Metrics for Numeric.Integration.TanhSinh:nonNegative from integration-0.2.1

analyze1.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
50%	50%	50%	0%	0%	0%	0%	2
75%	75%	25%	0%	0%	0%	0%	3
87.5%	87.5%	12.5%	0%	0%	0%	0%	4
93.8%	93.7%	6.2%	0%	0%	0%	0%	5
96.9%	96.8%	3.1%	0%	0%	0%	0%	6
98.4%	98.4%	1.6%	0%	0%	0%	0%	7
99.2%	99.2%	0.8%	0%	0%	0%	0%	8
99.6%	99.6%	0.4%	0%	0%	0%	0%	9
99.8%	99.8%	0.2%	0%	0%	0%	0%	10
99.9%	99.9%	0.1%	0%	0%	0%	0%	11
100%	99.9%	0%	0%	0%	0%	0%	12

Compiler

Compiled 7 to 5 computations (28.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

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

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

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

sample531.0ms (12.6%)

Results

373.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 192.0ms

ival-sub: 92.0ms (47.9% of total)

ival-div: 88.0ms (45.8% of total)

const: 10.0ms (5.2% of total)

backward-pass: 2.0ms (1% of total)

Bogosity

preprocess43.0ms (1%)

Algorithm

2×	egg-herbie

Rules

428×	`fnmadd-define`
424×	`sum3-define`
350×	`fma-define`
210×	`fmsub-define`
190×	`fnmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	23	16
2	52	15
3	123	15
4	301	15
5	590	15
6	1078	15
7	1318	15
8	1369	15
9	1409	15
10	1425	15
0	4	5
1	8	5
2	12	5
3	18	5
4	27	5
5	42	5
6	64	5
7	90	5
8	133	5
9	148	5
10	178	5
0	178	5

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(/ x (- 1 x))

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

Call 2

Inputs
(/ x (- 1 x))
(/ (neg x) (- 1 (neg x)))
(neg (/ (neg x) (- 1 (neg x))))

Outputs
(/ x (- 1 x))
(/ (neg x) (- 1 (neg x)))
(/ x (- -1 x))
(neg (/ (neg x) (- 1 (neg x))))
(/ x (+ x 1))

explain53.0ms (1.3%)

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`x`
-	-	`(-.f64 #s(literal 1 binary64) x)`
-	-	`#s(literal 1 binary64)`
-	-	`(/.f64 x (-.f64 #s(literal 1 binary64) x))`

Results

35.0ms

512×

valid

Compiler

Compiled 30 to 14 computations (53.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-sub: 4.0ms (44.3% of total)

ival-div: 4.0ms (44.3% of total)

const: 1.0ms (11.1% of total)

backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 6 to 4 computations (33.3% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

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

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Rules

76×	`sum3-define`
36×	`+-lowering-+.f64`
36×	`+-lowering-+.f32`
32×	`fma-define`
26×	`--lowering--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	10
1	8	10
2	12	10
3	18	10
4	27	10
5	42	10
6	64	10
7	90	10
8	133	10
9	148	10
10	178	10
0	178	10

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ x (- 1 x))
x
(- 1 x)
1

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

localize22.0ms (0.5%)

Localize:

Found 2 expressions of interest:

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

Results

16.0ms

256×

valid

Compiler

Compiled 12 to 5 computations (58.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-sub: 6.0ms (68.2% of total)

ival-div: 2.0ms (22.7% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series1.0ms (0%)

Counts

2 → 24

Calls

Call 1

Inputs
#<alt (/ x (- 1 x))>
#<alt (- 1 x)>

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

Calls

6 calls:

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

rewrite320.0ms (7.6%)

Algorithm

1×	batch-egg-rewrite

Rules

3022×	`/-lowering-/.f32`
3022×	`/-lowering-/.f64`
2548×	`-lowering-.f32`
2548×	`-lowering-.f64`
1614×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	8
1	27	8
2	185	8
3	1691	8
0	9653	8

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 394

Calls

Call 1

Inputs
(/ x (- 1 x))
(- 1 x)

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

simplify188.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

2602×	`sum3-define`
1734×	`fnmadd-define`
1578×	`fma-lowering-fma.f32`
1578×	`fma-lowering-fma.f64`
1294×	`fmsub-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	33	127
1	101	115
2	262	104
3	694	101
4	1552	101
5	3770	101
6	7870	101
0	8302	101

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 24

Calls

Call 1

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

Outputs
x
(* x (+ 1 x))
(*.f64 x (+.f64 x #s(literal 1 binary64)))
(* x (+ 1 (* x (+ 1 x))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 1 binary64)))))
(* x (+ 1 (* x (+ 1 (* x (+ 1 x))))))
(.f64 (+.f64 x #s(literal 1 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x x))))
-1
#s(literal -1 binary64)
(* -1 (+ 1 (/ 1 x)))
(+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x))
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x)) x))
(- (* -1 (/ (+ 1 (/ 1 x)) (pow x 2))) (+ 1 (/ 1 x)))
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x)) x)) x))
-1
#s(literal -1 binary64)
(* -1 (+ 1 (/ 1 x)))
(+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x))
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x)) x))
(- (* -1 (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1)
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x)) x)) x))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)

eval49.0ms (1.2%)

Compiler: Compiled 13021 to 1286 computations (90.1% saved)

prune585.0ms (13.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	413	5	418
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	413	6	419

Accuracy

100.0%

Counts

419 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 x (-.f64 #s(literal 1 binary64) x))
▶	99.8%	(/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
▶	50.3%	(*.f64 x (+.f64 x #s(literal 1 binary64)))
▶	51.2%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 1 binary64)))))
▶	51.0%	x
▶	50.0%	#s(literal -1 binary64)

Compiler

Compiled 62 to 42 computations (32.3% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

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

Rules

128×	`fma-define`
118×	`fma-lowering-fma.f32`
118×	`fma-lowering-fma.f64`
66×	`-lowering-.f32`
66×	`-lowering-.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	52
1	28	48
2	57	47
3	111	47
4	166	47
5	188	47
0	188	47

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize47.0ms (1.1%)

Localize:

Found 9 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x #s(literal 1 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64))))
✓	accuracy	100.0%	(*.f64 x (+.f64 x #s(literal 1 binary64)))
✓	accuracy	99.9%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 1 binary64)))))
✓	accuracy	100.0%	(+.f64 x #s(literal 1 binary64))
✓	accuracy	100.0%	(*.f64 x (+.f64 x #s(literal 1 binary64)))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)
✓	accuracy	100.0%	(+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))

Results

31.0ms

256×

valid

Compiler

Compiled 58 to 11 computations (81% saved)

Precisions

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

ival-div: 4.0ms (32.5% of total)

ival-add: 4.0ms (32.5% of total)

ival-mult: 4.0ms (32.5% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series3.0ms (0.1%)

Counts

7 → 84

Calls

Call 1

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

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

Calls

21 calls:

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

rewrite445.0ms (10.5%)

Algorithm

1×	batch-egg-rewrite

Rules

3250×	`-lowering-.f32`
3250×	`-lowering-.f64`
3010×	`/-lowering-/.f32`
3010×	`/-lowering-/.f64`
1980×	`sum5-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	35
1	74	32
2	599	31
3	6562	31
0	8001	31

Stop Event

1×	iter limit
1×	node limit

Counts

7 → 467

Calls

Call 1

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

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

simplify188.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

2112×	`fma-lowering-fma.f32`
2112×	`fma-lowering-fma.f64`
2066×	`fmm-def`
1858×	`-lowering-.f32`
1858×	`-lowering-.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	39	394
1	136	368
2	390	328
3	1546	325
4	5490	325
0	8591	325

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

Calls

Call 1

Inputs
x
(* x (+ 1 x))
(* x (+ 1 (* x (+ 1 x))))
(* x (+ 1 (* x (+ 1 (* x (+ 1 x))))))
-1
(* -1 (+ 1 (/ 1 x)))
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(- (* -1 (/ (+ 1 (/ 1 x)) (pow x 2))) (+ 1 (/ 1 x)))
-1
(* -1 (+ 1 (/ 1 x)))
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(- (* -1 (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1)
(/ 1 x)
(/ (+ 1 (* -1 x)) x)
(/ (+ 1 (* -1 x)) x)
(/ (+ 1 (* -1 x)) x)
-1
(- (/ 1 x) 1)
(- (/ 1 x) 1)
(- (/ 1 x) 1)
-1
(- (/ 1 x) 1)
(- (/ 1 x) 1)
(- (/ 1 x) 1)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
x
(* x (+ 1 x))
(* x (+ 1 x))
(* x (+ 1 x))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 x))
(* x (+ 1 (* x (+ 1 x))))
(* x (+ 1 (* x (+ 1 x))))
(pow x 3)
(* (pow x 3) (+ 1 (/ 1 x)))
(* (pow x 3) (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))))
(pow x 3)
(* (pow x 3) (+ 1 (/ 1 x)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)))
1
(+ 1 x)
(+ 1 (* x (+ 1 x)))
(+ 1 (* x (+ 1 x)))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))))

Outputs
x
(* x (+ 1 x))
(*.f64 x (+.f64 x #s(literal 1 binary64)))
(* x (+ 1 (* x (+ 1 x))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 1 binary64)))))
(* x (+ 1 (* x (+ 1 (* x (+ 1 x))))))
(.f64 x (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 x x))))
-1
#s(literal -1 binary64)
(* -1 (+ 1 (/ 1 x)))
(+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x))
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x)) x))
(- (* -1 (/ (+ 1 (/ 1 x)) (pow x 2))) (+ 1 (/ 1 x)))
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x)) x)) x))
-1
#s(literal -1 binary64)
(* -1 (+ 1 (/ 1 x)))
(+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x))
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x)) x))
(- (* -1 (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1)
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x)) x)) x))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (* -1 x)) x)
(+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x))
(/ (+ 1 (* -1 x)) x)
(+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x))
(/ (+ 1 (* -1 x)) x)
(+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x))
-1
#s(literal -1 binary64)
(- (/ 1 x) 1)
(+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x))
(- (/ 1 x) 1)
(+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x))
(- (/ 1 x) 1)
(+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x))
-1
#s(literal -1 binary64)
(- (/ 1 x) 1)
(+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x))
(- (/ 1 x) 1)
(+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x))
(- (/ 1 x) 1)
(+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
x
(* x (+ 1 x))
(*.f64 x (+.f64 x #s(literal 1 binary64)))
(* x (+ 1 x))
(*.f64 x (+.f64 x #s(literal 1 binary64)))
(* x (+ 1 x))
(*.f64 x (+.f64 x #s(literal 1 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 x)))
(*.f64 x (+.f64 x #s(literal 1 binary64)))
(* (pow x 2) (+ 1 (/ 1 x)))
(*.f64 x (+.f64 x #s(literal 1 binary64)))
(* (pow x 2) (+ 1 (/ 1 x)))
(*.f64 x (+.f64 x #s(literal 1 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 x)))
(*.f64 x (+.f64 x #s(literal 1 binary64)))
(* (pow x 2) (+ 1 (/ 1 x)))
(*.f64 x (+.f64 x #s(literal 1 binary64)))
(* (pow x 2) (+ 1 (/ 1 x)))
(*.f64 x (+.f64 x #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 x))
(*.f64 x (+.f64 x #s(literal 1 binary64)))
(* x (+ 1 (* x (+ 1 x))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 1 binary64)))))
(* x (+ 1 (* x (+ 1 x))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 1 binary64)))))
(pow x 3)
(.f64 x (.f64 x x))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 3) (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 1 binary64)))))
(* (pow x 3) (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 1 binary64)))))
(pow x 3)
(.f64 x (.f64 x x))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 1 binary64)))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 1 binary64)))))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 (* x (+ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64))))
(+ 1 (* x (+ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 x)))
(*.f64 x (+.f64 x #s(literal 1 binary64)))
(* (pow x 2) (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 2) (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 x)))
(*.f64 x (+.f64 x #s(literal 1 binary64)))
(* (pow x 2) (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 2) (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64))))

eval90.0ms (2.1%)

Compiler: Compiled 15460 to 1564 computations (89.9% saved)

prune72.0ms (1.7%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	722	1	723
Fresh	0	0	0
Picked	2	3	5
Done	0	1	1
Total	724	5	729

Accuracy

100.0%

Counts

729 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 x (-.f64 #s(literal 1 binary64) x))
▶	50.3%	(+.f64 (*.f64 x x) x)
✓	51.2%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 1 binary64)))))
✓	51.0%	x
✓	50.0%	#s(literal -1 binary64)

Compiler

Compiled 26 to 16 computations (38.5% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(+.f64 (*.f64 x x) x)

Rules

22×	`-lowering-.f32`
22×	`-lowering-.f64`
18×	`fma-define`
14×	`fma-lowering-fma.f32`
14×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	8
1	8	8
2	12	8
3	18	8
4	22	8
5	32	8
6	34	8
0	34	8

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+ (* x x) x)
(* x x)
x

Outputs
(+ (* x x) x)
(*.f64 x (+.f64 x #s(literal 1 binary64)))
(* x x)
(*.f64 x x)
x

localize15.0ms (0.3%)

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(+.f64 (*.f64 x x) x)

Results

10.0ms

256×

valid

Compiler

Compiled 11 to 4 computations (63.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-mult: 2.0ms (50.4% of total)

ival-add: 1.0ms (25.2% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series1.0ms (0%)

Counts

2 → 24

Calls

Call 1

Inputs
#<alt (+ (* x x) x)>
#<alt (* x x)>

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

Calls

6 calls:

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

rewrite313.0ms (7.4%)

Algorithm

1×	batch-egg-rewrite

Rules

2690×	`/-lowering-/.f32`
2690×	`/-lowering-/.f64`
2152×	`-lowering-.f32`
2152×	`-lowering-.f64`
2050×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	7
1	22	7
2	169	7
3	1724	7
0	8267	7

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 138

Calls

Call 1

Inputs
(+ (* x x) x)
(* x x)

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

simplify362.0ms (8.6%)

Algorithm

1×	egg-herbie

Rules

5872×	`-lowering-.f32`
5872×	`-lowering-.f64`
2528×	`cube-prod`
2280×	`/-lowering-/.f32`
2280×	`/-lowering-/.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	88
1	27	88
2	47	79
3	91	79
4	169	79
5	1151	79
6	2584	79
7	3398	79
8	4590	79
9	5780	79
10	6175	79
11	6398	79
12	6595	79
13	6797	79
14	7139	79
0	8328	79

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 24

Calls

Call 1

Inputs
x
(* x (+ 1 x))
(* x (+ 1 x))
(* x (+ 1 x))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

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

eval20.0ms (0.5%)

Compiler: Compiled 5644 to 418 computations (92.6% saved)

prune18.0ms (0.4%)

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	162	5	167

Accuracy

100.0%

Counts

167 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 x (-.f64 #s(literal 1 binary64) x))
✓	50.3%	(+.f64 (*.f64 x x) x)
✓	51.2%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal 1 binary64)))))
✓	51.0%	x
✓	50.0%	#s(literal -1 binary64)

Compiler

Compiled 60 to 30 computations (50% saved)

regimes6.0ms (0.1%)

Counts

7 → 1

Calls

Call 1

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

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

Calls

2 calls:

3.0ms	x
2.0ms	(/.f64 x (-.f64 #s(literal 1 binary64) x))

Results

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

Compiler

Compiled 8 to 5 computations (37.5% saved)

regimes4.0ms (0.1%)

Counts

4 → 3

Calls

Call 1

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

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

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
97.8%	3	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

3 → 3

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
97.8%	3	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

2 → 3

Calls

Call 1

Inputs
#s(literal -1 binary64)
x

Outputs
#s(literal -1 binary64)
x
#s(literal -1 binary64)

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
97.3%	3	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal -1 binary64)

Outputs
#s(literal -1 binary64)

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
50.0%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch20.0ms (0.5%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
9.0ms	0.7924255309365614	27.51874228315019
9.0ms	-10.409705051029164	-3.9866266862150597e-5

Results

9.0ms

256×

valid

Compiler

Compiled 170 to 119 computations (30% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-div: 2.0ms (51.6% of total)

ival-sub: 1.0ms (25.8% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch22.0ms (0.5%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
7.0ms	0.7924255309365614	27.51874228315019
13.0ms	-10.409705051029164	-3.9866266862150597e-5

Results

12.0ms

256×

valid

Compiler

Compiled 170 to 135 computations (20.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-div: 2.0ms (51.6% of total)

ival-sub: 1.0ms (25.8% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch19.0ms (0.5%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
8.0ms	0.7924255309365614	27.51874228315019
9.0ms	-10.409705051029164	-3.9866266862150597e-5

Results

10.0ms

256×

valid

Compiler

Compiled 106 to 87 computations (17.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-div: 3.0ms (63.9% of total)

ival-sub: 1.0ms (21.3% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
6×	`if-if-or-not_binary32`
4×	`*-commutative_binary64`
4×	`sub-neg_binary64`
2×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	47
1	33	47
2	36	47
3	38	47
4	39	47

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 x (-.f64 #s(literal 1 binary64) x))
(if (<=.f64 x #s(literal -3422735716801577/4503599627370496 binary64)) #s(literal -1 binary64) (if (<=.f64 x #s(literal 1 binary64)) (+.f64 (*.f64 x x) x) #s(literal -1 binary64)))
(if (<=.f64 x #s(literal -3422735716801577/4503599627370496 binary64)) #s(literal -1 binary64) (if (<=.f64 x #s(literal 1 binary64)) (*.f64 x (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)))
(if (<=.f64 x #s(literal -1 binary64)) #s(literal -1 binary64) (if (<=.f64 x #s(literal 1 binary64)) x #s(literal -1 binary64)))
#s(literal -1 binary64)

Outputs
(/.f64 x (-.f64 #s(literal 1 binary64) x))
(if (<=.f64 x #s(literal -3422735716801577/4503599627370496 binary64)) #s(literal -1 binary64) (if (<=.f64 x #s(literal 1 binary64)) (+.f64 (*.f64 x x) x) #s(literal -1 binary64)))
(if (<=.f64 x #s(literal -3422735716801577/4503599627370496 binary64)) #s(literal -1 binary64) (if (<=.f64 x #s(literal 1 binary64)) (+.f64 x (*.f64 x x)) #s(literal -1 binary64)))
(if (<=.f64 x #s(literal -3422735716801577/4503599627370496 binary64)) #s(literal -1 binary64) (if (<=.f64 x #s(literal 1 binary64)) (*.f64 x (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)))
(if (<=.f64 x #s(literal -1 binary64)) #s(literal -1 binary64) (if (<=.f64 x #s(literal 1 binary64)) x #s(literal -1 binary64)))
#s(literal -1 binary64)

soundness710.0ms (16.8%)

Rules

3250×	`-lowering-.f32`
3250×	`-lowering-.f64`
3010×	`/-lowering-/.f32`
3010×	`/-lowering-/.f64`
2602×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	33	127
1	101	115
2	262	104
3	694	101
4	1552	101
5	3770	101
6	7870	101
0	8302	101
0	10	35
1	74	32
2	599	31
3	6562	31
0	8001	31

Stop Event

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

Compiler

Compiled 76 to 39 computations (48.7% saved)

preprocess36.0ms (0.9%)

Compiler: Compiled 108 to 46 computations (57.4% saved)

Iter	Nodes	Cost
0	4	10
1	8	10
2	12	10
3	18	10
4	27	10
5	42	10
6	64	10
7	90	10
8	133	10
9	148	10
10	178	10
0	178	10

Iter	Nodes	Cost
0	4	10
1	8	10
2	12	10
3	18	10
4	27	10
5	42	10
6	64	10
7	90	10
8	133	10
9	148	10
10	178	10
0	178	10

analyze1.0ms (0%)

sample531.0ms (12.6%)

preprocess43.0ms (1%)

explain53.0ms (1.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify8.0ms (0.2%)

localize22.0ms (0.5%)

series1.0ms (0%)

rewrite320.0ms (7.6%)

simplify188.0ms (4.5%)

eval49.0ms (1.2%)

prune585.0ms (13.9%)

simplify10.0ms (0.2%)

localize47.0ms (1.1%)

series3.0ms (0.1%)

rewrite445.0ms (10.5%)

simplify188.0ms (4.5%)

eval90.0ms (2.1%)

prune72.0ms (1.7%)

simplify5.0ms (0.1%)

localize15.0ms (0.3%)

series1.0ms (0%)

rewrite313.0ms (7.4%)

simplify362.0ms (8.6%)

eval20.0ms (0.5%)

prune18.0ms (0.4%)

regimes6.0ms (0.1%)

regimes4.0ms (0.1%)

regimes2.0ms (0%)

regimes2.0ms (0%)

regimes1.0ms (0%)

bsearch20.0ms (0.5%)

bsearch22.0ms (0.5%)

bsearch19.0ms (0.5%)

simplify8.0ms (0.2%)

soundness710.0ms (16.8%)

preprocess36.0ms (0.9%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	4	10
1	8	10
2	12	10
3	18	10
4	27	10
5	42	10
6	64	10
7	90	10
8	133	10
9	148	10
10	178	10
0	178	10