Metrics for invcot (example 3.9)

analyze10.0ms (0.1%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	49.7%	50.3%	0%	0%	0%	0
0%	0%	49.7%	50.3%	0%	0%	0%	1
0%	0%	49.7%	50.3%	0%	0%	0%	2
25%	12.4%	37.3%	50.3%	0%	0%	0%	3
62.5%	31.1%	18.6%	50.3%	0%	0%	0%	4
81.3%	40.4%	9.3%	50.3%	0%	0%	0%	5
90.6%	45%	4.7%	50.3%	0%	0%	0%	6
95.3%	47.4%	2.3%	50.3%	0%	0%	0%	7
97.7%	48.5%	1.2%	50.3%	0%	0%	0%	8
98.8%	49.1%	0.6%	50.3%	0%	0%	0%	9
99.4%	49.4%	0.3%	50.3%	0%	0%	0%	10
99.7%	49.5%	0.1%	50.3%	0%	0%	0%	11
99.9%	49.6%	0.1%	50.3%	0%	0%	0%	12

Compiler

Compiled 16 to 11 computations (31.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

...c/correct-round.rkt:119:19: 4.0ms (60.5% of total)

ival-div: 1.0ms (15.1% of total)

ival-tan: 1.0ms (15.1% of total)

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

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

const: 0.0ms (0% of total)

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

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

sample7.2s (57.7%)

Results

5.1s	4439×	2	valid
1.1s	1341×	3	valid
540.0ms	2423×	1	valid
6.0ms	53×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 6.1s

ival-tan: 4.7s (77.4% of total)

ival-div: 509.0ms (8.3% of total)

...c/correct-round.rkt:119:19: 293.0ms (4.8% of total)

backward-pass: 267.0ms (4.4% of total)

ival-sub: 159.0ms (2.6% of total)

ival-<: 116.0ms (1.9% of total)

const: 19.0ms (0.3% of total)

ival-and: 18.0ms (0.3% of total)

Bogosity

preprocess40.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

156×	`fnmadd-define`
138×	`sum3-define`
112×	`fma-lowering-fma.f32`
112×	`fnmsub-define`
112×	`fmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	17
1	31	16
2	66	15
3	149	15
4	303	15
5	472	15
6	515	15
7	523	15
0	6	5
1	13	5
2	21	5
3	32	5
4	46	5
5	83	5
6	153	5
7	249	5
8	349	5
9	485	5
10	607	5
11	639	5
0	639	5

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

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

Call 2

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

Outputs
(- (/ 1 x) (/ 1 (tan x)))
(- (recip x) (cot x))
(- (/ 1 (neg x)) (/ 1 (tan (neg x))))
(- (cot x) (recip x))
(neg (- (/ 1 (neg x)) (/ 1 (tan (neg x)))))
(- (recip x) (cot x))

Symmetry

(negabs x)

explain536.0ms (4.3%)

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
256	-	-	`(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))`
0	-	-	`x`
0	-	-	`(/.f64 #s(literal 1 binary64) (tan.f64 x))`
0	-	-	`(/.f64 #s(literal 1 binary64) x)`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(tan.f64 x)`

Results

320.0ms	252×	2	valid
133.0ms	96×	3	valid
35.0ms	162×	1	valid
0.0ms	2×	0	valid

Compiler

Compiled 51 to 20 computations (60.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 384.0ms

ival-tan: 320.0ms (83.4% of total)

ival-div: 35.0ms (9.1% of total)

backward-pass: 19.0ms (5% of total)

ival-sub: 8.0ms (2.1% of total)

const: 2.0ms (0.5% of total)

eval0.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	7.0%	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify21.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

156×	`fnmadd-define`
138×	`sum3-define`
112×	`fma-lowering-fma.f32`
112×	`fnmsub-define`
112×	`fmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	13	13
2	21	13
3	32	13
4	46	13
5	83	13
6	153	13
7	249	13
8	349	13
9	485	13
10	607	13
11	639	13
0	639	13

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize252.0ms (2%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)
✓	accuracy	100.0%	(tan.f64 x)
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (tan.f64 x))
✓	accuracy	7.1%	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Results

179.0ms	126×	2	valid
41.0ms	48×	3	valid
19.0ms	81×	1	valid
0.0ms	1×	0	valid

Compiler

Compiled 21 to 7 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 200.0ms

ival-tan: 173.0ms (86.4% of total)

ival-div: 13.0ms (6.5% of total)

backward-pass: 9.0ms (4.5% of total)

ival-sub: 4.0ms (2% of total)

const: 1.0ms (0.5% of total)

series4.0ms (0%)

Counts

4 → 48

Calls

Call 1

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

Outputs
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))>
#<alt (* -1 (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (* -1 (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (- (/ 1 x) (/ (cos x) (sin x)))>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (* -1/3 (pow x 2))) x)>
#<alt (/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x)>
#<alt (/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x)>
#<alt (/ (cos x) (sin x))>
#<alt (/ (cos x) (sin x))>
#<alt (/ (cos x) (sin x))>
#<alt (/ (cos x) (sin x))>
#<alt (/ (cos x) (sin x))>
#<alt (/ (cos x) (sin x))>
#<alt (/ (cos x) (sin x))>
#<alt (/ (cos x) (sin x))>
#<alt x>
#<alt (* x (+ 1 (* 1/3 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(- (/ 1 x) (/ 1 (tan x)))
1.0ms	x	@	-inf	(- (/ 1 x) (/ 1 (tan x)))
1.0ms	x	@	0	(- (/ 1 x) (/ 1 (tan x)))
0.0ms	x	@	inf	(/ 1 (tan x))
0.0ms	x	@	-inf	(/ 1 (tan x))

rewrite174.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

2244×	`/-lowering-/.f32`
2244×	`/-lowering-/.f64`
2150×	`-lowering-.f32`
2150×	`-lowering-.f64`
752×	`sum5-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	35	11
2	185	11
3	1040	11
0	8018	11

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 476

Calls

Call 1

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

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

simplify223.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

2512×	`-lowering-.f32`
2512×	`-lowering-.f64`
2470×	`sum3-define`
1924×	`+-lowering-+.f64`
1924×	`+-lowering-+.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	67	302
1	186	269
2	560	266
3	1806	266
4	2709	266
5	4422	266
6	6045	266
7	6589	266
0	8077	266

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

Inputs
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(* -1 (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ (+ 1 (* -1/3 (pow x 2))) x)
(/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x)
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
(/ (cos x) (sin x))
x
(* x (+ 1 (* 1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))

Outputs
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 2/945 (* 1/4725 (pow x 2))))))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/945 binary64) (.f64 (*.f64 x x) #s(literal 1/4725 binary64))))))))
(* -1 (/ (cos x) (sin x)))
(/.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(* -1 (/ (cos x) (sin x)))
(/.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(- (/ 1 x) (/ (cos x) (sin x)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) (sin.f64 x)))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (* -1/3 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/3 binary64)))) x)
(/ (+ 1 (* (pow x 2) (- (* -1/45 (pow x 2)) 1/3))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))))) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45)) 1/3))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))))))) x)
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
(/ (cos x) (sin x))
(/.f64 (cos.f64 x) (sin.f64 x))
x
(* x (+ 1 (* 1/3 (pow x 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 x x))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal 2/15 binary64)))))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 x (*.f64 x #s(literal 17/315 binary64)))))))))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))

eval154.0ms (1.2%)

Compiler: Compiled 7681 to 1240 computations (83.9% saved)

prune60.0ms (0.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	521	3	524
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	522	3	525

Accuracy

99.5%

Counts

525 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))))))
▶	99.5%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
▶	98.6%	(*.f64 #s(literal 1/3 binary64) x)

Status

Accuracy

Program

▶

99.5%

(*.f64 x (-.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/45 binary64) (*.f64 (*.f64 x x) #s(literal -2/945 binary64))))))

▶

99.5%

(*.f64 x (-.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) #s(literal -1/45 binary64))))

▶

98.6%

(*.f64 #s(literal 1/3 binary64) x)

Compiler

Compiled 30 to 20 computations (33.3% saved)

simplify154.0ms (1.2%)

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64))))
✓	cost-diff	(-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))))
✓	cost-diff	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))))))
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(.f64 (.f64 x x) #s(literal -1/45 binary64))
✓	cost-diff	(-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))
✓	cost-diff	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
✓	cost-diff	(*.f64 #s(literal 1/3 binary64) x)

Rules

2142×	`sum3-define`
2072×	`sum4-define`
1540×	`fnmsub-define`
1424×	`fmsub-define`
1386×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	77
1	42	73
2	131	69
3	417	69
4	1198	69
5	2396	69
6	5132	69
7	7879	69
0	8039	69

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* 1/3 x)
1/3
x
(* x (- 1/3 (* (* x x) -1/45)))
x
(- 1/3 (* (* x x) -1/45))
1/3
(* (* x x) -1/45)
(* x x)
-1/45
(* x (- 1/3 (* (* x x) (+ -1/45 (* (* x x) -2/945)))))
x
(- 1/3 (* (* x x) (+ -1/45 (* (* x x) -2/945))))
1/3
(* (* x x) (+ -1/45 (* (* x x) -2/945)))
(* x x)
(+ -1/45 (* (* x x) -2/945))
-1/45
(* (* x x) -2/945)
-2/945

Outputs
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
1/3
#s(literal 1/3 binary64)
x
(* x (- 1/3 (* (* x x) -1/45)))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal 1/45 binary64))))
x
(- 1/3 (* (* x x) -1/45))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 1/45 binary64)))
1/3
#s(literal 1/3 binary64)
(* (* x x) -1/45)
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(* x x)
(*.f64 x x)
-1/45
#s(literal -1/45 binary64)
(* x (- 1/3 (* (* x x) (+ -1/45 (* (* x x) -2/945)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64)))))))
x
(- 1/3 (* (* x x) (+ -1/45 (* (* x x) -2/945))))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64))))))
1/3
#s(literal 1/3 binary64)
(* (* x x) (+ -1/45 (* (* x x) -2/945)))
(.f64 (.f64 x x) (-.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64)))))
(* x x)
(*.f64 x x)
(+ -1/45 (* (* x x) -2/945))
(-.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64))))
-1/45
#s(literal -1/45 binary64)
(* (* x x) -2/945)
(.f64 x (.f64 x #s(literal -2/945 binary64)))
-2/945
#s(literal -2/945 binary64)

localize143.0ms (1.1%)

Localize:

Found 9 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))
✓	accuracy	99.7%	(.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64))))
✓	accuracy	99.7%	(.f64 (.f64 x x) #s(literal -2/945 binary64))
✓	accuracy	99.5%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))))))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))
✓	accuracy	99.7%	(.f64 (.f64 x x) #s(literal -1/45 binary64))
✓	accuracy	99.6%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
✓	accuracy	99.5%	(*.f64 #s(literal 1/3 binary64) x)

Results

122.0ms

256×

valid

Compiler

Compiled 92 to 15 computations (83.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 27.0ms

ival-mult: 12.0ms (44.8% of total)

...c/correct-round.rkt:119:19: 11.0ms (41.1% of total)

ival-sub: 3.0ms (11.2% of total)

ival-add: 1.0ms (3.7% of total)

const: 0.0ms (0% of total)

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

series8.0ms (0.1%)

Counts

10 → 120

Calls

Call 1

Inputs
#<alt (* 1/3 x)>
#<alt (* x (- 1/3 (* (* x x) -1/45)))>
#<alt (- 1/3 (* (* x x) -1/45))>
#<alt (* (* x x) -1/45)>
#<alt (* x x)>
#<alt (* x (- 1/3 (* (* x x) (+ -1/45 (* (* x x) -2/945)))))>
#<alt (- 1/3 (* (* x x) (+ -1/45 (* (* x x) -2/945))))>
#<alt (* (* x x) (+ -1/45 (* (* x x) -2/945)))>
#<alt (* (* x x) -2/945)>
#<alt (+ -1/45 (* (* x x) -2/945))>

Outputs
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* 1/45 (pow x 3))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* 1/45 (pow x 3))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt 1/3>
#<alt (+ 1/3 (* 1/45 (pow x 2)))>
#<alt (+ 1/3 (* 1/45 (pow x 2)))>
#<alt (+ 1/3 (* 1/45 (pow x 2)))>
#<alt (* 1/45 (pow x 2))>
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* 1/45 (pow x 2))>
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))>
#<alt (* 2/945 (pow x 5))>
#<alt (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* 2/945 (pow x 5))>
#<alt (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))>
#<alt 1/3>
#<alt (+ 1/3 (* 1/45 (pow x 2)))>
#<alt (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))>
#<alt (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))>
#<alt (* 2/945 (pow x 4))>
#<alt (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* 2/945 (pow x 4))>
#<alt (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -1/45 (pow x 2))>
#<alt (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45))>
#<alt (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45))>
#<alt (* (pow x 2) (- (* -2/945 (pow x 2)) 1/45))>
#<alt (* -2/945 (pow x 4))>
#<alt (* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -2/945 (pow x 4))>
#<alt (* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -2/945 (pow x 2))>
#<alt -1/45>
#<alt (- (* -2/945 (pow x 2)) 1/45)>
#<alt (- (* -2/945 (pow x 2)) 1/45)>
#<alt (- (* -2/945 (pow x 2)) 1/45)>
#<alt (* -2/945 (pow x 2))>
#<alt (* -1 (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -2/945 (pow x 2))>
#<alt (* -1 (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>

Calls

30 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(- 1/3 (* (* x x) (+ -1/45 (* (* x x) -2/945))))
1.0ms	x	@	0	(* 1/3 x)
1.0ms	x	@	inf	(* x (- 1/3 (* (* x x) (+ -1/45 (* (* x x) -2/945)))))
0.0ms	x	@	inf	(* x (- 1/3 (* (* x x) -1/45)))
0.0ms	x	@	0	(* x (- 1/3 (* (* x x) -1/45)))

rewrite133.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

2100×	`fnmadd-define`
1858×	`sum3-define`
1428×	`fma-define`
1410×	`fma-lowering-fma.f32`
1410×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	66
1	44	62
2	136	58
3	436	58
4	1673	58
5	5627	58
0	8590	58

Stop Event

1×	iter limit
1×	node limit

Counts

10 → 313

Calls

Call 1

Inputs
(* 1/3 x)
(* x (- 1/3 (* (* x x) -1/45)))
(- 1/3 (* (* x x) -1/45))
(* (* x x) -1/45)
(* x x)
(* x (- 1/3 (* (* x x) (+ -1/45 (* (* x x) -2/945)))))
(- 1/3 (* (* x x) (+ -1/45 (* (* x x) -2/945))))
(* (* x x) (+ -1/45 (* (* x x) -2/945)))
(* (* x x) -2/945)
(+ -1/45 (* (* x x) -2/945))

Outputs
(+.f64 (*.f64 #s(literal 1/3 binary64) x) #s(literal 0 binary64))
(neg.f64 (*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/3 binary64)))
(neg.f64 (*.f64 #s(literal 1/3 binary64) (-.f64 #s(literal 0 binary64) x)))
(*.f64 #s(literal 1/3 binary64) x)
(*.f64 x #s(literal 1/3 binary64))
(+.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 x (.f64 x (.f64 x #s(literal 1/45 binary64)))))
(+.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))) (+.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/45 binary64)))) (.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64))))))
(+.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/45 binary64)))) (.f64 #s(literal 1/3 binary64) x))
(+.f64 #s(literal 0 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64))))))
(-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))))
(-.f64 #s(literal 0 binary64) (.f64 x (+.f64 (.f64 x (*.f64 x #s(literal -1/45 binary64))) #s(literal -1/3 binary64))))
(-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 #s(literal -1/3 binary64) x)))
(fma.f64 #s(literal 1/3 binary64) x (.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(fma.f64 x #s(literal 1/3 binary64) (.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(fma.f64 x (.f64 x (.f64 x #s(literal 1/45 binary64))) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x x) (.f64 x #s(literal 1/45 binary64)) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 #s(literal -1/45 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (-.f64 #s(literal 0 binary64) x) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) x (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x #s(literal -1/45 binary64)) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x #s(literal -1/45 binary64)) (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 #s(literal 1/3 binary64) x))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x (.f64 x #s(literal -1/45 binary64))) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x x)) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x #s(literal 1/45 binary64)) (.f64 x x) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))) #s(literal -1 binary64) (.f64 #s(literal 1/3 binary64) x))
(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) #s(literal -1/45 binary64) (*.f64 #s(literal 1/3 binary64) x))
(neg.f64 (.f64 x (+.f64 (.f64 x (*.f64 x #s(literal -1/45 binary64))) #s(literal -1/3 binary64))))
(neg.f64 (+.f64 (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 #s(literal -1/3 binary64) x)))
(neg.f64 (.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64))))))
(neg.f64 (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))) (-.f64 #s(literal 0 binary64) x)))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))) x)
(.f64 #s(literal -1 binary64) (.f64 x (+.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) #s(literal -1/3 binary64))))
(.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (.f64 x (*.f64 x #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))
(.f64 (+.f64 (.f64 x (*.f64 x #s(literal -1/45 binary64))) #s(literal -1/3 binary64)) (-.f64 #s(literal 0 binary64) x))
(+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))
(+.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))) #s(literal 0 binary64))
(+.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) #s(literal 1/3 binary64))
(+.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))))
(-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))))
(-.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64))
(-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) #s(literal -1/3 binary64)))
(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/45 binary64) #s(literal 1/3 binary64))
(fma.f64 #s(literal -1/45 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x)) #s(literal 1/3 binary64))
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(fma.f64 #s(literal 2/945 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x)) #s(literal -1/45 binary64))
(fma.f64 (.f64 x (.f64 x #s(literal 2/945 binary64))) #s(literal -1 binary64) #s(literal -1/45 binary64))
(fma.f64 (*.f64 x #s(literal 2/945 binary64)) (-.f64 #s(literal 0 binary64) x) #s(literal -1/45 binary64))

simplify241.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

2532×	`-lowering-.f32`
2532×	`-lowering-.f64`
2240×	`fma-lowering-fma.f32`
2240×	`fma-lowering-fma.f64`
1718×	`/-lowering-/.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	55	782
1	171	622
2	540	622
3	1499	618
4	3155	616
5	7550	616
0	8423	616

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

Inputs
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
1/3
(+ 1/3 (* 1/45 (pow x 2)))
(+ 1/3 (* 1/45 (pow x 2)))
(+ 1/3 (* 1/45 (pow x 2)))
(* 1/45 (pow x 2))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 2))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* 2/945 (pow x 5))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* 2/945 (pow x 5))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
1/3
(+ 1/3 (* 1/45 (pow x 2)))
(+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))
(+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))
(* 2/945 (pow x 4))
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* 2/945 (pow x 4))
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* -1/45 (pow x 2))
(* (pow x 2) (- (* -2/945 (pow x 2)) 1/45))
(* (pow x 2) (- (* -2/945 (pow x 2)) 1/45))
(* (pow x 2) (- (* -2/945 (pow x 2)) 1/45))
(* -2/945 (pow x 4))
(* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -2/945 (pow x 4))
(* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
(* -2/945 (pow x 2))
-1/45
(- (* -2/945 (pow x 2)) 1/45)
(- (* -2/945 (pow x 2)) 1/45)
(- (* -2/945 (pow x 2)) 1/45)
(* -2/945 (pow x 2))
(* -1 (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -1 (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -1 (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -2/945 (pow x 2))
(* -1 (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -1 (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -1 (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))

Outputs
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* 1/45 (pow x 3))
(.f64 x (.f64 #s(literal 1/45 binary64) (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* 1/45 (pow x 3))
(.f64 x (.f64 #s(literal 1/45 binary64) (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* 1/45 (pow x 2)))
(+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (.f64 x x)))
(+ 1/3 (* 1/45 (pow x 2)))
(+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (.f64 x x)))
(+ 1/3 (* 1/45 (pow x 2)))
(+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (.f64 x x)))
(* 1/45 (pow x 2))
(.f64 #s(literal 1/45 binary64) (.f64 x x))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (.f64 x x)))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (.f64 x x)))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (.f64 x x)))
(* 1/45 (pow x 2))
(.f64 #s(literal 1/45 binary64) (.f64 x x))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (.f64 x x)))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (.f64 x x)))
(* (pow x 2) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (.f64 x x)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 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)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))))
(* 2/945 (pow x 5))
(.f64 x (.f64 #s(literal 2/945 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64)))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))))
(* 2/945 (pow x 5))
(.f64 x (.f64 #s(literal 2/945 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))))
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* 1/45 (pow x 2)))
(+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (.f64 x x)))
(+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64)))))
(+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2)))))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64)))))
(* 2/945 (pow x 4))
(.f64 #s(literal 2/945 binary64) (.f64 x (.f64 x (.f64 x x))))
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64)))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64)))))
(* 2/945 (pow x 4))
(.f64 #s(literal 2/945 binary64) (.f64 x (.f64 x (.f64 x x))))
(* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64)))))
(* (pow x 4) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64)))))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* (pow x 2) (- (* -2/945 (pow x 2)) 1/45))
(.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64))))))
(* (pow x 2) (- (* -2/945 (pow x 2)) 1/45))
(.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64))))))
(* (pow x 2) (- (* -2/945 (pow x 2)) 1/45))
(.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64))))))
(* -2/945 (pow x 4))
(.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal -2/945 binary64)))
(* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64))))))
(* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64))))))
(* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64))))))
(* -2/945 (pow x 4))
(.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal -2/945 binary64)))
(* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64))))))
(* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64))))))
(* -1 (* (pow x 4) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64))))))
(* -2/945 (pow x 2))
(.f64 x (.f64 x #s(literal -2/945 binary64)))
(* -2/945 (pow x 2))
(.f64 x (.f64 x #s(literal -2/945 binary64)))
(* -2/945 (pow x 2))
(.f64 x (.f64 x #s(literal -2/945 binary64)))
(* -2/945 (pow x 2))
(.f64 x (.f64 x #s(literal -2/945 binary64)))
(* -2/945 (pow x 2))
(.f64 x (.f64 x #s(literal -2/945 binary64)))
(* -2/945 (pow x 2))
(.f64 x (.f64 x #s(literal -2/945 binary64)))
(* -2/945 (pow x 2))
(.f64 x (.f64 x #s(literal -2/945 binary64)))
(* -2/945 (pow x 2))
(.f64 x (.f64 x #s(literal -2/945 binary64)))
(* -2/945 (pow x 2))
(.f64 x (.f64 x #s(literal -2/945 binary64)))
(* -2/945 (pow x 2))
(.f64 x (.f64 x #s(literal -2/945 binary64)))
(* -2/945 (pow x 2))
(.f64 x (.f64 x #s(literal -2/945 binary64)))
(* -2/945 (pow x 2))
(.f64 x (.f64 x #s(literal -2/945 binary64)))
-1/45
#s(literal -1/45 binary64)
(- (* -2/945 (pow x 2)) 1/45)
(+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64))))
(- (* -2/945 (pow x 2)) 1/45)
(+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64))))
(- (* -2/945 (pow x 2)) 1/45)
(+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64))))
(* -2/945 (pow x 2))
(.f64 x (.f64 x #s(literal -2/945 binary64)))
(* -1 (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64))))
(* -1 (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64))))
(* -1 (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64))))
(* -2/945 (pow x 2))
(.f64 x (.f64 x #s(literal -2/945 binary64)))
(* -1 (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64))))
(* -1 (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64))))
(* -1 (* (pow x 2) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64))))

eval70.0ms (0.6%)

Compiler: Compiled 7425 to 921 computations (87.6% saved)

prune64.0ms (0.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	497	2	499
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	497	5	502

Accuracy

99.6%

Counts

502 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 (.f64 x x) (.f64 x (-.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64)))))))
▶	99.5%	(-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))))
✓	99.5%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))))))
✓	99.5%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
✓	98.6%	(*.f64 #s(literal 1/3 binary64) x)

Compiler

Compiled 60 to 40 computations (33.3% saved)

simplify155.0ms (1.2%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (.f64 x x) (.f64 x (-.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64))))))
✓	cost-diff	0	(*.f64 #s(literal 1/3 binary64) x)
✓	cost-diff	128	(-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 (.f64 x x) (.f64 x (-.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64)))))))
✓	cost-diff	0	(.f64 x (.f64 x #s(literal -1/45 binary64)))
✓	cost-diff	0	(.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64))))
✓	cost-diff	0	(*.f64 #s(literal 1/3 binary64) x)
✓	cost-diff	128	(-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))))

Rules

2352×	`sum3-define`
2336×	`sum4-define`
2134×	`fnmadd-define`
1400×	`fma-define`
1384×	`sum5-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	16	83
1	50	81
2	147	75
3	451	73
4	1562	73
5	4011	73
6	7523	73
0	8547	73

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(- (* 1/3 x) (* x (* x (* x -1/45))))
(* 1/3 x)
1/3
x
(* x (* x (* x -1/45)))
(* x (* x -1/45))
(* x -1/45)
-1/45
(- (* 1/3 x) (* (* x x) (* x (- -1/45 (* x (* x 2/945))))))
(* 1/3 x)
1/3
x
(* (* x x) (* x (- -1/45 (* x (* x 2/945)))))
(* x x)
(* x (- -1/45 (* x (* x 2/945))))
(- -1/45 (* x (* x 2/945)))
-1/45
(* x (* x 2/945))
(* x 2/945)
2/945

Outputs
(- (* 1/3 x) (* x (* x (* x -1/45))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal 1/45 binary64))))
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
1/3
#s(literal 1/3 binary64)
x
(* x (* x (* x -1/45)))
(.f64 x (.f64 #s(literal -1/45 binary64) (*.f64 x x)))
(* x (* x -1/45))
(.f64 #s(literal -1/45 binary64) (.f64 x x))
(* x -1/45)
(*.f64 x #s(literal -1/45 binary64))
-1/45
#s(literal -1/45 binary64)
(- (* 1/3 x) (* (* x x) (* x (- -1/45 (* x (* x 2/945))))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 (.f64 x (*.f64 x #s(literal 2/945 binary64))) #s(literal 1/45 binary64))))))
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
1/3
#s(literal 1/3 binary64)
x
(* (* x x) (* x (- -1/45 (* x (* x 2/945)))))
(.f64 (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64))) (.f64 x (*.f64 x x)))
(* x x)
(*.f64 x x)
(* x (- -1/45 (* x (* x 2/945))))
(.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))))
(- -1/45 (* x (* x 2/945)))
(+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))
-1/45
#s(literal -1/45 binary64)
(* x (* x 2/945))
(.f64 x (.f64 x #s(literal 2/945 binary64)))
(* x 2/945)
(*.f64 x #s(literal 2/945 binary64))
2/945
#s(literal 2/945 binary64)

localize94.0ms (0.8%)

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(.f64 x (.f64 x #s(literal 2/945 binary64)))
✓	accuracy	99.7%	(.f64 x (-.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64)))))
✓	accuracy	99.5%	(*.f64 #s(literal 1/3 binary64) x)
✓	accuracy	99.3%	(*.f64 x #s(literal 2/945 binary64))
✓	accuracy	99.8%	(.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64))))
✓	accuracy	99.7%	(.f64 x (.f64 x #s(literal -1/45 binary64)))
✓	accuracy	99.7%	(*.f64 x #s(literal -1/45 binary64))
✓	accuracy	99.5%	(*.f64 #s(literal 1/3 binary64) x)

Results

71.0ms

256×

valid

Compiler

Compiled 98 to 17 computations (82.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 34.0ms

ival-mult: 19.0ms (56% of total)

...c/correct-round.rkt:119:19: 11.0ms (32.4% of total)

ival-sub: 3.0ms (8.8% of total)

const: 0.0ms (0% of total)

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

series377.0ms (3%)

Counts

11 → 132

Calls

Call 1

Inputs
#<alt (- (* 1/3 x) (* x (* x (* x -1/45))))>
#<alt (* 1/3 x)>
#<alt (* x (* x (* x -1/45)))>
#<alt (* x (* x -1/45))>
#<alt (- (* 1/3 x) (* (* x x) (* x (- -1/45 (* x (* x 2/945))))))>
#<alt (* (* x x) (* x (- -1/45 (* x (* x 2/945)))))>
#<alt (* x x)>
#<alt (* x -1/45)>
#<alt (* x 2/945)>
#<alt (* x (- -1/45 (* x (* x 2/945))))>
#<alt (* x (* x 2/945))>

Outputs
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* 1/45 (pow x 3))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* 1/45 (pow x 3))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))>
#<alt (* 2/945 (pow x 5))>
#<alt (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* 2/945 (pow x 5))>
#<alt (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))>
#<alt (* -1/45 (pow x 3))>
#<alt (* (pow x 3) (- (* -2/945 (pow x 2)) 1/45))>
#<alt (* (pow x 3) (- (* -2/945 (pow x 2)) 1/45))>
#<alt (* (pow x 3) (- (* -2/945 (pow x 2)) 1/45))>
#<alt (* -2/945 (pow x 5))>
#<alt (* -1 (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -2/945 (pow x 5))>
#<alt (* -1 (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* -1/45 x)>
#<alt (* 2/945 x)>
#<alt (* 2/945 x)>
#<alt (* 2/945 x)>
#<alt (* 2/945 x)>
#<alt (* 2/945 x)>
#<alt (* 2/945 x)>
#<alt (* 2/945 x)>
#<alt (* 2/945 x)>
#<alt (* 2/945 x)>
#<alt (* 2/945 x)>
#<alt (* 2/945 x)>
#<alt (* 2/945 x)>
#<alt (* -1/45 x)>
#<alt (* x (- (* -2/945 (pow x 2)) 1/45))>
#<alt (* x (- (* -2/945 (pow x 2)) 1/45))>
#<alt (* x (- (* -2/945 (pow x 2)) 1/45))>
#<alt (* -2/945 (pow x 3))>
#<alt (* -1 (* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -2/945 (pow x 3))>
#<alt (* -1 (* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))>
#<alt (* 2/945 (pow x 2))>
#<alt (* 2/945 (pow x 2))>
#<alt (* 2/945 (pow x 2))>
#<alt (* 2/945 (pow x 2))>
#<alt (* 2/945 (pow x 2))>
#<alt (* 2/945 (pow x 2))>
#<alt (* 2/945 (pow x 2))>
#<alt (* 2/945 (pow x 2))>
#<alt (* 2/945 (pow x 2))>
#<alt (* 2/945 (pow x 2))>
#<alt (* 2/945 (pow x 2))>
#<alt (* 2/945 (pow x 2))>

Calls

33 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(- (* 1/3 x) (* x (* x (* x -1/45))))
0.0ms	x	@	-inf	(- (* 1/3 x) (* (* x x) (* x (- -1/45 (* x (* x 2/945))))))
0.0ms	x	@	-inf	(* x (* x (* x -1/45)))
0.0ms	x	@	0	(* x (- -1/45 (* x (* x 2/945))))
0.0ms	x	@	0	(- (* 1/3 x) (* x (* x (* x -1/45))))

rewrite166.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

2370×	`fma-lowering-fma.f32`
2370×	`fma-lowering-fma.f64`
1770×	`fmm-def`
1672×	`prod-diff`
1474×	`fnmsub-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	16	67
1	64	63
2	235	60
3	1244	58
4	7178	58
0	8725	58

Stop Event

1×	iter limit
1×	node limit

Counts

11 → 337

Calls

Call 1

Inputs
(- (* 1/3 x) (* x (* x (* x -1/45))))
(* 1/3 x)
(* x (* x (* x -1/45)))
(* x (* x -1/45))
(- (* 1/3 x) (* (* x x) (* x (- -1/45 (* x (* x 2/945))))))
(* (* x x) (* x (- -1/45 (* x (* x 2/945)))))
(* x x)
(* x -1/45)
(* x 2/945)
(* x (- -1/45 (* x (* x 2/945))))
(* x (* x 2/945))

Outputs
(+.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 x (.f64 (.f64 x x) #s(literal 1/45 binary64))))
(+.f64 (.f64 x (.f64 #s(literal -1/45 binary64) (.f64 x x))) (+.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 (.f64 x (*.f64 x x)) #s(literal 2/45 binary64))))
(+.f64 #s(literal 0 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal 1/45 binary64)))))
(+.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal 1/45 binary64)))) #s(literal 0 binary64))
(+.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/45 binary64))) (.f64 #s(literal 1/3 binary64) x))
(+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 2/45 binary64)) (+.f64 (.f64 x (.f64 #s(literal -1/45 binary64) (.f64 x x))) (*.f64 #s(literal 1/3 binary64) x)))
(+.f64 (+.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 (.f64 x (.f64 x x)) #s(literal 2/45 binary64))) (.f64 x (.f64 #s(literal -1/45 binary64) (*.f64 x x))))
(+.f64 (+.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 (.f64 x (.f64 x x)) #s(literal 2/45 binary64))) (+.f64 (.f64 x (.f64 #s(literal -1/45 binary64) (*.f64 x x))) #s(literal 0 binary64)))
(-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 x (.f64 #s(literal -1/45 binary64) (.f64 x x))))
(-.f64 (.f64 #s(literal 1/3 binary64) x) (+.f64 (.f64 x (.f64 #s(literal -1/45 binary64) (.f64 x x))) #s(literal 0 binary64)))
(-.f64 #s(literal 0 binary64) (.f64 x (-.f64 (.f64 #s(literal -1/45 binary64) (*.f64 x x)) #s(literal 1/3 binary64))))
(-.f64 #s(literal 0 binary64) (-.f64 (.f64 x (-.f64 (.f64 #s(literal -1/45 binary64) (*.f64 x x)) #s(literal 1/3 binary64))) #s(literal 0 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal 1/45 binary64))))))
(-.f64 #s(literal 0 binary64) (-.f64 (+.f64 (.f64 x (.f64 #s(literal -1/45 binary64) (.f64 x x))) #s(literal 0 binary64)) (.f64 #s(literal 1/3 binary64) x)))
(-.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal 1/45 binary64)))) #s(literal 0 binary64))
(fma.f64 #s(literal 1/3 binary64) x (.f64 x (.f64 (*.f64 x x) #s(literal 1/45 binary64))))
(fma.f64 x #s(literal 1/3 binary64) (.f64 x (.f64 (*.f64 x x) #s(literal 1/45 binary64))))
(fma.f64 x (.f64 (.f64 x x) #s(literal 1/45 binary64)) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 1/45 binary64))) #s(literal 0 binary64))
(fma.f64 x (.f64 (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal 1/45 binary64)))))
(fma.f64 x (+.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 1/45 binary64))) (.f64 (.f64 x x) #s(literal 0 binary64))) #s(literal 0 binary64))
(fma.f64 x (+.f64 (.f64 (.f64 x x) #s(literal 0 binary64)) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 1/45 binary64)))) #s(literal 0 binary64))
(fma.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 0 binary64))) (.f64 x (.f64 (*.f64 x x) #s(literal 1/45 binary64))))
(fma.f64 x (+.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64))))) (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64))))))) (.f64 x (.f64 (*.f64 x x) #s(literal 1/45 binary64))))
(fma.f64 x (+.f64 (.f64 #s(literal -1/45 binary64) (.f64 x x)) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 1/45 binary64)))) (.f64 x (.f64 (*.f64 x x) #s(literal 1/45 binary64))))
(fma.f64 x (+.f64 (.f64 (.f64 x x) #s(literal 0 binary64)) #s(literal 1/3 binary64)) (.f64 x (.f64 (*.f64 x x) #s(literal 1/45 binary64))))
(fma.f64 #s(literal -1/45 binary64) #s(literal 0 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal 1/45 binary64)))))
(fma.f64 #s(literal -1/45 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x #s(literal -1/45 binary64)) (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x #s(literal -1/45 binary64)) (.f64 x (.f64 #s(literal 0 binary64) x)) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 1/45 binary64)))))
(fma.f64 (.f64 #s(literal -1/45 binary64) (.f64 x x)) (-.f64 #s(literal 0 binary64) x) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 #s(literal -1/45 binary64) (.f64 x x)) (.f64 #s(literal 0 binary64) x) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 1/45 binary64)))))
(fma.f64 (.f64 x (.f64 #s(literal -1/45 binary64) (.f64 x x))) #s(literal -1 binary64) (.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x x) (.f64 x #s(literal 1/45 binary64)) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x x) (.f64 x #s(literal 0 binary64)) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal 1/45 binary64)))))
(fma.f64 #s(literal 0 binary64) (.f64 x (.f64 #s(literal -1/45 binary64) (.f64 x x))) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 1/45 binary64)))))
(fma.f64 (.f64 (.f64 x x) #s(literal 1/45 binary64)) x (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 #s(literal 2 binary64) #s(literal 0 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal 1/45 binary64)))))
(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x #s(literal -1/45 binary64)) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (.f64 #s(literal -1/45 binary64) (.f64 x x)) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x #s(literal 1/45 binary64)) (.f64 x x) (*.f64 #s(literal 1/3 binary64) x))
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(fma.f64 (.f64 x x) (.f64 x #s(literal 0 binary64)) (.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))))))))
(fma.f64 (.f64 x x) (+.f64 (.f64 x #s(literal 0 binary64)) (.f64 x #s(literal 1/45 binary64))) (neg.f64 (-.f64 (.f64 x (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -2/945 binary64))))) (*.f64 #s(literal 1/3 binary64) x))))
(fma.f64 (.f64 x x) (+.f64 (.f64 x #s(literal 1/45 binary64)) (.f64 x #s(literal 0 binary64))) (neg.f64 (-.f64 (.f64 x (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -2/945 binary64))))) (*.f64 #s(literal 1/3 binary64) x))))
(fma.f64 (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64))) #s(literal 0 binary64) (.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))))))))
(fma.f64 (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64))) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))) (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))) (.f64 x (.f64 #s(literal 0 binary64) x)) (.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64))))))))
(fma.f64 (.f64 x (.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))))) #s(literal -1 binary64) (.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x (+.f64 (.f64 x (.f64 x #s(literal 2/945 binary64))) #s(literal 1/45 binary64))) (.f64 x x) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))))) (.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64))))))))
(fma.f64 (.f64 (.f64 x x) #s(literal 1/45 binary64)) x (neg.f64 (-.f64 (.f64 x (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -2/945 binary64))))) (.f64 #s(literal 1/3 binary64) x))))
(fma.f64 #s(literal 2 binary64) #s(literal 0 binary64) (.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))))))))
(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x #s(literal -1/45 binary64)) (neg.f64 (-.f64 (.f64 x (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -2/945 binary64))))) (.f64 #s(literal 1/3 binary64) x))))
(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (.f64 #s(literal -1/45 binary64) (.f64 x x)) (neg.f64 (-.f64 (.f64 x (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -2/945 binary64))))) (.f64 #s(literal 1/3 binary64) x))))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64))))) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 0 binary64) (.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))))))))
(fma.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 x (.f64 x #s(literal 2/945 binary64))) #s(literal 1/45 binary64)) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64) (neg.f64 (-.f64 (.f64 x (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -2/945 binary64))))) (.f64 #s(literal 1/3 binary64) x))))
(fma.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64))))) (-.f64 #s(literal 0 binary64) x) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64))))) (.f64 #s(literal 0 binary64) x) (.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64))))))))
(fma.f64 (.f64 x #s(literal 1/45 binary64)) (.f64 x x) (neg.f64 (-.f64 (.f64 x (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -2/945 binary64))))) (.f64 #s(literal 1/3 binary64) x))))
(fma.f64 (.f64 x (.f64 x (+.f64 (.f64 x (.f64 x #s(literal 2/945 binary64))) #s(literal 1/45 binary64)))) x (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (+.f64 (.f64 x (.f64 x #s(literal 2/945 binary64))) #s(literal 1/45 binary64)) (.f64 x (.f64 x x)) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 #s(literal -1 binary64) (.f64 x (.f64 #s(literal -1/45 binary64) (.f64 x x))) (neg.f64 (-.f64 (.f64 x (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -2/945 binary64))))) (*.f64 #s(literal 1/3 binary64) x))))
(fma.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))))) (.f64 #s(literal 1/3 binary64) x))
(fma.f64 #s(literal -1 binary64) (+.f64 (.f64 x (.f64 #s(literal -1/45 binary64) (.f64 x x))) #s(literal 0 binary64)) (neg.f64 (-.f64 (.f64 x (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -2/945 binary64))))) (*.f64 #s(literal 1/3 binary64) x))))
(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) #s(literal -1/45 binary64) (neg.f64 (-.f64 (.f64 x (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -2/945 binary64))))) (.f64 #s(literal 1/3 binary64) x))))
(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64))) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x x)) (neg.f64 (-.f64 (.f64 x (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -2/945 binary64))))) (.f64 #s(literal 1/3 binary64) x))))
(fma.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 1/45 binary64))) x (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x #s(literal 2/945 binary64))))))
(fma.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 1/45 binary64))) x (neg.f64 (.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal 0 binary64)))))
(fma.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))))) x #s(literal 0 binary64))
(neg.f64 (.f64 x (-.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))))) #s(literal 1/3 binary64))))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64)))))))
(.f64 x (+.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))))) (.f64 (*.f64 x x) #s(literal 0 binary64))))
(.f64 x (+.f64 (.f64 (.f64 x x) #s(literal 0 binary64)) (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))))))))
(.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64)))))) x)
(+.f64 (.f64 x (.f64 #s(literal -1/45 binary64) (.f64 x x))) (.f64 x (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -2/945 binary64))))))
(+.f64 (.f64 x (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -2/945 binary64))))) (.f64 x (.f64 #s(literal -1/45 binary64) (.f64 x x))))
(-.f64 (.f64 x (.f64 #s(literal -1/45 binary64) (.f64 x x))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x #s(literal 2/945 binary64))))))
(fma.f64 x (.f64 #s(literal -1/45 binary64) (.f64 x x)) (.f64 x (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal -2/945 binary64))))))
(fma.f64 x (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -2/945 binary64)))) (.f64 x (.f64 #s(literal -1/45 binary64) (*.f64 x x))))
(fma.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal -2/945 binary64))))))
(fma.f64 (.f64 x #s(literal -1/45 binary64)) (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal -2/945 binary64))))))
(fma.f64 (.f64 #s(literal -1/45 binary64) (.f64 x x)) x (.f64 x (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal -2/945 binary64))))))
(fma.f64 (.f64 x x) (.f64 x #s(literal -1/45 binary64)) (.f64 x (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal -2/945 binary64))))))
(fma.f64 (.f64 x x) (.f64 x (.f64 (.f64 x x) #s(literal -2/945 binary64))) (.f64 x (.f64 #s(literal -1/45 binary64) (*.f64 x x))))
(fma.f64 (.f64 x #s(literal 2/945 binary64)) (.f64 x (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) (.f64 x (.f64 #s(literal -1/45 binary64) (*.f64 x x))))
(fma.f64 (.f64 (.f64 x x) #s(literal -2/945 binary64)) (.f64 x (.f64 x x)) (.f64 x (.f64 #s(literal -1/45 binary64) (*.f64 x x))))
(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x (.f64 x (.f64 x #s(literal 2/945 binary64)))) (.f64 x (.f64 #s(literal -1/45 binary64) (*.f64 x x))))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64)))) (.f64 x (.f64 #s(literal -1/45 binary64) (*.f64 x x))))
(fma.f64 (.f64 x (.f64 x x)) #s(literal -1/45 binary64) (.f64 x (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal -2/945 binary64))))))
(fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) #s(literal -2/945 binary64)) (.f64 x (.f64 #s(literal -1/45 binary64) (*.f64 x x))))
(fma.f64 #s(literal -1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x #s(literal 2/945 binary64))))) (.f64 x (.f64 #s(literal -1/45 binary64) (.f64 x x))))
(fma.f64 (.f64 x #s(literal -2/945 binary64)) (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 #s(literal -1/45 binary64) (*.f64 x x))))
(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x #s(literal 2/945 binary64))) (.f64 x (.f64 #s(literal -1/45 binary64) (*.f64 x x))))
(fma.f64 (.f64 x (.f64 (.f64 x x) #s(literal -2/945 binary64))) (.f64 x x) (.f64 x (.f64 #s(literal -1/45 binary64) (*.f64 x x))))
(fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 2/945 binary64)))) (-.f64 #s(literal 0 binary64) x) (.f64 x (.f64 #s(literal -1/45 binary64) (*.f64 x x))))
(fma.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -2/945 binary64)))) x (.f64 x (.f64 #s(literal -1/45 binary64) (*.f64 x x))))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x #s(literal -2/945 binary64)) (.f64 x (.f64 #s(literal -1/45 binary64) (*.f64 x x))))
(fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x x))) #s(literal -2/945 binary64) (.f64 x (.f64 #s(literal -1/45 binary64) (*.f64 x x))))
(fma.f64 (.f64 x (.f64 x (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))))) #s(literal 2/945 binary64) (.f64 x (.f64 #s(literal -1/45 binary64) (*.f64 x x))))
(fma.f64 (.f64 x (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) (.f64 x #s(literal 2/945 binary64)) (.f64 x (.f64 #s(literal -1/45 binary64) (*.f64 x x))))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))))))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64)))))
(.f64 (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64))) (.f64 x (*.f64 x x)))
(.f64 (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))) (*.f64 x x))
(.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))))
(.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))))) x)
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(exp.f64 (+.f64 (log.f64 x) (log.f64 x)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(*.f64 x x)
(*.f64 x #s(literal -1/45 binary64))
(*.f64 #s(literal -1/45 binary64) x)
(*.f64 x #s(literal 2/945 binary64))
(*.f64 #s(literal 2/945 binary64) x)
(+.f64 (.f64 x #s(literal -1/45 binary64)) (.f64 x (.f64 (.f64 x x) #s(literal -2/945 binary64))))
(+.f64 (.f64 x (.f64 (.f64 x x) #s(literal -2/945 binary64))) (.f64 x #s(literal -1/45 binary64)))
(-.f64 (.f64 x #s(literal -1/45 binary64)) (.f64 x (.f64 x (.f64 x #s(literal 2/945 binary64)))))
(fma.f64 x #s(literal -1/45 binary64) (.f64 x (.f64 (*.f64 x x) #s(literal -2/945 binary64))))
(fma.f64 x (.f64 (.f64 x x) #s(literal -2/945 binary64)) (*.f64 x #s(literal -1/45 binary64)))
(fma.f64 #s(literal -1/45 binary64) x (.f64 x (.f64 (*.f64 x x) #s(literal -2/945 binary64))))
(fma.f64 (.f64 x x) (.f64 x #s(literal -2/945 binary64)) (*.f64 x #s(literal -1/45 binary64)))
(fma.f64 (.f64 x #s(literal 2/945 binary64)) (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 x #s(literal -1/45 binary64)))
(fma.f64 (.f64 x (.f64 x #s(literal 2/945 binary64))) (-.f64 #s(literal 0 binary64) x) (*.f64 x #s(literal -1/45 binary64)))
(fma.f64 (.f64 (.f64 x x) #s(literal -2/945 binary64)) x (*.f64 x #s(literal -1/45 binary64)))
(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x #s(literal 2/945 binary64)) (*.f64 x #s(literal -1/45 binary64)))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x (.f64 x #s(literal 2/945 binary64))) (*.f64 x #s(literal -1/45 binary64)))
(fma.f64 (.f64 x (.f64 x x)) #s(literal -2/945 binary64) (*.f64 x #s(literal -1/45 binary64)))
(fma.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x #s(literal 2/945 binary64)))) (.f64 x #s(literal -1/45 binary64)))
(fma.f64 (.f64 x #s(literal -2/945 binary64)) (.f64 x x) (*.f64 x #s(literal -1/45 binary64)))
(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))) #s(literal 2/945 binary64) (*.f64 x #s(literal -1/45 binary64)))
(.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))))
(.f64 (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))) x)
(+.f64 #s(literal 0 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64))))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) #s(literal -2/945 binary64)))
(neg.f64 (.f64 (.f64 x x) #s(literal -2/945 binary64)))
(.f64 x (.f64 x #s(literal 2/945 binary64)))
(.f64 x (neg.f64 (.f64 x #s(literal -2/945 binary64))))
(.f64 (.f64 x x) #s(literal 2/945 binary64))
(.f64 #s(literal 2/945 binary64) (.f64 x x))
(.f64 #s(literal 2/945 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 x x))))
(.f64 (.f64 x #s(literal 2/945 binary64)) x)
(.f64 (.f64 x #s(literal 2/945 binary64)) (neg.f64 (-.f64 #s(literal 0 binary64) x)))
(.f64 (.f64 x (*.f64 x #s(literal 2/945 binary64))) #s(literal 1 binary64))
(.f64 (.f64 (*.f64 x x) #s(literal -2/945 binary64)) #s(literal -1 binary64))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) #s(literal -2/945 binary64))
(.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x #s(literal -2/945 binary64)))
(.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 2/945 binary64))))
(.f64 #s(literal -1 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64)))
(.f64 (.f64 x #s(literal -2/945 binary64)) (-.f64 #s(literal 0 binary64) x))
(.f64 #s(literal -2/945 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(.f64 (neg.f64 (.f64 x #s(literal -2/945 binary64))) x)
(.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x)) (.f64 x #s(literal 2/945 binary64)))
(.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 x x))) #s(literal 2/945 binary64))

simplify218.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

2298×	`-lowering-.f32`
2298×	`-lowering-.f64`
1596×	`fma-define`
1428×	`/-lowering-/.f32`
1428×	`/-lowering-/.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	56	742
1	158	642
2	500	642
3	1414	642
4	4000	640
0	8113	640

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 132

Calls

Call 1

Inputs
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(* 2/945 (pow x 5))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(* 2/945 (pow x 5))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(* -1/45 (pow x 3))
(* (pow x 3) (- (* -2/945 (pow x 2)) 1/45))
(* (pow x 3) (- (* -2/945 (pow x 2)) 1/45))
(* (pow x 3) (- (* -2/945 (pow x 2)) 1/45))
(* -2/945 (pow x 5))
(* -1 (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -1 (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -1 (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -2/945 (pow x 5))
(* -1 (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -1 (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -1 (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* -1/45 x)
(* 2/945 x)
(* 2/945 x)
(* 2/945 x)
(* 2/945 x)
(* 2/945 x)
(* 2/945 x)
(* 2/945 x)
(* 2/945 x)
(* 2/945 x)
(* 2/945 x)
(* 2/945 x)
(* 2/945 x)
(* -1/45 x)
(* x (- (* -2/945 (pow x 2)) 1/45))
(* x (- (* -2/945 (pow x 2)) 1/45))
(* x (- (* -2/945 (pow x 2)) 1/45))
(* -2/945 (pow x 3))
(* -1 (* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -2/945 (pow x 3))
(* -1 (* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(* 2/945 (pow x 2))
(* 2/945 (pow x 2))
(* 2/945 (pow x 2))
(* 2/945 (pow x 2))
(* 2/945 (pow x 2))
(* 2/945 (pow x 2))
(* 2/945 (pow x 2))
(* 2/945 (pow x 2))
(* 2/945 (pow x 2))
(* 2/945 (pow x 2))
(* 2/945 (pow x 2))
(* 2/945 (pow x 2))

Outputs
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* 1/45 (pow x 3))
(.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* 1/45 (pow x 3))
(.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* -1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(* -1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(* -1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(* -1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(* -1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(* -1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(* -1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(* -1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(* -1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(* -1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(* -1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(* -1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (*.f64 x x))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64)))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* 2/945 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64)))))))
(* 2/945 (pow x 5))
(.f64 (.f64 x x) (.f64 x (.f64 (*.f64 x x) #s(literal 2/945 binary64))))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64)))))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64)))))))
(* 2/945 (pow x 5))
(.f64 (.f64 x x) (.f64 x (.f64 (*.f64 x x) #s(literal 2/945 binary64))))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64)))))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/45 (* 1/3 (/ 1 (pow x 2)))) (pow x 2))) 2/945)))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64)))))))
(* -1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(* (pow x 3) (- (* -2/945 (pow x 2)) 1/45))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal -2/945 binary64)))))))
(* (pow x 3) (- (* -2/945 (pow x 2)) 1/45))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal -2/945 binary64)))))))
(* (pow x 3) (- (* -2/945 (pow x 2)) 1/45))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal -2/945 binary64)))))))
(* -2/945 (pow x 5))
(.f64 x (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal -2/945 binary64))))))
(* -1 (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal -2/945 binary64)))))))
(* -1 (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal -2/945 binary64)))))))
(* -1 (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal -2/945 binary64)))))))
(* -2/945 (pow x 5))
(.f64 x (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal -2/945 binary64))))))
(* -1 (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal -2/945 binary64)))))))
(* -1 (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal -2/945 binary64)))))))
(* -1 (* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal -2/945 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)
(* -1/45 x)
(*.f64 x #s(literal -1/45 binary64))
(* -1/45 x)
(*.f64 x #s(literal -1/45 binary64))
(* -1/45 x)
(*.f64 x #s(literal -1/45 binary64))
(* -1/45 x)
(*.f64 x #s(literal -1/45 binary64))
(* -1/45 x)
(*.f64 x #s(literal -1/45 binary64))
(* -1/45 x)
(*.f64 x #s(literal -1/45 binary64))
(* -1/45 x)
(*.f64 x #s(literal -1/45 binary64))
(* -1/45 x)
(*.f64 x #s(literal -1/45 binary64))
(* -1/45 x)
(*.f64 x #s(literal -1/45 binary64))
(* -1/45 x)
(*.f64 x #s(literal -1/45 binary64))
(* -1/45 x)
(*.f64 x #s(literal -1/45 binary64))
(* -1/45 x)
(*.f64 x #s(literal -1/45 binary64))
(* 2/945 x)
(*.f64 x #s(literal 2/945 binary64))
(* 2/945 x)
(*.f64 x #s(literal 2/945 binary64))
(* 2/945 x)
(*.f64 x #s(literal 2/945 binary64))
(* 2/945 x)
(*.f64 x #s(literal 2/945 binary64))
(* 2/945 x)
(*.f64 x #s(literal 2/945 binary64))
(* 2/945 x)
(*.f64 x #s(literal 2/945 binary64))
(* 2/945 x)
(*.f64 x #s(literal 2/945 binary64))
(* 2/945 x)
(*.f64 x #s(literal 2/945 binary64))
(* 2/945 x)
(*.f64 x #s(literal 2/945 binary64))
(* 2/945 x)
(*.f64 x #s(literal 2/945 binary64))
(* 2/945 x)
(*.f64 x #s(literal 2/945 binary64))
(* 2/945 x)
(*.f64 x #s(literal 2/945 binary64))
(* -1/45 x)
(*.f64 x #s(literal -1/45 binary64))
(* x (- (* -2/945 (pow x 2)) 1/45))
(.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal -2/945 binary64)))))
(* x (- (* -2/945 (pow x 2)) 1/45))
(.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal -2/945 binary64)))))
(* x (- (* -2/945 (pow x 2)) 1/45))
(.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal -2/945 binary64)))))
(* -2/945 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal -2/945 binary64))))
(* -1 (* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal -2/945 binary64)))))
(* -1 (* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal -2/945 binary64)))))
(* -1 (* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal -2/945 binary64)))))
(* -2/945 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal -2/945 binary64))))
(* -1 (* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal -2/945 binary64)))))
(* -1 (* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal -2/945 binary64)))))
(* -1 (* (pow x 3) (+ 2/945 (* 1/45 (/ 1 (pow x 2))))))
(.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal -2/945 binary64)))))
(* 2/945 (pow x 2))
(.f64 (.f64 x x) #s(literal 2/945 binary64))
(* 2/945 (pow x 2))
(.f64 (.f64 x x) #s(literal 2/945 binary64))
(* 2/945 (pow x 2))
(.f64 (.f64 x x) #s(literal 2/945 binary64))
(* 2/945 (pow x 2))
(.f64 (.f64 x x) #s(literal 2/945 binary64))
(* 2/945 (pow x 2))
(.f64 (.f64 x x) #s(literal 2/945 binary64))
(* 2/945 (pow x 2))
(.f64 (.f64 x x) #s(literal 2/945 binary64))
(* 2/945 (pow x 2))
(.f64 (.f64 x x) #s(literal 2/945 binary64))
(* 2/945 (pow x 2))
(.f64 (.f64 x x) #s(literal 2/945 binary64))
(* 2/945 (pow x 2))
(.f64 (.f64 x x) #s(literal 2/945 binary64))
(* 2/945 (pow x 2))
(.f64 (.f64 x x) #s(literal 2/945 binary64))
(* 2/945 (pow x 2))
(.f64 (.f64 x x) #s(literal 2/945 binary64))
(* 2/945 (pow x 2))
(.f64 (.f64 x x) #s(literal 2/945 binary64))

eval64.0ms (0.5%)

Compiler: Compiled 12704 to 843 computations (93.4% saved)

prune51.0ms (0.4%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	570	1	571
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	570	6	576

Accuracy

99.6%

Counts

576 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	(-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 (.f64 x x) (.f64 x (-.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64)))))))
✓	99.5%	(-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))))
▶	99.5%	(+.f64 (+.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 (.f64 x (.f64 x x)) #s(literal 2/45 binary64))) (.f64 x (.f64 #s(literal -1/45 binary64) (*.f64 x x))))
✓	99.5%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))))))
✓	99.5%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
✓	98.6%	(*.f64 #s(literal 1/3 binary64) x)

Compiler

Compiled 80 to 52 computations (35% saved)

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 (.f64 x (*.f64 x x)) #s(literal 2/45 binary64))
✓	cost-diff	0	(*.f64 #s(literal 1/3 binary64) x)
✓	cost-diff	128	(+.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 (.f64 x (.f64 x x)) #s(literal 2/45 binary64)))
✓	cost-diff	512	(+.f64 (+.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 (.f64 x (.f64 x x)) #s(literal 2/45 binary64))) (.f64 x (.f64 #s(literal -1/45 binary64) (*.f64 x x))))

Rules

176×	`fma-define`
168×	`fma-lowering-fma.f32`
168×	`fma-lowering-fma.f64`
94×	`-lowering-.f32`
94×	`-lowering-.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	50
1	32	47
2	76	41
3	161	40
4	211	40
5	227	40
0	227	40

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+ (+ (* 1/3 x) (* (* x (* x x)) 2/45)) (* x (* -1/45 (* x x))))
(+ (* 1/3 x) (* (* x (* x x)) 2/45))
(* 1/3 x)
1/3
x
(* (* x (* x x)) 2/45)
(* x (* x x))
(* x x)
2/45
(* x (* -1/45 (* x x)))
(* -1/45 (* x x))
-1/45

Outputs
(+ (+ (* 1/3 x) (* (* x (* x x)) 2/45)) (* x (* -1/45 (* x x))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal 1/45 binary64))))
(+ (* 1/3 x) (* (* x (* x x)) 2/45))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal 2/45 binary64))))
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
1/3
#s(literal 1/3 binary64)
x
(* (* x (* x x)) 2/45)
(.f64 x (.f64 (*.f64 x x) #s(literal 2/45 binary64)))
(* x (* x x))
(.f64 x (.f64 x x))
(* x x)
(*.f64 x x)
2/45
#s(literal 2/45 binary64)
(* x (* -1/45 (* x x)))
(.f64 x (.f64 (*.f64 x x) #s(literal -1/45 binary64)))
(* -1/45 (* x x))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
-1/45
#s(literal -1/45 binary64)

localize76.0ms (0.6%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(.f64 x (.f64 #s(literal -1/45 binary64) (*.f64 x x)))
✓	accuracy	99.8%	(.f64 (.f64 x (*.f64 x x)) #s(literal 2/45 binary64))
✓	accuracy	99.7%	(.f64 #s(literal -1/45 binary64) (.f64 x x))
✓	accuracy	99.5%	(*.f64 #s(literal 1/3 binary64) x)

Results

56.0ms

256×

valid

Compiler

Compiled 66 to 13 computations (80.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 33.0ms

...c/correct-round.rkt:119:19: 18.0ms (55.1% of total)

ival-mult: 12.0ms (36.7% of total)

ival-add: 2.0ms (6.1% of total)

const: 0.0ms (0% of total)

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

series2.0ms (0%)

Counts

6 → 72

Calls

Call 1

Inputs
#<alt (+ (+ (* 1/3 x) (* (* x (* x x)) 2/45)) (* x (* -1/45 (* x x))))>
#<alt (+ (* 1/3 x) (* (* x (* x x)) 2/45))>
#<alt (* 1/3 x)>
#<alt (* (* x (* x x)) 2/45)>
#<alt (* -1/45 (* x x))>
#<alt (* x (* -1/45 (* x x)))>

Outputs
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* 1/45 (pow x 2))))>
#<alt (* 1/45 (pow x 3))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* 1/45 (pow x 3))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* 2/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* 2/45 (pow x 2))))>
#<alt (* x (+ 1/3 (* 2/45 (pow x 2))))>
#<alt (* 2/45 (pow x 3))>
#<alt (* (pow x 3) (+ 2/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 2/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 2/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* 2/45 (pow x 3))>
#<alt (* (pow x 3) (+ 2/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 2/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 2/45 (* 1/3 (/ 1 (pow x 2)))))>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 2/45 (pow x 3))>
#<alt (* 2/45 (pow x 3))>
#<alt (* 2/45 (pow x 3))>
#<alt (* 2/45 (pow x 3))>
#<alt (* 2/45 (pow x 3))>
#<alt (* 2/45 (pow x 3))>
#<alt (* 2/45 (pow x 3))>
#<alt (* 2/45 (pow x 3))>
#<alt (* 2/45 (pow x 3))>
#<alt (* 2/45 (pow x 3))>
#<alt (* 2/45 (pow x 3))>
#<alt (* 2/45 (pow x 3))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 2))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>
#<alt (* -1/45 (pow x 3))>

Calls

18 calls:

Time	Variable		Point	Expression
0.0ms	x	@	-inf	(* (* x (* x x)) 2/45)
0.0ms	x	@	inf	(* (* x (* x x)) 2/45)
0.0ms	x	@	0	(+ (+ (* 1/3 x) (* (* x (* x x)) 2/45)) (* x (* -1/45 (* x x))))
0.0ms	x	@	inf	(+ (+ (* 1/3 x) (* (* x (* x x)) 2/45)) (* x (* -1/45 (* x x))))
0.0ms	x	@	0	(* (* x (* x x)) 2/45)

rewrite27.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

180×	`fma-define`
172×	`fma-lowering-fma.f32`
172×	`fma-lowering-fma.f64`
102×	`-lowering-.f32`
102×	`-lowering-.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	41
1	34	38
2	85	32
3	179	31
4	243	31
5	274	31
6	287	31
0	287	31

Stop Event

1×	iter limit
1×	saturated

Counts

6 → 62

Calls

Call 1

Inputs
(+ (+ (* 1/3 x) (* (* x (* x x)) 2/45)) (* x (* -1/45 (* x x))))
(+ (* 1/3 x) (* (* x (* x x)) 2/45))
(* 1/3 x)
(* (* x (* x x)) 2/45)
(* -1/45 (* x x))
(* x (* -1/45 (* x x)))

Outputs
(+.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 (.f64 x x) (.f64 x #s(literal 1/45 binary64))))
(+.f64 (.f64 x (.f64 x (.f64 x #s(literal 2/45 binary64)))) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))))
(+.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 2/45 binary64))))) (.f64 x (.f64 (.f64 x x) #s(literal -1/45 binary64))))
(+.f64 (.f64 x (.f64 (.f64 x x) #s(literal -1/45 binary64))) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 2/45 binary64))))))
(+.f64 (.f64 (.f64 x x) (.f64 x #s(literal 1/45 binary64))) (.f64 #s(literal 1/3 binary64) x))
(+.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))) (.f64 x (.f64 x (.f64 x #s(literal 2/45 binary64)))))
(fma.f64 #s(literal 1/3 binary64) x (.f64 (.f64 x x) (*.f64 x #s(literal 1/45 binary64))))
(fma.f64 x #s(literal 1/3 binary64) (.f64 (.f64 x x) (*.f64 x #s(literal 1/45 binary64))))
(fma.f64 x (.f64 (.f64 x x) #s(literal -1/45 binary64)) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 2/45 binary64))))))
(fma.f64 x (.f64 x (.f64 x #s(literal 2/45 binary64))) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64)))))
(fma.f64 x (.f64 x (.f64 x #s(literal 1/45 binary64))) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 2/45 binary64)))) (.f64 x (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
(fma.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))) (.f64 x (.f64 x (*.f64 x #s(literal 2/45 binary64)))))
(fma.f64 (.f64 x x) (.f64 x #s(literal -1/45 binary64)) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 2/45 binary64))))))
(fma.f64 (.f64 x x) (.f64 x #s(literal 2/45 binary64)) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64)))))
(fma.f64 (.f64 x x) (.f64 x #s(literal 1/45 binary64)) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 2/45 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64)))))
(fma.f64 (.f64 x (.f64 x x)) #s(literal -1/45 binary64) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 2/45 binary64))))))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 #s(literal 2/45 binary64) (.f64 x (.f64 x x)) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64)))))
(fma.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x x)) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 2/45 binary64))))))
(fma.f64 (.f64 (.f64 x x) #s(literal -1/45 binary64)) x (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 2/45 binary64))))))
(fma.f64 (.f64 x #s(literal -1/45 binary64)) (.f64 x x) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 2/45 binary64))))))
(fma.f64 (.f64 x (.f64 x #s(literal 2/45 binary64))) x (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64)))))
(fma.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) x (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 2/45 binary64)))) x (.f64 x (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
(fma.f64 (.f64 x #s(literal 2/45 binary64)) (.f64 x x) (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64)))))
(fma.f64 (.f64 x #s(literal 1/45 binary64)) (.f64 x x) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x x)) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))) x (.f64 x (.f64 x (*.f64 x #s(literal 2/45 binary64)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))) x)
(+.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 x (.f64 x (.f64 x #s(literal 2/45 binary64)))))
(+.f64 (.f64 x (.f64 x (.f64 x #s(literal 2/45 binary64)))) (.f64 #s(literal 1/3 binary64) x))
(fma.f64 #s(literal 1/3 binary64) x (.f64 x (.f64 x (*.f64 x #s(literal 2/45 binary64)))))
(fma.f64 x #s(literal 1/3 binary64) (.f64 x (.f64 x (*.f64 x #s(literal 2/45 binary64)))))
(fma.f64 x (.f64 x (.f64 x #s(literal 2/45 binary64))) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x x) (.f64 x #s(literal 2/45 binary64)) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 2/45 binary64) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 #s(literal 2/45 binary64) (.f64 x (.f64 x x)) (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x (.f64 x #s(literal 2/45 binary64))) x (*.f64 #s(literal 1/3 binary64) x))
(fma.f64 (.f64 x #s(literal 2/45 binary64)) (.f64 x x) (*.f64 #s(literal 1/3 binary64) x))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 2/45 binary64)))))
(.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 2/45 binary64)))) x)
(*.f64 #s(literal 1/3 binary64) x)
(*.f64 x #s(literal 1/3 binary64))
(.f64 x (.f64 x (*.f64 x #s(literal 2/45 binary64))))
(.f64 (.f64 x x) (*.f64 x #s(literal 2/45 binary64)))
(.f64 (.f64 x (*.f64 x x)) #s(literal 2/45 binary64))
(.f64 #s(literal 2/45 binary64) (.f64 x (*.f64 x x)))
(.f64 (.f64 x (*.f64 x #s(literal 2/45 binary64))) x)
(.f64 (.f64 x #s(literal 2/45 binary64)) (*.f64 x x))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(.f64 (.f64 x x) #s(literal -1/45 binary64))
(.f64 #s(literal -1/45 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal -1/45 binary64)) x)
(.f64 x (.f64 (*.f64 x x) #s(literal -1/45 binary64)))
(.f64 (.f64 x x) (*.f64 x #s(literal -1/45 binary64)))
(.f64 (.f64 x (*.f64 x x)) #s(literal -1/45 binary64))
(.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x x)))
(.f64 (.f64 (*.f64 x x) #s(literal -1/45 binary64)) x)
(.f64 (.f64 x #s(literal -1/45 binary64)) (*.f64 x x))

simplify315.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

5576×	`-lowering-.f32`
5576×	`-lowering-.f64`
3538×	`cube-prod`
2378×	`/-lowering-/.f32`
2378×	`/-lowering-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	404
1	69	356
2	174	356
3	377	356
4	595	356
5	1147	356
6	2046	356
7	2330	356
8	2778	356
9	3096	356
10	3495	356
11	3993	356
12	4574	356
13	4928	356
14	5135	356
15	5298	356
16	5470	356
17	5650	356
18	6398	356
19	7578	356
20	7990	356
0	8074	356

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

Inputs
(* 1/3 x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/45 (pow x 3))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/3 x)
(* x (+ 1/3 (* 2/45 (pow x 2))))
(* x (+ 1/3 (* 2/45 (pow x 2))))
(* x (+ 1/3 (* 2/45 (pow x 2))))
(* 2/45 (pow x 3))
(* (pow x 3) (+ 2/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 2/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 2/45 (* 1/3 (/ 1 (pow x 2)))))
(* 2/45 (pow x 3))
(* (pow x 3) (+ 2/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 2/45 (* 1/3 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 2/45 (* 1/3 (/ 1 (pow x 2)))))
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 2/45 (pow x 3))
(* 2/45 (pow x 3))
(* 2/45 (pow x 3))
(* 2/45 (pow x 3))
(* 2/45 (pow x 3))
(* 2/45 (pow x 3))
(* 2/45 (pow x 3))
(* 2/45 (pow x 3))
(* 2/45 (pow x 3))
(* 2/45 (pow x 3))
(* 2/45 (pow x 3))
(* 2/45 (pow x 3))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 2))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))
(* -1/45 (pow x 3))

Outputs
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* x (+ 1/3 (* 1/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* 1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* 1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* (pow x 3) (+ 1/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* x (+ 1/3 (* 2/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 2/45 binary64)))))
(* x (+ 1/3 (* 2/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 2/45 binary64)))))
(* x (+ 1/3 (* 2/45 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 2/45 binary64)))))
(* 2/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 2/45 binary64))))
(* (pow x 3) (+ 2/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 2/45 binary64)))))
(* (pow x 3) (+ 2/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 2/45 binary64)))))
(* (pow x 3) (+ 2/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 2/45 binary64)))))
(* 2/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 2/45 binary64))))
(* (pow x 3) (+ 2/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 2/45 binary64)))))
(* (pow x 3) (+ 2/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 2/45 binary64)))))
(* (pow x 3) (+ 2/45 (* 1/3 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 2/45 binary64)))))
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 2/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 2/45 binary64))))
(* 2/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 2/45 binary64))))
(* 2/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 2/45 binary64))))
(* 2/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 2/45 binary64))))
(* 2/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 2/45 binary64))))
(* 2/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 2/45 binary64))))
(* 2/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 2/45 binary64))))
(* 2/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 2/45 binary64))))
(* 2/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 2/45 binary64))))
(* 2/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 2/45 binary64))))
(* 2/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 2/45 binary64))))
(* 2/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 2/45 binary64))))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 2))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* -1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(* -1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(* -1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(* -1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(* -1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(* -1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(* -1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(* -1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(* -1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(* -1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(* -1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(* -1/45 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64))))

eval14.0ms (0.1%)

Compiler: Compiled 2207 to 117 computations (94.7% saved)

prune12.0ms (0.1%)

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	132	2	134
Fresh	0	0	0
Picked	1	0	1
Done	0	5	5
Total	133	7	140

Accuracy

99.6%

Counts

140 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.5%	(fma.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))) x (.f64 x (.f64 x (*.f64 x #s(literal 2/45 binary64)))))
✓	99.5%	(-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 (.f64 x x) (.f64 x (-.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64)))))))
✓	99.5%	(-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))))
	99.5%	(+.f64 (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 2/45 binary64)))) x) (.f64 x (.f64 #s(literal -1/45 binary64) (.f64 x x))))
✓	99.5%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))))))
✓	99.5%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
✓	98.6%	(*.f64 #s(literal 1/3 binary64) x)

Compiler

Compiled 211 to 108 computations (48.8% saved)

regimes6.0ms (0.1%)

Counts

9 → 1

Calls

Call 1

Inputs
(*.f64 #s(literal 1/3 binary64) x)
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
(-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))))))
(+.f64 (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 2/45 binary64)))) x) (.f64 x (.f64 #s(literal -1/45 binary64) (.f64 x x))))
(-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 (.f64 x x) (.f64 x (-.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64)))))))
(+.f64 (+.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 (.f64 x (.f64 x x)) #s(literal 2/45 binary64))) (.f64 x (.f64 #s(literal -1/45 binary64) (*.f64 x x))))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(fma.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64))) x (.f64 x (.f64 x (*.f64 x #s(literal 2/45 binary64)))))

Outputs
(-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 (.f64 x x) (.f64 x (-.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64)))))))

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
99.5%	1	`x`
99.5%	1	`(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes2.0ms (0%)

Counts

5 → 1

Calls

Call 1

Inputs
(*.f64 #s(literal 1/3 binary64) x)
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
(-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))))))
(+.f64 (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 2/45 binary64)))) x) (.f64 x (.f64 #s(literal -1/45 binary64) (.f64 x x))))

Outputs
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))))))

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
99.5%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

3 → 1

Calls

Call 1

Inputs

(*.f64 #s(literal 1/3 binary64) x)

(*.f64 x (-.f64 #s(literal 1/3 binary64) (*.f64 (*.f64 x x) #s(literal -1/45 binary64))))

(-.f64 (*.f64 #s(literal 1/3 binary64) x) (*.f64 x (*.f64 x (*.f64 x #s(literal -1/45 binary64)))))

Outputs
(-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))))

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
99.5%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes5.0ms (0%)

Counts

2 → 1

Calls

Call 1

Inputs
(*.f64 #s(literal 1/3 binary64) x)
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))

Outputs
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
99.5%	1	`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
(*.f64 #s(literal 1/3 binary64) x)

Outputs
(*.f64 #s(literal 1/3 binary64) x)

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
98.6%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify38.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

348×	`unsub-neg_binary64`
270×	`distribute-lft-neg-in_binary64`
216×	`neg-mul-1_binary64`
136×	`distribute-rgt-neg-in_binary64`
118×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	55
1	61	55
2	109	55
3	151	55
4	190	55
5	227	55
6	273	55
7	346	55
8	549	55
9	828	55
10	909	55
11	956	55
12	997	55
13	1004	55
14	1020	55

Stop Event

1×

saturated

Calls

Call 1

Inputs
(-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 (.f64 x x) (.f64 x (-.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64)))))))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))))))
(-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
(*.f64 #s(literal 1/3 binary64) x)

Outputs
(-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 (.f64 x x) (.f64 x (-.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal 2/945 binary64)))))))
(+.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 (.f64 x x) (.f64 x (-.f64 (.f64 x (.f64 x #s(literal 2/945 binary64))) #s(literal -1/45 binary64)))))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal -2/945 binary64))))))
(-.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 x (.f64 x (.f64 x #s(literal -1/45 binary64)))))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
(*.f64 #s(literal 1/3 binary64) x)

soundness1.3s (10.4%)

Rules

2512×	`-lowering-.f32`
2512×	`-lowering-.f64`
2470×	`sum3-define`
2100×	`fnmadd-define`
1924×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	66
1	44	62
2	136	58
3	436	58
4	1673	58
5	5627	58
0	8590	58
0	67	302
1	186	269
2	560	266
3	1806	266
4	2709	266
5	4422	266
6	6045	266
7	6589	266
0	8077	266

Stop Event

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

Compiler

Compiled 95 to 53 computations (44.2% saved)

preprocess55.0ms (0.4%)

Remove: (negabs x)
Compiler: Compiled 252 to 144 computations (42.9% saved)

Iter	Nodes	Cost
0	12	17
1	31	16
2	66	15
3	149	15
4	303	15
5	472	15
6	515	15
7	523	15
0	6	5
1	13	5
2	21	5
3	32	5
4	46	5
5	83	5
6	153	5
7	249	5
8	349	5
9	485	5
10	607	5
11	639	5
0	639	5

Iter	Nodes	Cost
0	6	13
1	13	13
2	21	13
3	32	13
4	46	13
5	83	13
6	153	13
7	249	13
8	349	13
9	485	13
10	607	13
11	639	13
0	639	13

Iter	Nodes	Cost
0	12	17
1	31	16
2	66	15
3	149	15
4	303	15
5	472	15
6	515	15
7	523	15
0	6	5
1	13	5
2	21	5
3	32	5
4	46	5
5	83	5
6	153	5
7	249	5
8	349	5
9	485	5
10	607	5
11	639	5
0	639	5

Iter	Nodes	Cost
0	6	13
1	13	13
2	21	13
3	32	13
4	46	13
5	83	13
6	153	13
7	249	13
8	349	13
9	485	13
10	607	13
11	639	13
0	639	13

analyze10.0ms (0.1%)

sample7.2s (57.7%)

preprocess40.0ms (0.3%)

explain536.0ms (4.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify21.0ms (0.2%)

localize252.0ms (2%)

series4.0ms (0%)

rewrite174.0ms (1.4%)

simplify223.0ms (1.8%)

eval154.0ms (1.2%)

prune60.0ms (0.5%)

simplify154.0ms (1.2%)

localize143.0ms (1.1%)

series8.0ms (0.1%)

rewrite133.0ms (1.1%)

simplify241.0ms (1.9%)

eval70.0ms (0.6%)

prune64.0ms (0.5%)

simplify155.0ms (1.2%)

localize94.0ms (0.8%)

series377.0ms (3%)

rewrite166.0ms (1.3%)

simplify218.0ms (1.7%)

eval64.0ms (0.5%)

prune51.0ms (0.4%)

simplify12.0ms (0.1%)

localize76.0ms (0.6%)

series2.0ms (0%)

rewrite27.0ms (0.2%)

simplify315.0ms (2.5%)

eval14.0ms (0.1%)

prune12.0ms (0.1%)

regimes6.0ms (0.1%)

regimes2.0ms (0%)

regimes2.0ms (0%)

regimes5.0ms (0%)

regimes1.0ms (0%)

simplify38.0ms (0.3%)

soundness1.3s (10.4%)

preprocess55.0ms (0.4%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	12	17
1	31	16
2	66	15
3	149	15
4	303	15
5	472	15
6	515	15
7	523	15
0	6	5
1	13	5
2	21	5
3	32	5
4	46	5
5	83	5
6	153	5
7	249	5
8	349	5
9	485	5
10	607	5
11	639	5
0	639	5

Iter	Nodes	Cost
0	6	13
1	13	13
2	21	13
3	32	13
4	46	13
5	83	13
6	153	13
7	249	13
8	349	13
9	485	13
10	607	13
11	639	13
0	639	13