s(literal 1/2 binary32))
(pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal -1 binary32))) #s(literal -1 binary32))
(fma.f32 x x #s(literal -1 binary32))
(fma.f32 x x (+.f32 (neg.f32 x) (+.f32 x #s(literal -1 binary32))))
(fma.f32 x #s(literal -1 binary32) (fma.f32 x x (+.f32 x #s(literal -1 binary32))))
(fma.f32 x (+.f32 x #s(literal -1 binary32)) (+.f32 x #s(literal -1 binary32)))
(fma.f32 x #s(literal 1 binary32) (fma.f32 x (+.f32 x #s(literal -1 binary32)) #s(literal -1 binary32)))
(fma.f32 x (+.f32 x #s(literal 1 binary32)) (+.f32 (neg.f32 x) #s(literal -1 binary32)))
(fma.f32 x (neg.f32 (*.f32 (+.f32 x #s(literal -1 binary32)) #s(literal -1 binary32))) (+.f32 x #s(literal -1 binary32)))
(fma.f32 #s(literal -1 binary32) x (fma.f32 x x (+.f32 x #s(literal -1 binary32))))
(fma.f32 #s(literal -1 binary32) (neg.f32 x) (fma.f32 x (+.f32 x #s(literal -1 binary32)) #s(literal -1 binary32)))
(fma.f32 #s(literal -1 binary32) (fma.f32 x (neg.f32 x) x) (+.f32 x #s(literal -1 binary32)))
(fma.f32 #s(literal -1 binary32) (+.f32 x #s(literal 1 binary32)) (fma.f32 x x x))
(fma.f32 #s(literal -1 binary32) (+.f32 x #s(literal 1 binary32)) (*.f32 (+.f32 x #s(literal 1 binary32)) x))
(fma.f32 (+.f32 x #s(literal -1 binary32)) x (+.f32 x #s(literal -1 binary32)))
(fma.f32 (fma.f32 x x (neg.f32 x)) #s(literal 1 binary32) (+.f32 x #s(literal -1 binary32)))
(fma.f32 (fma.f32 x x #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (+.f32 x #s(literal 1 binary32))) (fma.f32 x x (neg.f32 x)))
(fma.f32 (.f32 (fma.f32 x (+.f32 x #s(literal -1 binary32)) #s(literal -1 binary32)) (fma.f32 x (+.f32 x #s(literal -1 binary32)) #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 x (+.f32 x #s(literal -1 binary32)) (-.f32 #s(literal -1 binary32) x))) (neg.f32 (/.f32 (.f32 x x) (fma.f32 x (+.f32 x #s(literal -1 binary32)) (-.f32 #s(literal -1 binary32) x)))))
(fma.f32 (*.f32 x x) #s(literal 1 binary32) #s(literal -1 binary32))
(fma.f32 (*.f32 x x) #s(literal 1 binary32) (+.f32 (neg.f32 x) (+.f32 x #s(literal -1 binary32))))
(fma.f32 (fma.f32 x (*.f32 x x) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 x x #s(literal 1 binary32)) x)) (fma.f32 x x (neg.f32 x)))
(fma.f32 (fma.f32 x (*.f32 x x) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (fma.f32 x x x))) (fma.f32 x x (neg.f32 x)))
(fma.f32 #s(literal 1 binary32) x (fma.f32 x (+.f32 x #s(literal -1 binary32)) #s(literal -1 binary32)))
(fma.f32 #s(literal 1 binary32) (+.f32 x #s(literal -1 binary32)) (fma.f32 x x (neg.f32 x)))
(fma.f32 #s(literal 1 binary32) (fma.f32 x x (neg.f32 x)) (+.f32 x #s(literal -1 binary32)))
(fma.f32 #s(literal 1 binary32) (fma.f32 x (+.f32 x #s(literal -1 binary32)) #s(literal -1 binary32)) x)
(fma.f32 #s(literal 1 binary32) (*.f32 x x) #s(literal -1 binary32))
(fma.f32 #s(literal 1 binary32) (*.f32 x x) (+.f32 (neg.f32 x) (+.f32 x #s(literal -1 binary32))))
(fma.f32 #s(literal 1 binary32) (neg.f32 x) (fma.f32 x x (+.f32 x #s(literal -1 binary32))))
(fma.f32 (neg.f32 x) #s(literal -1 binary32) (fma.f32 x (+.f32 x #s(literal -1 binary32)) #s(literal -1 binary32)))
(fma.f32 (neg.f32 x) (neg.f32 x) #s(literal -1 binary32))
(fma.f32 (neg.f32 x) (neg.f32 x) (+.f32 (neg.f32 x) (+.f32 x #s(literal -1 binary32))))
(fma.f32 (neg.f32 x) (+.f32 (neg.f32 x) #s(literal 1 binary32)) (+.f32 x #s(literal -1 binary32)))
(fma.f32 (neg.f32 x) (*.f32 (+.f32 x #s(literal -1 binary32)) #s(literal -1 binary32)) (+.f32 x #s(literal -1 binary32)))
(fma.f32 (fma.f32 (fma.f32 x x (neg.f32 x)) (.f32 (+.f32 x #s(literal -1 binary32)) (.f32 x (fma.f32 x x (neg.f32 x)))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (+.f32 (fma.f32 (fma.f32 x x (neg.f32 x)) (fma.f32 x x (neg.f32 x)) #s(literal 1 binary32)) (fma.f32 x x (neg.f32 x)))) x)
(fma.f32 (fma.f32 (fma.f32 x x (neg.f32 x)) (.f32 (+.f32 x #s(literal -1 binary32)) (.f32 x (fma.f32 x x (neg.f32 x)))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (*.f32 (fma.f32 x x (neg.f32 x)) (fma.f32 x (+.f32 x #s(literal -1 binary32)) #s(literal 1 binary32))))) x)
(fma.f32 (fma.f32 x (neg.f32 x) x) #s(literal -1 binary32) (+.f32 x #s(literal -1 binary32)))
(fma.f32 (+.f32 x #s(literal 1 binary32)) x (+.f32 (neg.f32 x) #s(literal -1 binary32)))
(fma.f32 (+.f32 x #s(literal 1 binary32)) #s(literal -1 binary32) (fma.f32 x x x))
(fma.f32 (+.f32 x #s(literal 1 binary32)) #s(literal -1 binary32) (*.f32 (+.f32 x #s(literal 1 binary32)) x))
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(.f32 (sqrt.f32 (.f32 (fma.f32 x x (.f32 (fma.f32 x (+.f32 x #s(literal -1 binary32)) #s(literal -1 binary32)) (fma.f32 x (+.f32 x #s(literal -1 binary32)) (-.f32 #s(literal -1 binary32) x)))) (fma.f32 x x #s(literal -1 binary32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (fma.f32 x (-.f32 x (fma.f32 x (+.f32 x #s(literal -1 binary32)) #s(literal -1 binary32))) (.f32 (fma.f32 x (+.f32 x #s(literal -1 binary32)) #s(literal -1 binary32)) (fma.f32 x (+.f32 x #s(literal -1 binary32)) #s(literal -1 binary32)))))))
(.f32 (sqrt.f32 (.f32 (fma.f32 x x #s(literal -1 binary32)) (fma.f32 x (+.f32 x #s(literal -1 binary32)) (-.f32 #s(literal -1 binary32) x)))) (pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x (+.f32 x #s(literal -1 binary32)) (-.f32 #s(literal -1 binary32) x))) #s(literal 1/2 binary32)))
(.f32 (sqrt.f32 (.f32 (fma.f32 x x #s(literal -1 binary32)) (fma.f32 x (+.f32 x #s(literal -1 binary32)) (-.f32 #s(literal -1 binary32) x)))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x (+.f32 x #s(literal -1 binary32)) (-.f32 #s(literal -1 binary32) x)))))
(.f32 (sqrt.f32 (.f32 (fma.f32 x x #s(literal -1 binary32)) (fma.f32 x (+.f32 x #s(literal -1 binary32)) (-.f32 #s(literal -1 binary32) x)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (fma.f32 x (+.f32 x #s(literal -1 binary32)) (-.f32 #s(literal -1 binary32) x)))))
(*.f32 (pow.f32 (fma.f32 x x #s(literal -1 binary32)) #s(literal 1/4 binary32)) (pow.f32 (fma.f32 x x #s(literal -1 binary32)) #s(literal 1/4 binary32)))
(*.f32 (pow.f32 (+.f32 x #s(literal 1 binary32)) #s(literal 1/2 binary32)) (pow.f32 (+.f32 x #s(literal -1 binary32)) #s(literal 1/2 binary32)))
(*.f32 (sqrt.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (sqrt.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))
(*.f32 (sqrt.f32 (+.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 x #s(literal -1 binary32))))

simplify346.0ms (4.9%)

Memory

21.3MiB live, 482.4MiB 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	559
1	411	533
2	1143	526
3	3327	488
4	7966	488
0	8526	459

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

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))))))

Outputs
-1
#s(literal -1 binary32)
(- (pow x 2) 1)
(fma.f32 x x #s(literal -1 binary32))
(- (pow x 2) 1)
(fma.f32 x x #s(literal -1 binary32))
(- (pow x 2) 1)
(fma.f32 x x #s(literal -1 binary32))
(pow x 2)
(*.f32 x x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f32 x x #s(literal -1 binary32))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f32 x x #s(literal -1 binary32))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f32 x x #s(literal -1 binary32))
(pow x 2)
(*.f32 x x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f32 x x #s(literal -1 binary32))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f32 x x #s(literal -1 binary32))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f32 x x #s(literal -1 binary32))
(log (sqrt -1))
(log.f32 (sqrt.f32 #s(literal -1 binary32)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f32 (log.f32 (sqrt.f32 #s(literal -1 binary32))) (/.f32 x (sqrt.f32 #s(literal -1 binary32))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (fma.f32 x (*.f32 x #s(literal 1/6 binary32)) #s(literal 1 binary32)) (log.f32 (sqrt.f32 #s(literal -1 binary32))))
(+ (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.f32 x (fma.f32 x (.f32 x (/.f32 (.f32 (.f32 x x) #s(literal 3/40 binary32)) (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 5 binary32)))) (.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 #s(literal -1 binary32))) (fma.f32 x (*.f32 x #s(literal -1/6 binary32)) #s(literal -1 binary32)))) (log.f32 (sqrt.f32 #s(literal -1 binary32))))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+.f32 (log.f32 #s(literal 2 binary32)) (+.f32 (log.f32 x) (/.f32 #s(literal -1/4 binary32) (*.f32 x x))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(+.f32 (log.f32 #s(literal 2 binary32)) (+.f32 (log.f32 x) (/.f32 (+.f32 #s(literal -1/4 binary32) (/.f32 #s(literal -3/32 binary32) (.f32 x x))) (.f32 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))))
(+.f32 (log.f32 #s(literal 2 binary32)) (+.f32 (log.f32 x) (+.f32 (/.f32 (+.f32 #s(literal -3/32 binary32) (/.f32 #s(literal -5/96 binary32) (.f32 x x))) (.f32 x (.f32 x (.f32 x x)))) (/.f32 #s(literal -1/4 binary32) (*.f32 x x)))))
(+ (log -1/2) (log (/ -1 x)))
(+.f32 (log.f32 #s(literal -1/2 binary32)) (neg.f32 (log.f32 (neg.f32 x))))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+.f32 (/.f32 #s(literal 1/4 binary32) (*.f32 x x)) (+.f32 (log.f32 #s(literal -1/2 binary32)) (neg.f32 (log.f32 (neg.f32 x)))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+.f32 (+.f32 (neg.f32 (log.f32 (neg.f32 x))) (/.f32 #s(literal 3/32 binary32) (.f32 x (.f32 x (.f32 x x))))) (+.f32 (/.f32 #s(literal 1/4 binary32) (.f32 x x)) (log.f32 #s(literal -1/2 binary32))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(+.f32 (+.f32 (log.f32 #s(literal -1/2 binary32)) (neg.f32 (log.f32 (neg.f32 x)))) (+.f32 (/.f32 #s(literal 3/32 binary32) (.f32 x (.f32 x (.f32 x x)))) (+.f32 (/.f32 #s(literal 1/4 binary32) (.f32 x x)) (/.f32 #s(literal 5/96 binary32) (pow.f32 x #s(literal 6 binary32))))))
(sqrt -1)
(sqrt.f32 #s(literal -1 binary32))
(+ x (sqrt -1))
(+.f32 x (sqrt.f32 #s(literal -1 binary32)))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(fma.f32 x (fma.f32 x (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32))) #s(literal 1 binary32)) (sqrt.f32 #s(literal -1 binary32)))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(fma.f32 x (fma.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (fma.f32 x (*.f32 x #s(literal 1/8 binary32)) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (sqrt.f32 #s(literal -1 binary32)))
(* 2 x)
(*.f32 x #s(literal 2 binary32))
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(fma.f32 x #s(literal 2 binary32) (/.f32 #s(literal -1/2 binary32) x))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(fma.f32 x #s(literal 2 binary32) (/.f32 (+.f32 #s(literal -1/2 binary32) (/.f32 #s(literal -1/8 binary32) (*.f32 x x))) x))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(fma.f32 x (+.f32 #s(literal 2 binary32) (/.f32 (+.f32 #s(literal -1/8 binary32) (/.f32 #s(literal -1/16 binary32) (.f32 x x))) (.f32 x (.f32 x (.f32 x x))))) (/.f32 #s(literal -1/2 binary32) x))
(/ 1/2 x)
(/.f32 #s(literal 1/2 binary32) x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(/.f32 (-.f32 #s(literal 1/2 binary32) (/.f32 #s(literal -1/8 binary32) (*.f32 x x))) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(/.f32 (+.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 #s(literal 1/8 binary32) (/.f32 #s(literal 1/16 binary32) (.f32 x x))) (.f32 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))
(/.f32 (-.f32 (/.f32 #s(literal 1/8 binary32) (.f32 x x)) (+.f32 #s(literal -1/2 binary32) (/.f32 (+.f32 #s(literal -1/16 binary32) (/.f32 #s(literal -5/128 binary32) (.f32 x x))) (.f32 x (.f32 x (*.f32 x x)))))) x)
(sqrt -1)
(sqrt.f32 #s(literal -1 binary32))
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(fma.f32 x (*.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) #s(literal 1/2 binary32)) (sqrt.f32 #s(literal -1 binary32)))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f32 x (.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (fma.f32 x (.f32 x #s(literal 1/8 binary32)) #s(literal 1/2 binary32))) (sqrt.f32 #s(literal -1 binary32)))
(+ (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.f32 x (fma.f32 x (/.f32 (.f32 (.f32 (.f32 x x) #s(literal 1/16 binary32)) (.f32 x x)) (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 5 binary32))) (.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (fma.f32 x (.f32 x #s(literal 1/8 binary32)) #s(literal 1/2 binary32)))) (sqrt.f32 #s(literal -1 binary32)))
x
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(+.f32 x (/.f32 #s(literal -1/2 binary32) x))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(-.f32 x (/.f32 (-.f32 #s(literal 1/2 binary32) (/.f32 #s(literal -1/8 binary32) (*.f32 x x))) x))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(+.f32 (/.f32 #s(literal -1/2 binary32) x) (fma.f32 x (/.f32 (+.f32 #s(literal -1/8 binary32) (/.f32 #s(literal -1/16 binary32) (.f32 x x))) (.f32 x (.f32 x (.f32 x x)))) x))
(* -1 x)
(neg.f32 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))
(-.f32 (/.f32 #s(literal 1/2 binary32) x) x)
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))
(-.f32 (/.f32 (-.f32 #s(literal 1/2 binary32) (/.f32 #s(literal -1/8 binary32) (*.f32 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.f32 x (/.f32 (+.f32 #s(literal 1/8 binary32) (/.f32 #s(literal 1/16 binary32) (.f32 x x))) (.f32 x (.f32 x (.f32 x x)))) (-.f32 (/.f32 #s(literal 1/2 binary32) x) x))

eval75.0ms (1.1%)

Memory: -4.5MiB live, 84.3MiB allocated
Compiler: Compiled 12 458 to 2 041 computations (83.6% saved)

prune57.0ms (0.8%)

Memory

0.8MiB live, 157.3MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	411	0	411
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	411	5	416

Accuracy

100.0%

Counts

416 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	96.9%	(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))
✓	97.9%	(log.f32 (fma.f32 x #s(literal 2 binary32) (/.f32 #s(literal -1/2 binary32) x)))
✓	46.6%	(log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))
✓	46.6%	(log.f32 (+.f32 (sqrt.f32 (+.f32 (fma.f32 x (+.f32 x #s(literal -1 binary32)) #s(literal -1 binary32)) x)) x))
✓	96.8%	(log.f32 (+.f32 x x))

Compiler

Compiled 100 to 61 computations (39% saved)

regimes21.0ms (0.3%)

Memory

-23.7MiB live, 14.8MiB allocated

Counts

7 → 1

Calls

Call 1

Inputs
(log.f32 (+.f32 x x))
(log.f32 (fma.f32 x #s(literal 2 binary32) (/.f32 #s(literal -1/2 binary32) x)))
(log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))
(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))
(log.f32 (+.f32 (sqrt.f32 (+.f32 (fma.f32 x (+.f32 x #s(literal -1 binary32)) #s(literal -1 binary32)) x)) x))
(log.f32 (+.f32 x (sqrt.f32 (+.f32 (+.f32 x #s(literal -1 binary32)) (*.f32 x (+.f32 x #s(literal -1 binary32)))))))
(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))

Outputs
(log.f32 (fma.f32 x #s(literal 2 binary32) (/.f32 #s(literal -1/2 binary32) x)))

Calls

3 calls:

16.0ms	x
3.0ms	(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))
3.0ms	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))

Results

Accuracy	Segments	Branch
97.9%	1	`x`
97.9%	1	`(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))`
97.9%	1	`(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))`

Compiler

Compiled 21 to 14 computations (33.3% saved)

regimes4.0ms (0.1%)

Memory

8.2MiB live, 8.3MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(log.f32 (+.f32 x x))

Outputs
(log.f32 (+.f32 x x))

Calls

3 calls:

1.0ms	(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))
1.0ms	x
1.0ms	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))

Results

Accuracy	Segments	Branch
96.8%	1	`x`
96.8%	1	`(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))`
96.8%	1	`(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))`

Compiler

Compiled 21 to 14 computations (33.3% saved)

simplify7.0ms (0.1%)

Memory

11.1MiB live, 11.1MiB 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.f32 (fma.f32 x #s(literal 2 binary32) (/.f32 #s(literal -1/2 binary32) x)))
(log.f32 (+.f32 x x))

Outputs
(log.f32 (fma.f32 x #s(literal 2 binary32) (/.f32 #s(literal -1/2 binary32) x)))
(log.f32 (+.f32 x x))

soundness219.0ms (3.1%)

Memory

-3.5MiB live, 146.6MiB 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	559
1	411	533
2	1143	526
3	3327	488
4	7966	488
0	8526	459

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 25 to 17 computations (32% saved)

preprocess30.0ms (0.4%)

Memory: 0.1MiB live, 76.9MiB allocated
Compiler: Compiled 70 to 48 computations (31.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

sample418.0ms (5.9%)

preprocess1.2s (17.5%)

explain220.0ms (3.1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify652.0ms (9.3%)

localize75.0ms (1.1%)

series5.0ms (0.1%)

rewrite413.0ms (5.9%)

simplify371.0ms (5.3%)

eval87.0ms (1.2%)

prune54.0ms (0.8%)

simplify486.0ms (6.9%)

localize113.0ms (1.6%)

series118.0ms (1.7%)

rewrite108.0ms (1.5%)

simplify472.0ms (6.7%)

eval153.0ms (2.2%)

prune131.0ms (1.9%)

simplify786.0ms (11.2%)

localize28.0ms (0.4%)

series1.0ms (0%)

rewrite352.0ms (5%)

simplify346.0ms (4.9%)

eval75.0ms (1.1%)

prune57.0ms (0.8%)

regimes21.0ms (0.3%)

regimes4.0ms (0.1%)

simplify7.0ms (0.1%)

soundness219.0ms (3.1%)

preprocess30.0ms (0.4%)

end0.0ms (0%)

Profiling