Metrics for invcot (example 3.9)

analyze7.0ms (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: 4.0ms

...c/correct-round.rkt:119:19: 2.0ms (47.4% of total)

ival-div: 1.0ms (23.7% of total)

ival-tan: 1.0ms (23.7% of total)

ival-<: 1.0ms (23.7% 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)

sample7.4s (60.8%)

Results

4.8s	4495×	2	valid
1.2s	1303×	3	valid
880.0ms	2415×	1	valid
4.0ms	43×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 6.4s

ival-tan: 5.0s (77.1% of total)

ival-div: 574.0ms (8.9% of total)

...c/correct-round.rkt:119:19: 402.0ms (6.2% of total)

backward-pass: 216.0ms (3.3% of total)

ival-sub: 158.0ms (2.4% of total)

ival-<: 99.0ms (1.5% of total)

const: 16.0ms (0.2% of total)

ival-and: 11.0ms (0.2% of total)

Bogosity

preprocess36.0ms (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	20
1	29	19
2	64	18
3	146	18
4	300	18
5	464	18
6	507	18
7	515	18
0	6	6
1	12	6
2	20	6
3	31	6
4	45	6
5	82	6
6	152	6
7	248	6
8	350	6
9	486	6
10	607	6
11	639	6
0	639	6

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

Symmetry

(negabs x)

explain393.0ms (3.2%)

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

264.0ms	288×	2	valid
67.0ms	82×	3	valid
26.0ms	140×	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: 307.0ms

ival-tan: 253.0ms (82.3% of total)

ival-div: 31.0ms (10.1% of total)

backward-pass: 14.0ms (4.6% of total)

ival-sub: 8.0ms (2.6% of total)

const: 2.0ms (0.7% 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
▶	6.5%	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify19.0ms (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	15
1	12	15
2	20	15
3	31	15
4	45	15
5	82	15
6	152	15
7	248	15
8	350	15
9	486	15
10	607	15
11	639	15
0	639	15

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)

localize273.0ms (2.3%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (tan.f64 x))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)
✓	accuracy	100.0%	(tan.f64 x)
✓	accuracy	6.5%	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Results

218.0ms	144×	2	valid
31.0ms	41×	3	valid
12.0ms	70×	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: 237.0ms

ival-tan: 201.0ms (84.8% of total)

ival-div: 24.0ms (10.1% of total)

backward-pass: 7.0ms (3% of total)

ival-sub: 5.0ms (2.1% of total)

const: 1.0ms (0.4% of total)

series6.0ms (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))

rewrite196.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

2434×	`-lowering-.f32`
2434×	`-lowering-.f64`
2300×	`/-lowering-/.f32`
2300×	`/-lowering-/.f64`
1480×	`sum5-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	47	13
2	483	13
3	6182	13
0	8127	13

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 222

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

simplify186.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

2522×	`-lowering-.f32`
2522×	`-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	287
2	559	281
3	1807	281
4	2717	281
5	4432	281
6	6049	281
7	6591	281
0	8079	281

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 x (*.f64 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 x (.f64 x (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 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 (.f64 x 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 x (.f64 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 x (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (*.f64 x 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))

eval28.0ms (0.2%)

Compiler: Compiled 5571 to 677 computations (87.8% saved)

prune32.0ms (0.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	267	3	270
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	268	3	271

Accuracy

99.5%

Counts

271 → 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 x (*.f64 x #s(literal -2/945 binary64)))))))
▶	99.4%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
▶	98.9%	(*.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 x (*.f64 x #s(literal -2/945 binary64)))))))

▶

99.4%

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

▶

98.9%

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

Compiler

Compiled 30 to 21 computations (30% saved)

simplify132.0ms (1.1%)

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 x (.f64 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 x (.f64 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 x (*.f64 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

1976×	`sum3-define`
1920×	`sum4-define`
1820×	`fma-define`
1616×	`fma-lowering-fma.f32`
1616×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	93
1	42	89
2	132	85
3	426	85
4	1208	85
5	2367	85
6	5311	85
0	8040	85

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

localize100.0ms (0.8%)

Localize:

Found 9 expressions of interest:

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

64.0ms

256×

valid

Compiler

Compiled 95 to 16 computations (83.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 43.0ms

ival-mult: 28.0ms (64.7% of total)

...c/correct-round.rkt:119:19: 11.0ms (25.4% of total)

ival-sub: 2.0ms (4.6% of total)

ival-add: 1.0ms (2.3% 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 -2/945)>
#<alt (* 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 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 (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

30 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(* x (- 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)))

rewrite268.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

5384×	`-lowering-.f32`
5384×	`-lowering-.f64`
2582×	`/-lowering-/.f32`
2582×	`/-lowering-/.f64`
1428×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	74
1	83	71
2	675	67
0	8126	67

Stop Event

1×	iter limit
1×	node limit

Counts

10 → 287

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 -2/945)
(* x (* x -2/945))

Outputs
(*.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 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)))))
(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/135 binary64) (.f64 (.f64 x x) #s(literal 1/2025 binary64))))) (.f64 x (-.f64 #s(literal 1/27 binary64) (.f64 #s(literal -1/91125 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))) (.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1/2025 binary64))))))
(/.f64 (.f64 x (-.f64 #s(literal 1/27 binary64) (.f64 #s(literal -1/91125 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/135 binary64) (.f64 (*.f64 x x) #s(literal 1/2025 binary64))))))
(/.f64 (.f64 x (-.f64 #s(literal 1/27 binary64) (.f64 #s(literal -1/91125 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (+.f64 #s(literal 1/9 binary64) (.f64 (.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 (.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64)))) (-.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(/.f64 (neg.f64 (.f64 x (-.f64 #s(literal 1/27 binary64) (.f64 #s(literal -1/91125 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/135 binary64) (.f64 (*.f64 x x) #s(literal 1/2025 binary64)))))))
(/.f64 (neg.f64 (.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64))))) (+.f64 (.f64 x (*.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64)))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/3 binary64) x) #s(literal 3 binary64)) (pow.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/45 binary64)))) #s(literal 3 binary64))) (+.f64 (.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 #s(literal 1/3 binary64) x)) (-.f64 (.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 #s(literal 1/3 binary64) x) (.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64))))))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/3 binary64) x) (.f64 #s(literal 1/3 binary64) x)) (.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 #s(literal 1/3 binary64) x) (.f64 x (.f64 x (.f64 x #s(literal 1/45 binary64))))))
(/.f64 (.f64 x (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/27 binary64) (.f64 #s(literal -1/91125 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/135 binary64) (.f64 (*.f64 x x) #s(literal 1/2025 binary64)))))))
(/.f64 (.f64 x (+.f64 #s(literal -1/9 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64)))))) (+.f64 (.f64 x (*.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64)))
(/.f64 (.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64))))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/27 binary64) (.f64 #s(literal -1/91125 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) x) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/135 binary64) (.f64 (*.f64 x x) #s(literal 1/2025 binary64)))))))
(/.f64 (.f64 (+.f64 #s(literal -1/9 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))))) x) (+.f64 (.f64 x (*.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64)))
(/.f64 (.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 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 1/27 binary64) (.f64 #s(literal -1/91125 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/135 binary64) (.f64 (.f64 x x) #s(literal 1/2025 binary64)))))) x))
(.f64 (-.f64 #s(literal 1/27 binary64) (.f64 #s(literal -1/91125 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/135 binary64) (.f64 (*.f64 x x) #s(literal 1/2025 binary64)))))))
(.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64))) (.f64 (/.f64 #s(literal -1 binary64) (+.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64))) x))
(.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64))) (/.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64))))))
(.f64 (.f64 x (-.f64 #s(literal 1/27 binary64) (.f64 #s(literal -1/91125 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/135 binary64) (.f64 (.f64 x x) #s(literal 1/2025 binary64)))))))
(.f64 (.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64)))) (/.f64 #s(literal -1 binary64) (+.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64))))
(.f64 (/.f64 (.f64 x (-.f64 #s(literal 1/27 binary64) (.f64 #s(literal -1/91125 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (+.f64 #s(literal 1/729 binary64) (.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/135 binary64) (.f64 (.f64 x x) #s(literal 1/2025 binary64)))) (.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/135 binary64) (.f64 (.f64 x x) #s(literal 1/2025 binary64)))) (.f64 (.f64 x x) (+.f64 #s(literal -1/135 binary64) (.f64 (.f64 x x) #s(literal 1/2025 binary64)))))))) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/135 binary64) (.f64 (.f64 x x) #s(literal 1/2025 binary64)))) (-.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/135 binary64) (.f64 (*.f64 x x) #s(literal 1/2025 binary64)))) #s(literal 1/9 binary64)))))
(.f64 (/.f64 (.f64 x (-.f64 #s(literal 1/27 binary64) (.f64 #s(literal -1/91125 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (-.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/135 binary64) (.f64 (.f64 x x) #s(literal 1/2025 binary64)))) (.f64 (.f64 x x) (+.f64 #s(literal -1/135 binary64) (.f64 (.f64 x x) #s(literal 1/2025 binary64))))))) (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/135 binary64) (.f64 (*.f64 x x) #s(literal 1/2025 binary64))))))
(.f64 (/.f64 (.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64)))) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64)))) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))))
(.f64 (/.f64 (.f64 x (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64)))) (+.f64 #s(literal 1/27 binary64) (.f64 #s(literal -1/91125 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 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 (/.f64 #s(literal 1/27 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/135 binary64) (.f64 (.f64 x x) #s(literal 1/2025 binary64)))))) (neg.f64 (/.f64 (.f64 #s(literal -1/91125 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/135 binary64) (.f64 (.f64 x x) #s(literal 1/2025 binary64))))))))
(+.f64 (/.f64 #s(literal -1/9 binary64) (+.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64))) (neg.f64 (/.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 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 #s(literal 1/27 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/135 binary64) (.f64 (.f64 x x) #s(literal 1/2025 binary64)))))) (/.f64 (.f64 #s(literal -1/91125 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/135 binary64) (.f64 (.f64 x x) #s(literal 1/2025 binary64)))))))
(-.f64 (/.f64 #s(literal -1/9 binary64) (+.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64))) (/.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64)))) (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 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))
(fma.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) #s(literal -1/45 binary64) #s(literal 1/3 binary64))
(fma.f64 #s(literal -1 binary64) (.f64 x (.f64 x #s(literal -1/45 binary64))) #s(literal 1/3 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 x #s(literal -1/45 binary64)) #s(literal 1/3 binary64))
(fma.f64 #s(literal 1/45 binary64) (*.f64 x x) #s(literal 1/3 binary64))
(neg.f64 (/.f64 (-.f64 #s(literal 1/27 binary64) (.f64 #s(literal -1/91125 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/135 binary64) (.f64 (.f64 x x) #s(literal 1/2025 binary64))))))))
(neg.f64 (/.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64))) (+.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/27 binary64) (.f64 #s(literal -1/91125 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/135 binary64) (.f64 (.f64 x x) #s(literal 1/2025 binary64)))))))
(neg.f64 (/.f64 (+.f64 #s(literal -1/9 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))))) (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))))
(/.f64 (-.f64 #s(literal 1/27 binary64) (.f64 #s(literal -1/91125 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/135 binary64) (.f64 (.f64 x x) #s(literal 1/2025 binary64))))))
(/.f64 (-.f64 #s(literal 1/27 binary64) (.f64 #s(literal -1/91125 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (+.f64 #s(literal 1/9 binary64) (.f64 (.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 (-.f64 #s(literal 1/27 binary64) (.f64 #s(literal -1/91125 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64)))) (-.f64 #s(literal 1/9 binary64) (.f64 #s(literal 1/135 binary64) (.f64 x x)))))
(/.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/2025 binary64))) (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/27 binary64) (.f64 #s(literal -1/91125 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/135 binary64) (.f64 (.f64 x x) #s(literal 1/2025 binary64)))))))
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/27 binary64) (.f64 #s(literal -1/91125 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (neg.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) (-.f64 (.f64 x (*.f64 x #s(literal 1/45 binary64))) #s(literal 1/3 binary64))))))
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(/.f64 (neg.f64 (+.f64 (.f64 #s(literal -1/91125 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -8/843908625 binary64))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (neg.f64 (+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64)))) (.f64 (.f64 x (.f64 #s(literal -2/945 binary64) (.f64 x (.f64 x x)))) (-.f64 (.f64 x (.f64 #s(literal -2/945 binary64) (.f64 x (.f64 x x)))) (.f64 x (*.f64 x #s(literal -1/45 binary64))))))))
(/.f64 (neg.f64 (.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64))))) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64)))))) (neg.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4/893025 binary64)))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))))) (-.f64 (.f64 x (.f64 #s(literal -2/945 binary64) (.f64 x (.f64 x x)))) (.f64 x (.f64 x #s(literal -1/45 binary64)))))
(/.f64 (.f64 (.f64 x x) (+.f64 (neg.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -8/843908625 binary64)))) #s(literal 1/91125 binary64))) (+.f64 (neg.f64 (.f64 x (.f64 (.f64 x #s(literal -2/945 binary64)) (+.f64 (.f64 x (*.f64 x #s(literal -2/945 binary64))) #s(literal 1/45 binary64))))) #s(literal -1/2025 binary64)))
(/.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/2025 binary64) (neg.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -4/893025 binary64))))) (+.f64 #s(literal 1/45 binary64) (neg.f64 (.f64 (.f64 x x) #s(literal 2/945 binary64)))))
(/.f64 (.f64 (.f64 x x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64))))))
(/.f64 (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4/893025 binary64)))) #s(literal -1/2025 binary64))) (+.f64 (.f64 x (.f64 x #s(literal -2/945 binary64))) #s(literal 1/45 binary64)))
(/.f64 (.f64 (+.f64 (neg.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -8/843908625 binary64)))) #s(literal 1/91125 binary64)) (.f64 x x)) (+.f64 (neg.f64 (.f64 x (.f64 (.f64 x #s(literal -2/945 binary64)) (+.f64 (.f64 x (*.f64 x #s(literal -2/945 binary64))) #s(literal 1/45 binary64))))) #s(literal -1/2025 binary64)))
(/.f64 (.f64 (+.f64 #s(literal -1/2025 binary64) (neg.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -4/893025 binary64)))) (.f64 x x)) (+.f64 #s(literal 1/45 binary64) (neg.f64 (.f64 (.f64 x x) #s(literal 2/945 binary64)))))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64))))))
(/.f64 (.f64 (+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4/893025 binary64)))) #s(literal -1/2025 binary64)) (.f64 x x)) (+.f64 (.f64 x (.f64 x #s(literal -2/945 binary64))) #s(literal 1/45 binary64)))
(.f64 x (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64))))))
(.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64)))))
(.f64 (+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64)))) (.f64 x x))
(.f64 (+.f64 #s(literal -1/91125 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -8/843908625 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2025 binary64) (.f64 x (.f64 (.f64 x #s(literal -2/945 binary64)) (+.f64 (.f64 x (.f64 x #s(literal -2/945 binary64))) #s(literal 1/45 binary64)))))) (.f64 x x)))
(.f64 (+.f64 #s(literal -1/91125 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -8/843908625 binary64)))) (/.f64 (.f64 x x) (+.f64 #s(literal 1/2025 binary64) (.f64 x (.f64 (.f64 x #s(literal -2/945 binary64)) (+.f64 (.f64 x (*.f64 x #s(literal -2/945 binary64))) #s(literal 1/45 binary64)))))))
(.f64 (+.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -4/893025 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64)))) (*.f64 x x)))
(.f64 (+.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -4/893025 binary64))) (/.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64)))))
(.f64 (.f64 x (+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64))))) x)
(.f64 (+.f64 (.f64 #s(literal -1/91125 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -8/843908625 binary64))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64)))) (.f64 (.f64 x (.f64 #s(literal -2/945 binary64) (.f64 x (.f64 x x)))) (-.f64 (.f64 x (.f64 #s(literal -2/945 binary64) (.f64 x (.f64 x x)))) (.f64 x (.f64 x #s(literal -1/45 binary64))))))))
(.f64 (.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64))))) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 (.f64 x x) #s(literal 2/945 binary64))))) (/.f64 #s(literal 1 binary64) (.f64 (.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 -1/91125 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -8/843908625 binary64)))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2025 binary64) (.f64 x (.f64 (.f64 x #s(literal -2/945 binary64)) (+.f64 (.f64 x (.f64 x #s(literal -2/945 binary64))) #s(literal 1/45 binary64)))))))
(.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -4/893025 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/45 binary64) (.f64 (*.f64 x x) #s(literal 2/945 binary64)))))
(.f64 (/.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/91125 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -8/843908625 binary64)))))) (+.f64 #s(literal 1/8303765625 binary64) (.f64 (.f64 x (.f64 (.f64 x #s(literal -2/945 binary64)) (+.f64 (.f64 x (.f64 x #s(literal -2/945 binary64))) #s(literal 1/45 binary64)))) (.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4/893025 binary64)))) (.f64 (+.f64 (.f64 x (.f64 x #s(literal -2/945 binary64))) #s(literal 1/45 binary64)) (+.f64 (.f64 x (.f64 x #s(literal -2/945 binary64))) #s(literal 1/45 binary64))))))) (+.f64 #s(literal 1/4100625 binary64) (.f64 (.f64 x (.f64 (.f64 x #s(literal -2/945 binary64)) (+.f64 (.f64 x (.f64 x #s(literal -2/945 binary64))) #s(literal 1/45 binary64)))) (-.f64 (.f64 x (.f64 (.f64 x #s(literal -2/945 binary64)) (+.f64 (.f64 x (.f64 x #s(literal -2/945 binary64))) #s(literal 1/45 binary64)))) #s(literal 1/2025 binary64)))))
(.f64 (/.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/91125 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -8/843908625 binary64)))))) (-.f64 #s(literal 1/4100625 binary64) (.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 4/893025 binary64)))) (.f64 (+.f64 (.f64 x (.f64 x #s(literal -2/945 binary64))) #s(literal 1/45 binary64)) (+.f64 (.f64 x (.f64 x #s(literal -2/945 binary64))) #s(literal 1/45 binary64)))))) (+.f64 #s(literal 1/2025 binary64) (.f64 (.f64 (.f64 x x) #s(literal 2/945 binary64)) (+.f64 (.f64 x (.f64 x #s(literal -2/945 binary64))) #s(literal 1/45 binary64)))))
(.f64 (/.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -4/893025 binary64))))) (+.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -4/893025 binary64)))) (+.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal -2/945 binary64)))))
(.f64 (/.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -4/893025 binary64))))) (-.f64 #s(literal -1/91125 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -8/843908625 binary64))))) (+.f64 #s(literal 1/2025 binary64) (.f64 #s(literal -2/945 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/45 binary64) (.f64 x (.f64 x #s(literal -2/945 binary64))))))))
(*.f64 x #s(literal -2/945 binary64))
(*.f64 #s(literal -2/945 binary64) x)
(.f64 x (.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 (.f64 x #s(literal -2/945 binary64)) x)

simplify154.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

2644×	`-lowering-.f32`
2644×	`-lowering-.f64`
1732×	`fma-define`
1206×	`fma-lowering-fma.f32`
1206×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	54	753
1	161	709
2	474	709
3	1239	707
4	2936	705
5	7984	705
0	8053	705

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

eval58.0ms (0.5%)

Compiler: Compiled 15018 to 1071 computations (92.9% saved)

prune37.0ms (0.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	421	4	425
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	421	7	428

Accuracy

100.0%

Counts

428 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(/.f64 (.f64 (+.f64 #s(literal -1/9 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))))) x) (+.f64 (.f64 x (*.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64)))
▶	99.9%	(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))))
▶	99.4%	(+.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/45 binary64)))) (.f64 #s(literal 1/3 binary64) x))
▶	99.5%	(.f64 x (-.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 #s(literal -2/945 binary64) (.f64 x (.f64 x 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 x (*.f64 x #s(literal -2/945 binary64)))))))
✓	99.4%	(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
✓	98.9%	(*.f64 #s(literal 1/3 binary64) x)

Compiler

Compiled 96 to 66 computations (31.3% saved)

simplify214.0ms (1.8%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))))
✓	cost-diff	0	(+.f64 #s(literal -1/9 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64)))))
✓	cost-diff	0	(.f64 (+.f64 #s(literal -1/9 binary64) (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal 1/2025 binary64))))) x)
✓	cost-diff	0	(/.f64 (.f64 (+.f64 #s(literal -1/9 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))))) x) (+.f64 (.f64 x (*.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64)))
✓	cost-diff	0	(.f64 x (.f64 x #s(literal 1/45 binary64)))
✓	cost-diff	0	(+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))))
✓	cost-diff	128	(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))))
✓	cost-diff	0	(*.f64 x #s(literal 1/45 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	128	(+.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/45 binary64)))) (.f64 #s(literal 1/3 binary64) x))
✓	cost-diff	0	(.f64 x (.f64 #s(literal -2/945 binary64) (.f64 x (.f64 x x))))
✓	cost-diff	0	(-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 #s(literal -2/945 binary64) (.f64 x (.f64 x x)))))
✓	cost-diff	256	(-.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 #s(literal -2/945 binary64) (.f64 x (.f64 x x))))) (.f64 x (.f64 x #s(literal -1/45 binary64))))
✓	cost-diff	256	(.f64 x (-.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 #s(literal -2/945 binary64) (.f64 x (.f64 x x))))) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))

Rules

2194×	`-lowering-.f32`
2194×	`-lowering-.f64`
1848×	`fnmadd-define`
1264×	`fma-lowering-fma.f32`
1264×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	33	216
1	84	201
2	227	184
3	671	184
4	1449	184
5	3491	184
0	8091	184

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* x (- (- 1/3 (* x (* -2/945 (* x (* x x))))) (* x (* x -1/45))))
x
(- (- 1/3 (* x (* -2/945 (* x (* x x))))) (* x (* x -1/45)))
(- 1/3 (* x (* -2/945 (* x (* x x)))))
1/3
(* x (* -2/945 (* x (* x x))))
(* -2/945 (* x (* x x)))
-2/945
(* x (* x x))
(* x x)
(* x (* x -1/45))
(* x -1/45)
-1/45
(+ (* x (* x (* x 1/45))) (* 1/3 x))
(* x (* x (* x 1/45)))
x
(* x (* x 1/45))
(* x 1/45)
1/45
(* 1/3 x)
1/3
(/ x (/ 1 (+ 1/3 (* x (* x 1/45)))))
x
(/ 1 (+ 1/3 (* x (* x 1/45))))
1
(+ 1/3 (* x (* x 1/45)))
1/3
(* x (* x 1/45))
(* x 1/45)
1/45
(/ (* (+ -1/9 (* x (* x (* (* x x) 1/2025)))) x) (+ (* x (* x 1/45)) -1/3))
(* (+ -1/9 (* x (* x (* (* x x) 1/2025)))) x)
(+ -1/9 (* x (* x (* (* x x) 1/2025))))
-1/9
(* x (* x (* (* x x) 1/2025)))
x
(* x (* (* x x) 1/2025))
(* (* x x) 1/2025)
(* x x)
1/2025
(+ (* x (* x 1/45)) -1/3)
(* x (* x 1/45))
(* x 1/45)
1/45
-1/3

Outputs
(* x (- (- 1/3 (* x (* -2/945 (* x (* x x))))) (* x (* x -1/45))))
(.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 (* -2/945 (* x (* x x))))) (* x (* x -1/45)))
(+.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 (* x (* -2/945 (* x (* x x)))))
(+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 2/945 binary64))))
1/3
#s(literal 1/3 binary64)
(* x (* -2/945 (* x (* x x))))
(.f64 x (.f64 #s(literal -2/945 binary64) (.f64 x (.f64 x x))))
(* -2/945 (* x (* x x)))
(.f64 #s(literal -2/945 binary64) (.f64 x (*.f64 x x)))
-2/945
#s(literal -2/945 binary64)
(* x (* x x))
(.f64 x (.f64 x x))
(* x x)
(*.f64 x x)
(* x (* x -1/45))
(.f64 x (.f64 x #s(literal -1/45 binary64)))
(* x -1/45)
(*.f64 x #s(literal -1/45 binary64))
-1/45
#s(literal -1/45 binary64)
(+ (* x (* x (* x 1/45))) (* 1/3 x))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* x (* x (* x 1/45)))
(.f64 (.f64 x x) (*.f64 x #s(literal 1/45 binary64)))
x
(* x (* x 1/45))
(.f64 x (.f64 x #s(literal 1/45 binary64)))
(* x 1/45)
(*.f64 x #s(literal 1/45 binary64))
1/45
#s(literal 1/45 binary64)
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
1/3
#s(literal 1/3 binary64)
(/ x (/ 1 (+ 1/3 (* x (* x 1/45)))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
x
(/ 1 (+ 1/3 (* x (* x 1/45))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))))
1
#s(literal 1 binary64)
(+ 1/3 (* x (* x 1/45)))
(+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))
1/3
#s(literal 1/3 binary64)
(* x (* x 1/45))
(.f64 x (.f64 x #s(literal 1/45 binary64)))
(* x 1/45)
(*.f64 x #s(literal 1/45 binary64))
1/45
#s(literal 1/45 binary64)
(/ (* (+ -1/9 (* x (* x (* (* x x) 1/2025)))) x) (+ (* x (* x 1/45)) -1/3))
(/.f64 (.f64 x (+.f64 #s(literal -1/9 binary64) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 1/2025 binary64))))))) (+.f64 #s(literal -1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(* (+ -1/9 (* x (* x (* (* x x) 1/2025)))) x)
(.f64 x (+.f64 #s(literal -1/9 binary64) (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal 1/2025 binary64)))))))
(+ -1/9 (* x (* x (* (* x x) 1/2025))))
(+.f64 #s(literal -1/9 binary64) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal 1/2025 binary64))))))
-1/9
#s(literal -1/9 binary64)
(* x (* x (* (* x x) 1/2025)))
(.f64 x (.f64 x (.f64 x (.f64 x #s(literal 1/2025 binary64)))))
x
(* x (* (* x x) 1/2025))
(.f64 x (.f64 x (*.f64 x #s(literal 1/2025 binary64))))
(* (* x x) 1/2025)
(.f64 x (.f64 x #s(literal 1/2025 binary64)))
(* x x)
(*.f64 x x)
1/2025
#s(literal 1/2025 binary64)
(+ (* x (* x 1/45)) -1/3)
(+.f64 #s(literal -1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))
(* x (* x 1/45))
(.f64 x (.f64 x #s(literal 1/45 binary64)))
(* x 1/45)
(*.f64 x #s(literal 1/45 binary64))
1/45
#s(literal 1/45 binary64)
-1/3
#s(literal -1/3 binary64)

localize156.0ms (1.3%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(.f64 (.f64 x x) #s(literal 1/2025 binary64))
✓	accuracy	99.7%	(*.f64 x #s(literal 1/45 binary64))
✓	accuracy	99.5%	(.f64 (+.f64 #s(literal -1/9 binary64) (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal 1/2025 binary64))))) x)
✓	accuracy	99.5%	(/.f64 (.f64 (+.f64 #s(literal -1/9 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))))) x) (+.f64 (.f64 x (*.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64)))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))))
✓	accuracy	100.0%	(+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))
✓	accuracy	99.8%	(.f64 x (.f64 x #s(literal 1/45 binary64)))
✓	accuracy	99.7%	(*.f64 x #s(literal 1/45 binary64))
✓	accuracy	99.9%	(.f64 x (.f64 x (*.f64 x #s(literal 1/45 binary64))))
✓	accuracy	99.8%	(.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)
✓	accuracy	99.8%	(.f64 #s(literal -2/945 binary64) (.f64 x (*.f64 x x)))
✓	accuracy	99.8%	(.f64 x (.f64 x #s(literal -1/45 binary64)))
✓	accuracy	99.7%	(*.f64 x #s(literal -1/45 binary64))
✓	accuracy	99.5%	(.f64 x (-.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 #s(literal -2/945 binary64) (.f64 x (.f64 x x))))) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))

Results

110.0ms

256×

valid

Compiler

Compiled 245 to 34 computations (86.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 68.0ms

...c/correct-round.rkt:119:19: 28.0ms (41.5% of total)

ival-mult: 25.0ms (37% of total)

ival-add: 7.0ms (10.4% of total)

ival-div: 5.0ms (7.4% of total)

ival-sub: 2.0ms (3% of total)

const: 0.0ms (0% of total)

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

series11.0ms (0.1%)

Counts

20 → 240

Calls

Call 1

Inputs
#<alt (* x (- (- 1/3 (* x (* -2/945 (* x (* x x))))) (* x (* x -1/45))))>
#<alt (- (- 1/3 (* x (* -2/945 (* x (* x x))))) (* x (* x -1/45)))>
#<alt (- 1/3 (* x (* -2/945 (* x (* x x)))))>
#<alt (* x (* -2/945 (* x (* x x))))>
#<alt (+ (* x (* x (* x 1/45))) (* 1/3 x))>
#<alt (* x (* x (* x 1/45)))>
#<alt (* x (* x 1/45))>
#<alt (* x 1/45)>
#<alt (/ x (/ 1 (+ 1/3 (* x (* x 1/45)))))>
#<alt (/ 1 (+ 1/3 (* x (* x 1/45))))>
#<alt (+ 1/3 (* x (* x 1/45)))>
#<alt (/ (* (+ -1/9 (* x (* x (* (* x x) 1/2025)))) x) (+ (* x (* x 1/45)) -1/3))>
#<alt (* (+ -1/9 (* x (* x (* (* x x) 1/2025)))) x)>
#<alt (+ -1/9 (* x (* x (* (* x x) 1/2025))))>
#<alt (* x (* x (* (* x x) 1/2025)))>
#<alt (* x -1/45)>
#<alt (* x (* x -1/45))>
#<alt (* -2/945 (* x (* x x)))>
#<alt (* 1/3 x)>
#<alt (* (* x x) 1/2025)>

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 (* 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 1/3>
#<alt (+ 1/3 (* 2/945 (pow x 4)))>
#<alt (+ 1/3 (* 2/945 (pow x 4)))>
#<alt (+ 1/3 (* 2/945 (pow x 4)))>
#<alt (* 2/945 (pow x 4))>
#<alt (* (pow x 4) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))>
#<alt (* (pow x 4) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))>
#<alt (* (pow x 4) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))>
#<alt (* 2/945 (pow x 4))>
#<alt (* (pow x 4) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))>
#<alt (* (pow x 4) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))>
#<alt (* (pow x 4) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))>
#<alt (* -2/945 (pow x 4))>
#<alt (* -2/945 (pow x 4))>
#<alt (* -2/945 (pow x 4))>
#<alt (* -2/945 (pow x 4))>
#<alt (* -2/945 (pow x 4))>
#<alt (* -2/945 (pow x 4))>
#<alt (* -2/945 (pow x 4))>
#<alt (* -2/945 (pow x 4))>
#<alt (* -2/945 (pow x 4))>
#<alt (* -2/945 (pow x 4))>
#<alt (* -2/945 (pow x 4))>
#<alt (* -2/945 (pow x 4))>
#<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 (* 1/45 (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 (* 1/45 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 (* 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 3>
#<alt (+ 3 (* -1/5 (pow x 2)))>
#<alt (+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))>
#<alt (+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))>
#<alt (/ 45 (pow x 2))>
#<alt (/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))>
#<alt (/ 45 (pow x 2))>
#<alt (/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (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 (* 1/3 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 (* -1/9 x)>
#<alt (* x (- (* 1/2025 (pow x 4)) 1/9))>
#<alt (* x (- (* 1/2025 (pow x 4)) 1/9))>
#<alt (* x (- (* 1/2025 (pow x 4)) 1/9))>
#<alt (* 1/2025 (pow x 5))>
#<alt (* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))>
#<alt (* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))>
#<alt (* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))>
#<alt (* 1/2025 (pow x 5))>
#<alt (* -1 (* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025)))>
#<alt (* -1 (* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025)))>
#<alt (* -1 (* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025)))>
#<alt -1/9>
#<alt (- (* 1/2025 (pow x 4)) 1/9)>
#<alt (- (* 1/2025 (pow x 4)) 1/9)>
#<alt (- (* 1/2025 (pow x 4)) 1/9)>
#<alt (* 1/2025 (pow x 4))>
#<alt (* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))>
#<alt (* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))>
#<alt (* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))>
#<alt (* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))>
#<alt (* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* 1/2025 (pow x 4))>
#<alt (* 1/2025 (pow x 4))>
#<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 (* -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 (* -2/945 (pow x 3))>
#<alt (* -2/945 (pow x 3))>
#<alt (* -2/945 (pow x 3))>
#<alt (* -2/945 (pow x 3))>
#<alt (* -2/945 (pow x 3))>
#<alt (* -2/945 (pow x 3))>
#<alt (* -2/945 (pow x 3))>
#<alt (* -2/945 (pow x 3))>
#<alt (* -2/945 (pow x 3))>
#<alt (* -2/945 (pow x 3))>
#<alt (* -2/945 (pow x 3))>
#<alt (* -2/945 (pow x 3))>
#<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 (* 1/2025 (pow x 2))>
#<alt (* 1/2025 (pow x 2))>
#<alt (* 1/2025 (pow x 2))>
#<alt (* 1/2025 (pow x 2))>
#<alt (* 1/2025 (pow x 2))>
#<alt (* 1/2025 (pow x 2))>
#<alt (* 1/2025 (pow x 2))>
#<alt (* 1/2025 (pow x 2))>
#<alt (* 1/2025 (pow x 2))>
#<alt (* 1/2025 (pow x 2))>
#<alt (* 1/2025 (pow x 2))>
#<alt (* 1/2025 (pow x 2))>

Calls

60 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(/ (* (+ -1/9 (* x (* x (* (* x x) 1/2025)))) x) (+ (* x (* x 1/45)) -1/3))
1.0ms	x	@	inf	(/ (* (+ -1/9 (* x (* x (* (* x x) 1/2025)))) x) (+ (* x (* x 1/45)) -1/3))
0.0ms	x	@	inf	(+ (* x (* x (* x 1/45))) (* 1/3 x))
0.0ms	x	@	inf	(* (+ -1/9 (* x (* x (* (* x x) 1/2025)))) x)
0.0ms	x	@	inf	(- 1/3 (* x (* -2/945 (* x (* x x)))))

rewrite374.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

3662×	`-lowering-.f32`
3662×	`-lowering-.f64`
3570×	`/-lowering-/.f32`
3570×	`/-lowering-/.f64`
1812×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	33	156
1	180	140
2	1489	125
0	8234	125

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 813

Calls

Call 1

Inputs
(* x (- (- 1/3 (* x (* -2/945 (* x (* x x))))) (* x (* x -1/45))))
(- (- 1/3 (* x (* -2/945 (* x (* x x))))) (* x (* x -1/45)))
(- 1/3 (* x (* -2/945 (* x (* x x)))))
(* x (* -2/945 (* x (* x x))))
(+ (* x (* x (* x 1/45))) (* 1/3 x))
(* x (* x (* x 1/45)))
(* x (* x 1/45))
(* x 1/45)
(/ x (/ 1 (+ 1/3 (* x (* x 1/45)))))
(/ 1 (+ 1/3 (* x (* x 1/45))))
(+ 1/3 (* x (* x 1/45)))
(/ (* (+ -1/9 (* x (* x (* (* x x) 1/2025)))) x) (+ (* x (* x 1/45)) -1/3))
(* (+ -1/9 (* x (* x (* (* x x) 1/2025)))) x)
(+ -1/9 (* x (* x (* (* x x) 1/2025))))
(* x (* x (* (* x x) 1/2025)))
(* x -1/45)
(* x (* x -1/45))
(* -2/945 (* x (* x x)))
(* 1/3 x)
(* (* x x) 1/2025)

Outputs
(+.f64 (.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/945 binary64) (.f64 (.f64 x x) (.f64 x x))))) (.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64)))
(+.f64 (.f64 (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/945 binary64) (.f64 (.f64 x x) (.f64 x x)))) x) (.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64)))
(fma.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/945 binary64) (.f64 (.f64 x x) (.f64 x x)))) (.f64 (.f64 x (*.f64 x x)) #s(literal 1/45 binary64)))
(fma.f64 (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/945 binary64) (.f64 (.f64 x x) (.f64 x x)))) x (.f64 (.f64 x (*.f64 x x)) #s(literal 1/45 binary64)))
(/.f64 x (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) (.f64 x (+.f64 (.f64 x (.f64 (.f64 x x) #s(literal -2/945 binary64))) (*.f64 x #s(literal -1/45 binary64)))))))
(/.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x (+.f64 (.f64 x (.f64 (.f64 x x) #s(literal -2/945 binary64))) (*.f64 x #s(literal -1/45 binary64))))) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/945 binary64) (.f64 (.f64 x x) (.f64 x x)))) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/945 binary64) (.f64 (.f64 x x) (.f64 x x))))) (.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (+.f64 (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/945 binary64) (.f64 (.f64 x x) (.f64 x x)))) (.f64 x (.f64 x #s(literal -1/45 binary64)))))) (.f64 x (+.f64 (.f64 (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/945 binary64) (.f64 (.f64 x x) (.f64 x x)))) (.f64 (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/945 binary64) (.f64 (.f64 x x) (.f64 x x)))) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/945 binary64) (.f64 (.f64 x x) (.f64 x x)))))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal -1/91125 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/945 binary64) (.f64 (.f64 x x) (.f64 x x)))) (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 x (.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/945 binary64) (.f64 (.f64 x x) (.f64 x x)))) (.f64 x (.f64 x #s(literal -1/45 binary64)))) (-.f64 #s(literal 1/3 binary64) (.f64 x (+.f64 (.f64 x (.f64 (.f64 x x) #s(literal -2/945 binary64))) (*.f64 x #s(literal -1/45 binary64)))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/945 binary64) (.f64 (.f64 x x) (.f64 x x)))) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/945 binary64) (.f64 (.f64 x x) (.f64 x x))))) (.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (+.f64 (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/945 binary64) (.f64 (.f64 x x) (.f64 x x)))) (.f64 x (.f64 x #s(literal -1/45 binary64)))))) (.f64 (+.f64 (.f64 (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/945 binary64) (.f64 (.f64 x x) (.f64 x x)))) (.f64 (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/945 binary64) (.f64 (.f64 x x) (.f64 x x)))) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/945 binary64) (.f64 (.f64 x x) (.f64 x x)))))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal -1/91125 binary64)))) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/945 binary64) (.f64 (.f64 x x) (.f64 x x)))) (.f64 x (.f64 x #s(literal -1/45 binary64)))) (.f64 (.f64 (+.f64 (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/945 binary64) (.f64 (.f64 x x) (.f64 x x)))) (.f64 x (.f64 x #s(literal -1/45 binary64)))) (-.f64 #s(literal 1/3 binary64) (.f64 x (+.f64 (.f64 x (.f64 (.f64 x x) #s(literal -2/945 binary64))) (*.f64 x #s(literal -1/45 binary64)))))) x)))
(/.f64 (.f64 x (+.f64 (.f64 (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/945 binary64) (.f64 (.f64 x x) (.f64 x x)))) (.f64 (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/945 binary64) (.f64 (.f64 x x) (.f64 x x)))) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/945 binary64) (.f64 (.f64 x x) (.f64 x x)))))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/91125 binary64))))) (+.f64 (.f64 (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/945 binary64) (.f64 (.f64 x x) (.f64 x x)))) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/945 binary64) (.f64 (.f64 x x) (.f64 x x))))) (.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (+.f64 (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -2/945 binary64) (.f64 (.f64 x x) (.f64 x x)))) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))))
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(.f64 (+.f64 #s(literal -1/729 binary64) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1/8303765625 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64)))) (.f64 (.f64 x x) #s(literal 1/2025 binary64))) (-.f64 #s(literal 1/81 binary64) (.f64 (.f64 #s(literal -1/9 binary64) x) (.f64 x (.f64 (*.f64 x x) #s(literal 1/2025 binary64))))))))
(.f64 (+.f64 #s(literal -1/729 binary64) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1/8303765625 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64)))) (.f64 (.f64 x x) #s(literal 1/2025 binary64))) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/2025 binary64))) #s(literal 1/9 binary64))))))
(.f64 (-.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64)))) (.f64 (.f64 x x) #s(literal 1/2025 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1/9 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64))))))
(.f64 (neg.f64 (+.f64 #s(literal -1/729 binary64) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1/8303765625 binary64))))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64))) #s(literal 1/9 binary64)))))))
(.f64 (neg.f64 (-.f64 #s(literal 1/81 binary64) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64)))) (.f64 (.f64 x x) #s(literal 1/2025 binary64))))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal -1/9 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64)))))))
(.f64 (-.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64)))) (.f64 (.f64 x x) #s(literal 1/2025 binary64))) #s(literal 1/81 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64))) #s(literal 1/9 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 x (*.f64 x #s(literal -1/45 binary64)))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 x (*.f64 x #s(literal 1/45 binary64)))) #s(literal 2 binary64)))
(/.f64 (.f64 x (.f64 (*.f64 x x) #s(literal 1/2025 binary64))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (.f64 x #s(literal -1/45 binary64))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) (.f64 x #s(literal 1/45 binary64))) (/.f64 #s(literal 1 binary64) x))
(pow.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) #s(literal 2 binary64))
(pow.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) #s(literal 2 binary64))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))))
(.f64 x (.f64 (.f64 x #s(literal -1/45 binary64)) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))
(.f64 x (.f64 (.f64 x #s(literal 1/45 binary64)) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64)))
(.f64 (.f64 x x) (.f64 (.f64 x #s(literal 1/45 binary64)) (*.f64 x #s(literal 1/45 binary64))))
(.f64 (.f64 x x) (.f64 (.f64 x #s(literal -1/45 binary64)) (*.f64 x #s(literal -1/45 binary64))))
(.f64 (.f64 x x) (.f64 #s(literal -1/45 binary64) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))
(.f64 (.f64 x x) (.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64)))))
(.f64 (.f64 x x) (pow.f64 (neg.f64 (*.f64 x #s(literal -1/45 binary64))) #s(literal 2 binary64)))
(.f64 (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2025 binary64)))
(.f64 (.f64 x #s(literal -1/45 binary64)) (.f64 x (.f64 x (*.f64 x #s(literal -1/45 binary64)))))
(.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (.f64 x (*.f64 x #s(literal -1/45 binary64))))
(.f64 (.f64 x #s(literal 1/45 binary64)) (.f64 (.f64 x (*.f64 x x)) #s(literal 1/45 binary64)))
(.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) (.f64 x (*.f64 x #s(literal 1/45 binary64))))
(.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64)) (*.f64 x #s(literal 1/45 binary64)))
(.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/2025 binary64))))
(.f64 #s(literal 1/2025 binary64) (.f64 (.f64 x x) (.f64 x x)))
(.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) (.f64 x x))
(.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))) x)
(.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/2025 binary64))
(.f64 (.f64 (.f64 x #s(literal 1/45 binary64)) (.f64 x #s(literal 1/45 binary64))) (*.f64 x x))
(.f64 (.f64 (.f64 x #s(literal -1/45 binary64)) (.f64 x #s(literal -1/45 binary64))) (*.f64 x x))
(.f64 (.f64 (.f64 x #s(literal -1/45 binary64)) (.f64 x #s(literal -1/45 binary64))) (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 2 binary64)))
(.f64 (.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) x) (*.f64 x #s(literal -1/45 binary64)))
(.f64 (.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (*.f64 x x)) #s(literal -1/45 binary64))
(.f64 (.f64 (.f64 x (.f64 x #s(literal -1/45 binary64))) (*.f64 x #s(literal -1/45 binary64))) x)
(.f64 (.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) (*.f64 x x)) #s(literal 1/45 binary64))
(.f64 (.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) (*.f64 x #s(literal 1/45 binary64))) x)
(.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/2025 binary64))
(.f64 (pow.f64 (neg.f64 (.f64 x #s(literal -1/45 binary64))) #s(literal 2 binary64)) (*.f64 x x))
(.f64 (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 2 binary64)) (.f64 (.f64 x #s(literal -1/45 binary64)) (.f64 x #s(literal -1/45 binary64))))
(.f64 (pow.f64 (neg.f64 (.f64 x x)) #s(literal 2 binary64)) #s(literal 1/2025 binary64))
(.f64 (pow.f64 (.f64 (-.f64 #s(literal 0 binary64) x) x) #s(literal 2 binary64)) #s(literal 1/2025 binary64))
(.f64 (pow.f64 (.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1/45 binary64)) #s(literal 2 binary64)) (*.f64 x x))
(/.f64 #s(literal -1/45 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 x #s(literal -1/45 binary64))
(*.f64 #s(literal -1/45 binary64) x)
(/.f64 (*.f64 x #s(literal -1/45 binary64)) (/.f64 #s(literal 1 binary64) 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 (.f64 #s(literal -2/945 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 (.f64 x #s(literal -2/945 binary64)) x) (/.f64 #s(literal 1 binary64) x))
(.f64 x (.f64 (*.f64 x x) #s(literal -2/945 binary64)))
(.f64 #s(literal -2/945 binary64) (.f64 x (*.f64 x x)))
(.f64 (.f64 x x) (*.f64 x #s(literal -2/945 binary64)))
(.f64 (.f64 x (*.f64 x x)) #s(literal -2/945 binary64))
(.f64 (.f64 x #s(literal -2/945 binary64)) (*.f64 x x))
(.f64 (.f64 #s(literal -2/945 binary64) (*.f64 x x)) x)
(.f64 (.f64 (*.f64 x #s(literal -2/945 binary64)) x) x)
(/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 x #s(literal 1/3 binary64))
(*.f64 #s(literal 1/3 binary64) x)
(/.f64 (*.f64 x #s(literal 1/2025 binary64)) (/.f64 #s(literal 1 binary64) x))
(.f64 x (.f64 x #s(literal 1/2025 binary64)))
(.f64 (.f64 x x) #s(literal 1/2025 binary64))
(.f64 #s(literal 1/2025 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal 1/2025 binary64)) x)

simplify215.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

2868×	`-lowering-.f32`
2868×	`-lowering-.f64`
1554×	`+-lowering-+.f64`
1554×	`+-lowering-+.f32`
1530×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	108	1522
1	299	1449
2	792	1445
3	2019	1441
4	4681	1439
0	8198	1439

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

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 (* 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))))))
1/3
(+ 1/3 (* 2/945 (pow x 4)))
(+ 1/3 (* 2/945 (pow x 4)))
(+ 1/3 (* 2/945 (pow x 4)))
(* 2/945 (pow x 4))
(* (pow x 4) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))
(* (pow x 4) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))
(* (pow x 4) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))
(* 2/945 (pow x 4))
(* (pow x 4) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))
(* (pow x 4) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))
(* (pow x 4) (+ 2/945 (* 1/3 (/ 1 (pow x 4)))))
(* -2/945 (pow x 4))
(* -2/945 (pow x 4))
(* -2/945 (pow x 4))
(* -2/945 (pow x 4))
(* -2/945 (pow x 4))
(* -2/945 (pow x 4))
(* -2/945 (pow x 4))
(* -2/945 (pow x 4))
(* -2/945 (pow x 4))
(* -2/945 (pow x 4))
(* -2/945 (pow x 4))
(* -2/945 (pow x 4))
(* 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)))))
(* 1/45 (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))
(* 1/45 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)
(* 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)))))
3
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* (pow x 2) (- (* 1/75 (pow x 2)) 1/5)))
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/75 (* -1/1125 (pow x 2)))) 1/5)))
(/ 45 (pow x 2))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (pow x 2))
(/ 45 (pow x 2))
(/ (- 45 (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (* 675 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 45 (/ 10125 (pow x 4))) (+ (* 675 (/ 1 (pow x 2))) (* 151875 (/ 1 (pow x 6))))) (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)))))
(* 1/3 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)))))
(* -1/9 x)
(* x (- (* 1/2025 (pow x 4)) 1/9))
(* x (- (* 1/2025 (pow x 4)) 1/9))
(* x (- (* 1/2025 (pow x 4)) 1/9))
(* 1/2025 (pow x 5))
(* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* (pow x 5) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* 1/2025 (pow x 5))
(* -1 (* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025)))
(* -1 (* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025)))
(* -1 (* (pow x 5) (- (* 1/9 (/ 1 (pow x 4))) 1/2025)))
-1/9
(- (* 1/2025 (pow x 4)) 1/9)
(- (* 1/2025 (pow x 4)) 1/9)
(- (* 1/2025 (pow x 4)) 1/9)
(* 1/2025 (pow x 4))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* 1/2025 (pow x 4))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(* 1/2025 (pow x 4))
(* 1/2025 (pow x 4))
(* 1/2025 (pow x 4))
(* 1/2025 (pow x 4))
(* 1/2025 (pow x 4))
(* 1/2025 (pow x 4))
(* 1/2025 (pow x 4))
(* 1/2025 (pow x 4))
(* 1/2025 (pow x 4))
(* 1/2025 (pow x 4))
(* 1/2025 (pow x 4))
(* 1/2025 (pow x 4))
(* -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)
(* -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))
(* -2/945 (pow x 3))
(* -2/945 (pow x 3))
(* -2/945 (pow x 3))
(* -2/945 (pow x 3))
(* -2/945 (pow x 3))
(* -2/945 (pow x 3))
(* -2/945 (pow x 3))
(* -2/945 (pow x 3))
(* -2/945 (pow x 3))
(* -2/945 (pow x 3))
(* -2/945 (pow x 3))
(* -2/945 (pow x 3))
(* 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)
(* 1/2025 (pow x 2))
(* 1/2025 (pow x 2))
(* 1/2025 (pow x 2))
(* 1/2025 (pow x 2))
(* 1/2025 (pow x 2))
(* 1/2025 (pow x 2))
(* 1/2025 (pow x 2))
(* 1/2025 (pow x 2))
(* 1/2025 (pow x 2))
(* 1/2025 (pow x 2))
(* 1/2025 (pow x 2))
(* 1/2025 (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 x (*.f64 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 x (*.f64 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 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))))))
(* (pow x 5) (+ 2/945 (* 1/45 (/ 1 (pow x 2)))))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 2/945 binary64) (/.f64 #s(literal 1/45 binary64) (.f64 x x))))
(* (pow x 5) (+ 2/945 (+ (/ 1/3 (pow x 4)) (* 1/45 (/ 1 (pow x 2))))))
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(- (* 1/2025 (pow x 4)) 1/9)
(+.f64 #s(literal -1/9 binary64) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/2025 binary64))))
(- (* 1/2025 (pow x 4)) 1/9)
(+.f64 #s(literal -1/9 binary64) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/2025 binary64))))
(- (* 1/2025 (pow x 4)) 1/9)
(+.f64 #s(literal -1/9 binary64) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/2025 binary64))))
(* 1/2025 (pow x 4))
(.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/2025 binary64)))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(+.f64 #s(literal -1/9 binary64) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/2025 binary64))))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(+.f64 #s(literal -1/9 binary64) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/2025 binary64))))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(+.f64 #s(literal -1/9 binary64) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/2025 binary64))))
(* 1/2025 (pow x 4))
(.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/2025 binary64)))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(+.f64 #s(literal -1/9 binary64) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/2025 binary64))))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(+.f64 #s(literal -1/9 binary64) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/2025 binary64))))
(* (pow x 4) (- 1/2025 (* 1/9 (/ 1 (pow x 4)))))
(+.f64 #s(literal -1/9 binary64) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/2025 binary64))))
(* 1/2025 (pow x 4))
(.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/2025 binary64)))
(* 1/2025 (pow x 4))
(.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/2025 binary64)))
(* 1/2025 (pow x 4))
(.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/2025 binary64)))
(* 1/2025 (pow x 4))
(.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/2025 binary64)))
(* 1/2025 (pow x 4))
(.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/2025 binary64)))
(* 1/2025 (pow x 4))
(.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/2025 binary64)))
(* 1/2025 (pow x 4))
(.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/2025 binary64)))
(* 1/2025 (pow x 4))
(.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/2025 binary64)))
(* 1/2025 (pow x 4))
(.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/2025 binary64)))
(* 1/2025 (pow x 4))
(.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/2025 binary64)))
(* 1/2025 (pow x 4))
(.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/2025 binary64)))
(* 1/2025 (pow x 4))
(.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/2025 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))
(* -1/45 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)))
(* -2/945 (pow x 3))
(.f64 #s(literal -2/945 binary64) (.f64 x (*.f64 x x)))
(* -2/945 (pow x 3))
(.f64 #s(literal -2/945 binary64) (.f64 x (*.f64 x x)))
(* -2/945 (pow x 3))
(.f64 #s(literal -2/945 binary64) (.f64 x (*.f64 x x)))
(* -2/945 (pow x 3))
(.f64 #s(literal -2/945 binary64) (.f64 x (*.f64 x x)))
(* -2/945 (pow x 3))
(.f64 #s(literal -2/945 binary64) (.f64 x (*.f64 x x)))
(* -2/945 (pow x 3))
(.f64 #s(literal -2/945 binary64) (.f64 x (*.f64 x x)))
(* -2/945 (pow x 3))
(.f64 #s(literal -2/945 binary64) (.f64 x (*.f64 x x)))
(* -2/945 (pow x 3))
(.f64 #s(literal -2/945 binary64) (.f64 x (*.f64 x x)))
(* -2/945 (pow x 3))
(.f64 #s(literal -2/945 binary64) (.f64 x (*.f64 x x)))
(* -2/945 (pow x 3))
(.f64 #s(literal -2/945 binary64) (.f64 x (*.f64 x x)))
(* -2/945 (pow x 3))
(.f64 #s(literal -2/945 binary64) (.f64 x (*.f64 x x)))
(* -2/945 (pow x 3))
(.f64 #s(literal -2/945 binary64) (.f64 x (*.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)
(* 1/2025 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2025 binary64))
(* 1/2025 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2025 binary64))
(* 1/2025 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2025 binary64))
(* 1/2025 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2025 binary64))
(* 1/2025 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2025 binary64))
(* 1/2025 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2025 binary64))
(* 1/2025 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2025 binary64))
(* 1/2025 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2025 binary64))
(* 1/2025 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2025 binary64))
(* 1/2025 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2025 binary64))
(* 1/2025 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2025 binary64))
(* 1/2025 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2025 binary64))

eval144.0ms (1.2%)

Compiler: Compiled 34491 to 2125 computations (93.8% saved)

prune77.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	1140	3	1143
Fresh	0	0	0
Picked	4	0	4
Done	2	1	3
Total	1146	4	1150

Accuracy

100.0%

Counts

1150 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(/.f64 (.f64 x #s(literal -1/9 binary64)) (+.f64 (.f64 x (*.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64)))
▶	99.9%	(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64))))
▶	99.3%	(/.f64 x #s(literal 3 binary64))
✓	99.5%	(.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)))))))

Compiler

Compiled 42 to 30 computations (28.6% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

New	Metric	Program
✓	cost-diff	(.f64 x (.f64 x #s(literal 1/45 binary64)))
✓	cost-diff	(+.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64))
✓	cost-diff	(*.f64 x #s(literal -1/9 binary64))
✓	cost-diff	(/.f64 (.f64 x #s(literal -1/9 binary64)) (+.f64 (.f64 x (*.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64)))
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(.f64 (.f64 x x) #s(literal -1/5 binary64))
✓	cost-diff	(+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64)))
✓	cost-diff	(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64))))
✓	cost-diff	(/.f64 x #s(literal 3 binary64))

Rules

38×	`-lowering-.f32`
38×	`-lowering-.f64`
16×	`*-commutative`
16×	`fma-lowering-fma.f32`
16×	`fma-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	63
1	28	61
2	40	61
3	43	61
0	43	61

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ x 3)
x
3
(/ x (+ 3 (* (* x x) -1/5)))
x
(+ 3 (* (* x x) -1/5))
3
(* (* x x) -1/5)
(* x x)
-1/5
(/ (* x -1/9) (+ (* x (* x 1/45)) -1/3))
(* x -1/9)
x
-1/9
(+ (* x (* x 1/45)) -1/3)
(* x (* x 1/45))
(* x 1/45)
1/45
-1/3

Outputs
(/ x 3)
(/.f64 x #s(literal 3 binary64))
x
3
#s(literal 3 binary64)
(/ x (+ 3 (* (* x x) -1/5)))
(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64))))
x
(+ 3 (* (* x x) -1/5))
(+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64)))
3
#s(literal 3 binary64)
(* (* x x) -1/5)
(.f64 (.f64 x x) #s(literal -1/5 binary64))
(* x x)
(*.f64 x x)
-1/5
#s(literal -1/5 binary64)
(/ (* x -1/9) (+ (* x (* x 1/45)) -1/3))
(/.f64 (.f64 x #s(literal -1/9 binary64)) (+.f64 (.f64 x (*.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64)))
(* x -1/9)
(*.f64 x #s(literal -1/9 binary64))
x
-1/9
#s(literal -1/9 binary64)
(+ (* x (* x 1/45)) -1/3)
(+.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64))
(* x (* x 1/45))
(.f64 x (.f64 x #s(literal 1/45 binary64)))
(* x 1/45)
(*.f64 x #s(literal 1/45 binary64))
1/45
#s(literal 1/45 binary64)
-1/3
#s(literal -1/3 binary64)

localize98.0ms (0.8%)

Localize:

Found 9 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(.f64 x (.f64 x #s(literal 1/45 binary64)))
✓	accuracy	99.7%	(*.f64 x #s(literal 1/45 binary64))
✓	accuracy	99.5%	(*.f64 x #s(literal -1/9 binary64))
✓	accuracy	99.5%	(/.f64 (.f64 x #s(literal -1/9 binary64)) (+.f64 (.f64 x (*.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64)))
✓	accuracy	100.0%	(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64))))
✓	accuracy	100.0%	(+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64)))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.7%	(.f64 (.f64 x x) #s(literal -1/5 binary64))
✓	accuracy	100.0%	(/.f64 x #s(literal 3 binary64))

Results

80.0ms

256×

valid

Compiler

Compiled 67 to 17 computations (74.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 62.0ms

ival-mult: 36.0ms (58.3% of total)

...c/correct-round.rkt:119:19: 13.0ms (21.1% of total)

ival-add: 7.0ms (11.3% of total)

ival-div: 6.0ms (9.7% 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 (/ x 3)>
#<alt (/ x (+ 3 (* (* x x) -1/5)))>
#<alt (+ 3 (* (* x x) -1/5))>
#<alt (* (* x x) -1/5)>
#<alt (* x x)>
#<alt (/ (* x -1/9) (+ (* x (* x 1/45)) -1/3))>
#<alt (* x -1/9)>
#<alt (+ (* x (* x 1/45)) -1/3)>
#<alt (* x (* x 1/45))>
#<alt (* x 1/45)>

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 (* (pow x 2) (+ 1/45 (* 1/675 (pow x 2))))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 1/675 (* 1/10125 (pow x 2))))))))>
#<alt (/ -5 x)>
#<alt (* -1 (/ (+ 5 (* 75 (/ 1 (pow x 2)))) x))>
#<alt (/ (- (* -1 (/ (+ 75 (* 1125 (/ 1 (pow x 2)))) (pow x 2))) 5) x)>
#<alt (/ (- (* -1 (/ (+ 1125 (* 16875 (/ 1 (pow x 2)))) (pow x 4))) (+ 5 (* 75 (/ 1 (pow x 2))))) x)>
#<alt (/ -5 x)>
#<alt (* -1 (/ (+ 5 (* 75 (/ 1 (pow x 2)))) x))>
#<alt (* -1 (/ (+ 5 (+ (* 75 (/ 1 (pow x 2))) (/ 1125 (pow x 4)))) x))>
#<alt (* -1 (/ (+ 5 (+ (* 75 (/ 1 (pow x 2))) (+ (* 16875 (/ 1 (pow x 6))) (/ 1125 (pow x 4))))) x))>
#<alt 3>
#<alt (+ 3 (* -1/5 (pow x 2)))>
#<alt (+ 3 (* -1/5 (pow x 2)))>
#<alt (+ 3 (* -1/5 (pow x 2)))>
#<alt (* -1/5 (pow x 2))>
#<alt (* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))>
#<alt (* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))>
#<alt (* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))>
#<alt (* -1/5 (pow x 2))>
#<alt (* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))>
#<alt (* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))>
#<alt (* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))>
#<alt (* -1/5 (pow x 2))>
#<alt (* -1/5 (pow x 2))>
#<alt (* -1/5 (pow x 2))>
#<alt (* -1/5 (pow x 2))>
#<alt (* -1/5 (pow x 2))>
#<alt (* -1/5 (pow x 2))>
#<alt (* -1/5 (pow x 2))>
#<alt (* -1/5 (pow x 2))>
#<alt (* -1/5 (pow x 2))>
#<alt (* -1/5 (pow x 2))>
#<alt (* -1/5 (pow x 2))>
#<alt (* -1/5 (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 (* 1/675 (pow x 2))))))>
#<alt (* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 1/675 (* 1/10125 (pow x 2))))))))>
#<alt (/ -5 x)>
#<alt (* -1 (/ (+ 5 (* 75 (/ 1 (pow x 2)))) x))>
#<alt (/ (- (* -1 (/ (+ 75 (* 1125 (/ 1 (pow x 2)))) (pow x 2))) 5) x)>
#<alt (/ (- (* -1 (/ (+ 1125 (* 16875 (/ 1 (pow x 2)))) (pow x 4))) (+ 5 (* 75 (/ 1 (pow x 2))))) x)>
#<alt (/ -5 x)>
#<alt (* -1 (/ (+ 5 (* 75 (/ 1 (pow x 2)))) x))>
#<alt (* -1 (/ (+ 5 (+ (* 75 (/ 1 (pow x 2))) (/ 1125 (pow x 4)))) x))>
#<alt (* -1 (/ (+ 5 (+ (* 75 (/ 1 (pow x 2))) (+ (* 16875 (/ 1 (pow x 6))) (/ 1125 (pow x 4))))) x))>
#<alt (* -1/9 x)>
#<alt (* -1/9 x)>
#<alt (* -1/9 x)>
#<alt (* -1/9 x)>
#<alt (* -1/9 x)>
#<alt (* -1/9 x)>
#<alt (* -1/9 x)>
#<alt (* -1/9 x)>
#<alt (* -1/9 x)>
#<alt (* -1/9 x)>
#<alt (* -1/9 x)>
#<alt (* -1/9 x)>
#<alt -1/3>
#<alt (- (* 1/45 (pow x 2)) 1/3)>
#<alt (- (* 1/45 (pow x 2)) 1/3)>
#<alt (- (* 1/45 (pow x 2)) 1/3)>
#<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 (* 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)>

Calls

30 calls:

Time	Variable		Point	Expression
4.0ms	x	@	0	(/ (* x -1/9) (+ (* x (* x 1/45)) -1/3))
0.0ms	x	@	inf	(/ x (+ 3 (* (* x x) -1/5)))
0.0ms	x	@	inf	(* (* x x) -1/5)
0.0ms	x	@	-inf	(* x -1/9)
0.0ms	x	@	inf	(* x -1/9)

rewrite279.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

3278×	`-lowering-.f32`
3278×	`-lowering-.f64`
2100×	`/-lowering-/.f32`
2100×	`/-lowering-/.f64`
2048×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	54
1	81	52
2	527	52
3	4976	52
0	8087	52

Stop Event

1×	iter limit
1×	node limit

Counts

10 → 342

Calls

Call 1

Inputs
(/ x 3)
(/ x (+ 3 (* (* x x) -1/5)))
(+ 3 (* (* x x) -1/5))
(* (* x x) -1/5)
(* x x)
(/ (* x -1/9) (+ (* x (* x 1/45)) -1/3))
(* x -1/9)
(+ (* x (* x 1/45)) -1/3)
(* x (* x 1/45))
(* x 1/45)

Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 3 binary64) x)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 x #s(literal -3 binary64)))
(neg.f64 (/.f64 x #s(literal -3 binary64)))
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 x #s(literal -3 binary64))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 3 binary64) x)))
(/.f64 x #s(literal 3 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -3 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3 binary64) x))
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(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64))) #s(literal -1/27 binary64)))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64)))))))
(/.f64 (neg.f64 (+.f64 (neg.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64)))) #s(literal 1/9 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
(/.f64 (neg.f64 (+.f64 (neg.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64)))) #s(literal 1/9 binary64))) (neg.f64 (+.f64 (.f64 (.f64 x x) #s(literal -1/45 binary64)) #s(literal -1/3 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64))))) (neg.f64 (+.f64 #s(literal -1/3 binary64) (.f64 (.f64 x x) #s(literal -1/45 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/9 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) (+.f64 (.f64 (/.f64 #s(literal 1/9 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) (/.f64 #s(literal 1/9 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) (.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) (/.f64 #s(literal 1/9 binary64) (+.f64 (.f64 (*.f64 x x) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) (.f64 (/.f64 #s(literal 1/9 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) (/.f64 #s(literal 1/9 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))) (+.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) (/.f64 #s(literal 1/9 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))))
(/.f64 (.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64))) (.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/8303765625 binary64))) #s(literal -1/19683 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64)))))) (+.f64 (.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/8303765625 binary64)) (-.f64 #s(literal 1/729 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/2460375 binary64)))))
(/.f64 (.f64 (+.f64 (.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/8303765625 binary64)) #s(literal -1/729 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64)))))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal 1/91125 binary64))) #s(literal 1/27 binary64)))
(/.f64 (.f64 (+.f64 (.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/8303765625 binary64)) #s(literal -1/729 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) (+.f64 (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/4100625 binary64)) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1/18225 binary64)))))
(/.f64 (.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/4100625 binary64)) #s(literal -1/81 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) (+.f64 (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/2025 binary64))) #s(literal 1/9 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 1/45 binary64)) #s(literal -1/3 binary64))) #s(literal -1 binary64))
(.f64 (+.f64 (.f64 (*.f64 x x) #s(literal 1/45 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64))
(.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64))) #s(literal -1/27 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))))))
(.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64))) #s(literal -1/27 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))))) #s(literal 1 binary64)))
(.f64 #s(literal 1 binary64) (+.f64 (.f64 (*.f64 x x) #s(literal 1/45 binary64)) #s(literal -1/3 binary64)))
(.f64 (+.f64 #s(literal -1/9 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (*.f64 x x) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
(.f64 (+.f64 #s(literal -1/9 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (*.f64 x x) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) #s(literal 1 binary64)))
(.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64))) #s(literal -1/27 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64)))))))
(.f64 (+.f64 (neg.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64)))) #s(literal 1/9 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (*.f64 x x) #s(literal -1/45 binary64)) #s(literal -1/3 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64))))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal 1/91125 binary64))) #s(literal -1/27 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 1/45 binary64)) #s(literal 1/3 binary64))) (+.f64 #s(literal -1/9 binary64) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/2025 binary64)))))
(.f64 (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64)))))
(.f64 (/.f64 (+.f64 #s(literal -1/9 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64)))) (+.f64 #s(literal -1/9 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64))))) (+.f64 (.f64 (*.f64 x x) #s(literal 1/45 binary64)) #s(literal -1/3 binary64)))
(.f64 (/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64))) #s(literal -1/27 binary64)) (+.f64 (.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/8303765625 binary64)) (.f64 (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) #s(literal -1/135 binary64))) (.f64 (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) #s(literal -1/135 binary64))) (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) #s(literal -1/135 binary64))))))) (+.f64 (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/4100625 binary64)) (.f64 (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) #s(literal -1/135 binary64))) (-.f64 (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) #s(literal -1/135 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64)))))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64))) #s(literal -1/27 binary64)) (.f64 (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal -1/135 binary64)))) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64))) (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) #s(literal -1/135 binary64)))))) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64))) (-.f64 #s(literal 1/9 binary64) (.f64 (.f64 x x) #s(literal -1/135 binary64)))))
(.f64 (/.f64 (+.f64 #s(literal -1/9 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64)))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64))) #s(literal 1/27 binary64))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2025 binary64))) (+.f64 #s(literal 1/9 binary64) (.f64 (*.f64 x x) #s(literal -1/135 binary64)))))
(.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 #s(literal 1/45 binary64))
(*.f64 #s(literal 1/45 binary64) x)

simplify247.0ms (2%)

Algorithm

1×	egg-herbie

Rules

2054×	`-lowering-.f32`
2054×	`-lowering-.f64`
2048×	`sum4-define`
1808×	`fnmsub-define`
1422×	`fma-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	80	703
1	216	678
2	602	666
3	1602	664
4	3594	660
5	6543	660
0	8229	660

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 (* (pow x 2) (+ 1/45 (* 1/675 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 1/675 (* 1/10125 (pow x 2))))))))
(/ -5 x)
(* -1 (/ (+ 5 (* 75 (/ 1 (pow x 2)))) x))
(/ (- (* -1 (/ (+ 75 (* 1125 (/ 1 (pow x 2)))) (pow x 2))) 5) x)
(/ (- (* -1 (/ (+ 1125 (* 16875 (/ 1 (pow x 2)))) (pow x 4))) (+ 5 (* 75 (/ 1 (pow x 2))))) x)
(/ -5 x)
(* -1 (/ (+ 5 (* 75 (/ 1 (pow x 2)))) x))
(* -1 (/ (+ 5 (+ (* 75 (/ 1 (pow x 2))) (/ 1125 (pow x 4)))) x))
(* -1 (/ (+ 5 (+ (* 75 (/ 1 (pow x 2))) (+ (* 16875 (/ 1 (pow x 6))) (/ 1125 (pow x 4))))) x))
3
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* -1/5 (pow x 2)))
(+ 3 (* -1/5 (pow x 2)))
(* -1/5 (pow x 2))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* -1/5 (pow x 2))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (pow x 2))
(* -1/5 (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 (* 1/675 (pow x 2))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 1/675 (* 1/10125 (pow x 2))))))))
(/ -5 x)
(* -1 (/ (+ 5 (* 75 (/ 1 (pow x 2)))) x))
(/ (- (* -1 (/ (+ 75 (* 1125 (/ 1 (pow x 2)))) (pow x 2))) 5) x)
(/ (- (* -1 (/ (+ 1125 (* 16875 (/ 1 (pow x 2)))) (pow x 4))) (+ 5 (* 75 (/ 1 (pow x 2))))) x)
(/ -5 x)
(* -1 (/ (+ 5 (* 75 (/ 1 (pow x 2)))) x))
(* -1 (/ (+ 5 (+ (* 75 (/ 1 (pow x 2))) (/ 1125 (pow x 4)))) x))
(* -1 (/ (+ 5 (+ (* 75 (/ 1 (pow x 2))) (+ (* 16875 (/ 1 (pow x 6))) (/ 1125 (pow x 4))))) x))
(* -1/9 x)
(* -1/9 x)
(* -1/9 x)
(* -1/9 x)
(* -1/9 x)
(* -1/9 x)
(* -1/9 x)
(* -1/9 x)
(* -1/9 x)
(* -1/9 x)
(* -1/9 x)
(* -1/9 x)
-1/3
(- (* 1/45 (pow x 2)) 1/3)
(- (* 1/45 (pow x 2)) 1/3)
(- (* 1/45 (pow x 2)) 1/3)
(* 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))
(* 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)

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 (* (pow x 2) (+ 1/45 (* 1/675 (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 1/675 binary64))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 1/675 (* 1/10125 (pow x 2))))))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/675 binary64) (.f64 (*.f64 x x) #s(literal 1/10125 binary64)))))))))
(/ -5 x)
(/.f64 #s(literal -5 binary64) x)
(* -1 (/ (+ 5 (* 75 (/ 1 (pow x 2)))) x))
(/.f64 (+.f64 #s(literal -5 binary64) (/.f64 #s(literal -75 binary64) (*.f64 x x))) x)
(/ (- (* -1 (/ (+ 75 (* 1125 (/ 1 (pow x 2)))) (pow x 2))) 5) x)
(/.f64 (+.f64 #s(literal -5 binary64) (/.f64 (+.f64 #s(literal -75 binary64) (/.f64 (/.f64 #s(literal -1125 binary64) x) x)) (*.f64 x x))) x)
(/ (- (* -1 (/ (+ 1125 (* 16875 (/ 1 (pow x 2)))) (pow x 4))) (+ 5 (* 75 (/ 1 (pow x 2))))) x)
(/.f64 (+.f64 #s(literal -5 binary64) (.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 (/.f64 (+.f64 #s(literal 1125 binary64) (/.f64 #s(literal 16875 binary64) (.f64 x x))) (.f64 x x)) #s(literal 75 binary64)))) x)
(/ -5 x)
(/.f64 #s(literal -5 binary64) x)
(* -1 (/ (+ 5 (* 75 (/ 1 (pow x 2)))) x))
(/.f64 (+.f64 #s(literal -5 binary64) (/.f64 #s(literal -75 binary64) (*.f64 x x))) x)
(* -1 (/ (+ 5 (+ (* 75 (/ 1 (pow x 2))) (/ 1125 (pow x 4)))) x))
(/.f64 (+.f64 #s(literal -5 binary64) (/.f64 (+.f64 #s(literal -75 binary64) (/.f64 (/.f64 #s(literal -1125 binary64) x) x)) (*.f64 x x))) x)
(* -1 (/ (+ 5 (+ (* 75 (/ 1 (pow x 2))) (+ (* 16875 (/ 1 (pow x 6))) (/ 1125 (pow x 4))))) x))
(/.f64 (+.f64 #s(literal -5 binary64) (+.f64 (/.f64 (+.f64 #s(literal -75 binary64) (/.f64 (/.f64 #s(literal -1125 binary64) x) x)) (.f64 x x)) (/.f64 #s(literal -16875 binary64) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))))) x)
3
#s(literal 3 binary64)
(+ 3 (* -1/5 (pow x 2)))
(+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64)))
(+ 3 (* -1/5 (pow x 2)))
(+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64)))
(+ 3 (* -1/5 (pow x 2)))
(+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64)))
(* -1/5 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/5 binary64))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64)))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64)))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64)))
(* -1/5 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/5 binary64))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64)))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64)))
(* (pow x 2) (- (* 3 (/ 1 (pow x 2))) 1/5))
(+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64)))
(* -1/5 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/5 binary64))
(* -1/5 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/5 binary64))
(* -1/5 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/5 binary64))
(* -1/5 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/5 binary64))
(* -1/5 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/5 binary64))
(* -1/5 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/5 binary64))
(* -1/5 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/5 binary64))
(* -1/5 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/5 binary64))
(* -1/5 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/5 binary64))
(* -1/5 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/5 binary64))
(* -1/5 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/5 binary64))
(* -1/5 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/5 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 (* 1/675 (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 1/675 binary64))))))
(* x (+ 1/3 (* (pow x 2) (+ 1/45 (* (pow x 2) (+ 1/675 (* 1/10125 (pow x 2))))))))
(.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/675 binary64) (.f64 (*.f64 x x) #s(literal 1/10125 binary64)))))))))
(/ -5 x)
(/.f64 #s(literal -5 binary64) x)
(* -1 (/ (+ 5 (* 75 (/ 1 (pow x 2)))) x))
(/.f64 (+.f64 #s(literal -5 binary64) (/.f64 #s(literal -75 binary64) (*.f64 x x))) x)
(/ (- (* -1 (/ (+ 75 (* 1125 (/ 1 (pow x 2)))) (pow x 2))) 5) x)
(/.f64 (+.f64 #s(literal -5 binary64) (/.f64 (+.f64 #s(literal -75 binary64) (/.f64 (/.f64 #s(literal -1125 binary64) x) x)) (*.f64 x x))) x)
(/ (- (* -1 (/ (+ 1125 (* 16875 (/ 1 (pow x 2)))) (pow x 4))) (+ 5 (* 75 (/ 1 (pow x 2))))) x)
(/.f64 (+.f64 #s(literal -5 binary64) (.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 (/.f64 (+.f64 #s(literal 1125 binary64) (/.f64 #s(literal 16875 binary64) (.f64 x x))) (.f64 x x)) #s(literal 75 binary64)))) x)
(/ -5 x)
(/.f64 #s(literal -5 binary64) x)
(* -1 (/ (+ 5 (* 75 (/ 1 (pow x 2)))) x))
(/.f64 (+.f64 #s(literal -5 binary64) (/.f64 #s(literal -75 binary64) (*.f64 x x))) x)
(* -1 (/ (+ 5 (+ (* 75 (/ 1 (pow x 2))) (/ 1125 (pow x 4)))) x))
(/.f64 (+.f64 #s(literal -5 binary64) (/.f64 (+.f64 #s(literal -75 binary64) (/.f64 (/.f64 #s(literal -1125 binary64) x) x)) (*.f64 x x))) x)
(* -1 (/ (+ 5 (+ (* 75 (/ 1 (pow x 2))) (+ (* 16875 (/ 1 (pow x 6))) (/ 1125 (pow x 4))))) x))
(/.f64 (+.f64 #s(literal -5 binary64) (+.f64 (/.f64 (+.f64 #s(literal -75 binary64) (/.f64 (/.f64 #s(literal -1125 binary64) x) x)) (.f64 x x)) (/.f64 #s(literal -16875 binary64) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))))) x)
(* -1/9 x)
(*.f64 x #s(literal -1/9 binary64))
(* -1/9 x)
(*.f64 x #s(literal -1/9 binary64))
(* -1/9 x)
(*.f64 x #s(literal -1/9 binary64))
(* -1/9 x)
(*.f64 x #s(literal -1/9 binary64))
(* -1/9 x)
(*.f64 x #s(literal -1/9 binary64))
(* -1/9 x)
(*.f64 x #s(literal -1/9 binary64))
(* -1/9 x)
(*.f64 x #s(literal -1/9 binary64))
(* -1/9 x)
(*.f64 x #s(literal -1/9 binary64))
(* -1/9 x)
(*.f64 x #s(literal -1/9 binary64))
(* -1/9 x)
(*.f64 x #s(literal -1/9 binary64))
(* -1/9 x)
(*.f64 x #s(literal -1/9 binary64))
(* -1/9 x)
(*.f64 x #s(literal -1/9 binary64))
-1/3
#s(literal -1/3 binary64)
(- (* 1/45 (pow x 2)) 1/3)
(+.f64 (.f64 #s(literal 1/45 binary64) (.f64 x x)) #s(literal -1/3 binary64))
(- (* 1/45 (pow x 2)) 1/3)
(+.f64 (.f64 #s(literal 1/45 binary64) (.f64 x x)) #s(literal -1/3 binary64))
(- (* 1/45 (pow x 2)) 1/3)
(+.f64 (.f64 #s(literal 1/45 binary64) (.f64 x x)) #s(literal -1/3 binary64))
(* 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 (.f64 #s(literal 1/45 binary64) (.f64 x x)) #s(literal -1/3 binary64))
(* (pow x 2) (- 1/45 (* 1/3 (/ 1 (pow x 2)))))
(+.f64 (.f64 #s(literal 1/45 binary64) (.f64 x x)) #s(literal -1/3 binary64))
(* (pow x 2) (- 1/45 (* 1/3 (/ 1 (pow x 2)))))
(+.f64 (.f64 #s(literal 1/45 binary64) (.f64 x x)) #s(literal -1/3 binary64))
(* 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 (.f64 #s(literal 1/45 binary64) (.f64 x x)) #s(literal -1/3 binary64))
(* (pow x 2) (- 1/45 (* 1/3 (/ 1 (pow x 2)))))
(+.f64 (.f64 #s(literal 1/45 binary64) (.f64 x x)) #s(literal -1/3 binary64))
(* (pow x 2) (- 1/45 (* 1/3 (/ 1 (pow x 2)))))
(+.f64 (.f64 #s(literal 1/45 binary64) (.f64 x x)) #s(literal -1/3 binary64))
(* 1/45 (pow x 2))
(.f64 #s(literal 1/45 binary64) (.f64 x x))
(* 1/45 (pow x 2))
(.f64 #s(literal 1/45 binary64) (.f64 x x))
(* 1/45 (pow x 2))
(.f64 #s(literal 1/45 binary64) (.f64 x x))
(* 1/45 (pow x 2))
(.f64 #s(literal 1/45 binary64) (.f64 x x))
(* 1/45 (pow x 2))
(.f64 #s(literal 1/45 binary64) (.f64 x x))
(* 1/45 (pow x 2))
(.f64 #s(literal 1/45 binary64) (.f64 x x))
(* 1/45 (pow x 2))
(.f64 #s(literal 1/45 binary64) (.f64 x x))
(* 1/45 (pow x 2))
(.f64 #s(literal 1/45 binary64) (.f64 x x))
(* 1/45 (pow x 2))
(.f64 #s(literal 1/45 binary64) (.f64 x x))
(* 1/45 (pow x 2))
(.f64 #s(literal 1/45 binary64) (.f64 x x))
(* 1/45 (pow x 2))
(.f64 #s(literal 1/45 binary64) (.f64 x x))
(* 1/45 (pow x 2))
(.f64 #s(literal 1/45 binary64) (.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))

eval52.0ms (0.4%)

Compiler: Compiled 10715 to 1012 computations (90.6% saved)

prune53.0ms (0.4%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	461	1	462
Fresh	0	0	0
Picked	0	3	3
Done	0	1	1
Total	461	5	466

Accuracy

100.0%

Counts

466 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(/.f64 (.f64 x #s(literal -1/9 binary64)) (+.f64 (.f64 x (*.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64)))
	99.0%	(/.f64 (*.f64 x #s(literal -1/9 binary64)) #s(literal -1/3 binary64))
✓	99.9%	(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64))))
✓	99.3%	(/.f64 x #s(literal 3 binary64))
✓	99.5%	(.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)))))))

Compiler

Compiled 174 to 90 computations (48.3% saved)

regimes7.0ms (0.1%)

Counts

12 → 1

Calls

Call 1

Inputs
(*.f64 #s(literal 1/3 binary64) x)
(/.f64 x #s(literal 3 binary64))
(/.f64 (*.f64 x #s(literal -1/9 binary64)) #s(literal -1/3 binary64))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64))))
(+.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/45 binary64)))) (.f64 #s(literal 1/3 binary64) x))
(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))))
(/.f64 (.f64 x #s(literal -1/9 binary64)) (+.f64 (.f64 x (*.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64)))
(.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)))))))
(.f64 x (-.f64 (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 #s(literal -2/945 binary64) (.f64 x (.f64 x x))))) (.f64 x (*.f64 x #s(literal -1/45 binary64)))))
(/.f64 (.f64 (+.f64 #s(literal -1/9 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))))) x) (+.f64 (.f64 x (*.f64 x #s(literal 1/45 binary64))) #s(literal -1/3 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Outputs
(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64))))

Calls

2 calls:

4.0ms	x
3.0ms	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	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

4 → 1

Calls

Call 1

Inputs
(*.f64 #s(literal 1/3 binary64) x)
(/.f64 x #s(literal 3 binary64))
(/.f64 (*.f64 x #s(literal -1/9 binary64)) #s(literal -1/3 binary64))
(.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:

2.0ms

Results

Accuracy	Segments	Branch
99.4%	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 #s(literal 3 binary64))
(/.f64 (*.f64 x #s(literal -1/9 binary64)) #s(literal -1/3 binary64))

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
99.3%	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
98.9%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	24
1	24	24
2	39	24
3	47	24
4	53	24
5	55	24

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 x (+.f64 #s(literal 3 binary64) (.f64 (.f64 x x) #s(literal -1/5 binary64))))
(.f64 x (-.f64 #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
(/.f64 x #s(literal 3 binary64))
(*.f64 #s(literal 1/3 binary64) x)

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

soundness819.0ms (6.8%)

Rules

5384×	`-lowering-.f32`
5384×	`-lowering-.f64`
2868×	`-lowering-.f32`
2868×	`-lowering-.f64`
2582×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	108	1522
1	299	1449
2	792	1445
3	2019	1441
4	4681	1439
0	8198	1439
0	15	74
1	83	71
2	675	67
0	8126	67
0	67	302
1	186	287
2	559	281
3	1807	281
4	2717	281
5	4432	281
6	6049	281
7	6591	281
0	8079	281

Stop Event

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

Compiler

Compiled 97 to 66 computations (32% saved)

preprocess44.0ms (0.4%)

Remove: (negabs x)
Compiler: Compiled 158 to 102 computations (35.4% saved)

Iter	Nodes	Cost
0	12	20
1	29	19
2	64	18
3	146	18
4	300	18
5	464	18
6	507	18
7	515	18
0	6	6
1	12	6
2	20	6
3	31	6
4	45	6
5	82	6
6	152	6
7	248	6
8	350	6
9	486	6
10	607	6
11	639	6
0	639	6

Iter	Nodes	Cost
0	6	15
1	12	15
2	20	15
3	31	15
4	45	15
5	82	15
6	152	15
7	248	15
8	350	15
9	486	15
10	607	15
11	639	15
0	639	15

Iter	Nodes	Cost
0	12	20
1	29	19
2	64	18
3	146	18
4	300	18
5	464	18
6	507	18
7	515	18
0	6	6
1	12	6
2	20	6
3	31	6
4	45	6
5	82	6
6	152	6
7	248	6
8	350	6
9	486	6
10	607	6
11	639	6
0	639	6

Iter	Nodes	Cost
0	6	15
1	12	15
2	20	15
3	31	15
4	45	15
5	82	15
6	152	15
7	248	15
8	350	15
9	486	15
10	607	15
11	639	15
0	639	15

analyze7.0ms (0.1%)

sample7.4s (60.8%)

preprocess36.0ms (0.3%)

explain393.0ms (3.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify19.0ms (0.2%)

localize273.0ms (2.3%)

series6.0ms (0%)

rewrite196.0ms (1.6%)

simplify186.0ms (1.5%)

eval28.0ms (0.2%)

prune32.0ms (0.3%)

simplify132.0ms (1.1%)

localize100.0ms (0.8%)

series8.0ms (0.1%)

rewrite268.0ms (2.2%)

simplify154.0ms (1.3%)

eval58.0ms (0.5%)

prune37.0ms (0.3%)

simplify214.0ms (1.8%)

localize156.0ms (1.3%)

series11.0ms (0.1%)

rewrite374.0ms (3.1%)

simplify215.0ms (1.8%)

eval144.0ms (1.2%)

prune77.0ms (0.6%)

simplify6.0ms (0%)

localize98.0ms (0.8%)

series8.0ms (0.1%)

rewrite279.0ms (2.3%)

simplify247.0ms (2%)

eval52.0ms (0.4%)

prune53.0ms (0.4%)

regimes7.0ms (0.1%)

regimes2.0ms (0%)

regimes2.0ms (0%)

regimes1.0ms (0%)

simplify9.0ms (0.1%)

soundness819.0ms (6.8%)

preprocess44.0ms (0.4%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	12	20
1	29	19
2	64	18
3	146	18
4	300	18
5	464	18
6	507	18
7	515	18
0	6	6
1	12	6
2	20	6
3	31	6
4	45	6
5	82	6
6	152	6
7	248	6
8	350	6
9	486	6
10	607	6
11	639	6
0	639	6

Iter	Nodes	Cost
0	6	15
1	12	15
2	20	15
3	31	15
4	45	15
5	82	15
6	152	15
7	248	15
8	350	15
9	486	15
10	607	15
11	639	15
0	639	15