Metrics for invcot (example 3.9)

analyze8.0ms (0.1%)

Memory

-30.4MiB live, 6.6MiB allocated

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 12 computations (25% saved)

sample9.3s (65.1%)

Memory

80.8MiB live, 10 289.0MiB allocated

Samples

7.3s	3 830×	2	valid
1.5s	4 339×	1	valid
9.0ms	87×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 8.5s

ival-tan: 7.3s (86.1% of total)

ival-div: 508.0ms (6% of total)

const: 230.0ms (2.7% of total)

adjust: 220.0ms (2.6% of total)

ival-sub: 99.0ms (1.2% of total)

ival-<: 93.0ms (1.1% of total)

exact: 12.0ms (0.1% of total)

ival-and: 12.0ms (0.1% of total)

ival-assert: 4.0ms (0% of total)

Bogosity

preprocess30.0ms (0.2%)

Memory

-30.7MiB live, 32.5MiB allocated

Algorithm

1×	egg-herbie

Rules

112×	`lower-fma.f64`
112×	`lower-fma.f32`
80×	`lower-*.f64`
80×	`lower-*.f32`
48×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	21	19
2	54	16
3	131	16
4	204	16
5	228	16
6	230	16
0	6	8
0	10	8
1	14	8
2	22	8
3	31	8
4	43	8
5	63	8
6	102	8
7	134	8
8	192	8
9	225	8
10	247	8
0	247	8

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

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

Symmetry

(negabs x)

explain826.0ms (5.8%)

Memory

3.4MiB live, 638.4MiB allocated

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	-	-	`(/.f64 #s(literal 1 binary64) x)`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(tan.f64 x)`
0	-	-	`(/.f64 #s(literal 1 binary64) (tan.f64 x))`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))`	cancellation	256	0

Confusion

	Predicted +	Predicted -
+	256	0
-	0	0

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	256	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
1	256

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

716.0ms	252×	2	valid
56.0ms	258×	1	valid
0.0ms	2×	0	valid

Compiler

Compiled 60 to 28 computations (53.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 750.0ms

ival-tan: 707.0ms (94.3% of total)

ival-div: 20.0ms (2.7% of total)

ival-sub: 11.0ms (1.5% of total)

adjust: 10.0ms (1.3% of total)

exact: 1.0ms (0.1% of total)

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

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

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.3MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	5.6%	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify24.0ms (0.2%)

Memory

-18.5MiB live, 18.0MiB allocated

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

112×	`lower-fma.f64`
112×	`lower-fma.f32`
80×	`lower-*.f64`
80×	`lower-*.f32`
48×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	19
0	10	19
1	14	19
2	22	19
3	31	19
4	43	19
5	63	19
6	102	19
7	134	19
8	192	19
9	225	19
10	247	19
0	247	19

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

localize398.0ms (2.8%)

Memory

-2.8MiB live, 196.5MiB allocated

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	5.6%	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Samples

361.0ms	126×	2	valid
25.0ms	129×	1	valid
0.0ms	1×	0	valid

Compiler

Compiled 21 to 8 computations (61.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 375.0ms

ival-tan: 357.0ms (95.1% of total)

ival-div: 10.0ms (2.7% of total)

adjust: 5.0ms (1.3% of total)

ival-sub: 3.0ms (0.8% of total)

exact: 0.0ms (0% of total)

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

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

series4.0ms (0%)

Memory

3.0MiB live, 3.0MiB allocated

Counts

4 → 48

Calls

Call 1

Inputs
#<alt (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))>
#<alt (/.f64 #s(literal 1 binary64) x)>
#<alt (/.f64 #s(literal 1 binary64) (tan.f64 x))>
#<alt (tan.f64 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))

rewrite273.0ms (1.9%)

Memory

24.9MiB live, 140.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

3 072×	`lower-fma.f64`
3 072×	`lower-fma.f32`
2 002×	`lower-*.f64`
2 002×	`lower-*.f32`
1 374×	`frac-times`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	17
0	10	17
1	49	17
2	454	17
3	5706	17
0	9203	17

Stop Event

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

Counts

4 → 277

Calls

Call 1

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

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

simplify630.0ms (4.4%)

Memory

0.2MiB live, 630.3MiB allocated

Algorithm

1×	egg-herbie

Rules

18 970×	`lower-fma.f64`
18 970×	`lower-fma.f32`
3 656×	`lower-*.f64`
3 656×	`lower-*.f32`
3 436×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	324
1	179	324
2	458	318
3	1321	318
4	2085	318
5	3083	318
6	3670	318
7	3941	318
8	5080	318
9	7268	318
0	8431	300

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 47

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

eval40.0ms (0.3%)

Memory: -10.9MiB live, 105.0MiB allocated
Compiler: Compiled 5 981 to 755 computations (87.4% saved)

prune36.0ms (0.2%)

Memory

19.1MiB live, 96.2MiB allocated

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	322	2	324
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	323	2	325

Accuracy

99.5%

Counts

325 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
▶	99.4%	(*.f64 #s(literal 1/3 binary64) x)

Compiler

Compiled 13 to 9 computations (30.8% saved)

simplify5.0ms (0%)

Memory

11.2MiB live, 11.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

38×	`lower-*.f32`
32×	`lower-*.f64`
24×	`lower-fma.f32`
22×	`lower-fma.f64`
12×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	25
0	12	25
1	24	25
2	31	25
3	36	25
0	36	25

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize37.0ms (0.3%)

Memory

-28.4MiB live, 56.9MiB allocated

Localize:

Found 4 expressions of interest:

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

Samples

28.0ms

256×

valid

Compiler

Compiled 29 to 10 computations (65.5% saved)

Precisions

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

const: 14.0ms (66.3% of total)

ival-mult: 6.0ms (28.4% of total)

ival-add: 1.0ms (4.7% of total)

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

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

series4.0ms (0%)

Memory

4.2MiB live, 4.2MiB allocated

Counts

4 → 48

Calls

Call 1

Inputs
#<alt (*.f64 #s(literal 1/3 binary64) x)>
#<alt (.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))>
#<alt (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))>
#<alt (*.f64 x #s(literal 1/45 binary64))>

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 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

12 calls:

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

rewrite330.0ms (2.3%)

Memory

12.5MiB live, 644.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

7 308×	`lower-fma.f32`
7 306×	`lower-fma.f64`
5 168×	`lower-/.f64`
5 168×	`lower-/.f32`
4 704×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
0	12	20
1	39	20
2	213	20
3	1647	20
0	8175	20

Stop Event

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

Counts

4 → 362

Calls

Call 1

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

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))
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(.f64 (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/756680642578125 binary64)) #s(literal 1/19683 binary64)) (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64)) (+.f64 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))) #s(literal -1/9 binary64)) (.f64 (.f64 x x) #s(literal 1/135 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/8303765625 binary64)) #s(literal 1/729 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/2460375 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))) #s(literal -1/9 binary64)) (.f64 (*.f64 x x) #s(literal 1/135 binary64))))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/8303765625 binary64)) #s(literal -1/729 binary64)) (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/135 binary64) #s(literal 1/9 binary64)) (.f64 (fma.f64 (.f64 x x) #s(literal -1/135 binary64) #s(literal 1/9 binary64)) (fma.f64 (.f64 x x) #s(literal -1/135 binary64) #s(literal 1/9 binary64))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/8303765625 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.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) (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/135 binary64) #s(literal 1/9 binary64)) (-.f64 (fma.f64 (.f64 x x) #s(literal -1/135 binary64) #s(literal 1/9 binary64)) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))))) (.f64 #s(literal 1/4100625 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x)))))))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/8303765625 binary64)) #s(literal -1/729 binary64)) (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64)) (+.f64 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))) #s(literal -1/9 binary64)) (.f64 (.f64 x x) #s(literal 1/135 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.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 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))) #s(literal -1/9 binary64)) (.f64 (*.f64 x x) #s(literal 1/135 binary64))))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/8303765625 binary64)) #s(literal -1/729 binary64)) (/.f64 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))) #s(literal -1/9 binary64)) (fma.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) (fma.f64 #s(literal 1/4100625 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/18225 binary64) #s(literal 1/81 binary64)))) (fma.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/8303765625 binary64)) #s(literal -1/729 binary64)) (/.f64 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))) #s(literal -1/9 binary64)) (neg.f64 (fma.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) (fma.f64 #s(literal 1/4100625 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/18225 binary64) #s(literal 1/81 binary64)))) (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64)))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/8303765625 binary64)) #s(literal -1/729 binary64)) (/.f64 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))) #s(literal -1/9 binary64)) (neg.f64 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))) #s(literal -1/9 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4100625 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/18225 binary64) #s(literal 1/81 binary64)))) (fma.f64 (*.f64 x x) #s(literal -1/45 binary64) #s(literal 1/3 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/8303765625 binary64)) #s(literal -1/729 binary64)) (/.f64 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))) #s(literal -1/9 binary64)) (-.f64 #s(literal 1/9 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4100625 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/18225 binary64) #s(literal 1/81 binary64)))) (-.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 1/45 binary64))))))
(.f64 (/.f64 (fma.f64 #s(literal 1/4100625 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/81 binary64)) (fma.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) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))) #s(literal 1/9 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))) (fma.f64 (.f64 x x) #s(literal 1/135 binary64) #s(literal 1/9 binary64))))))
(.f64 (/.f64 (fma.f64 #s(literal 1/4100625 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/81 binary64)) (/.f64 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))) #s(literal -1/9 binary64)) (fma.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) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))) #s(literal 1/9 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64))))
(.f64 (/.f64 (fma.f64 #s(literal 1/4100625 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/81 binary64)) (/.f64 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))) #s(literal -1/9 binary64)) (neg.f64 (fma.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) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))) #s(literal 1/9 binary64))) (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64)))))
(.f64 (/.f64 (fma.f64 #s(literal 1/4100625 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/81 binary64)) (/.f64 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))) #s(literal -1/9 binary64)) (neg.f64 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))) #s(literal -1/9 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))) #s(literal 1/9 binary64))) (fma.f64 (.f64 x x) #s(literal -1/45 binary64) #s(literal 1/3 binary64))))
(.f64 (/.f64 (fma.f64 #s(literal 1/4100625 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1/81 binary64)) (/.f64 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))) #s(literal -1/9 binary64)) (-.f64 #s(literal 1/9 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))) #s(literal 1/9 binary64))) (-.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64))))))
(*.f64 x #s(literal 1/45 binary64))
(*.f64 #s(literal 1/45 binary64) x)

simplify350.0ms (2.4%)

Memory

-0.4MiB live, 350.2MiB allocated

Algorithm

1×	egg-herbie

Rules

6 632×	`lower-*.f64`
6 632×	`lower-*.f32`
4 134×	`cube-prod`
3 308×	`lower-pow.f64`
3 308×	`lower-pow.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	240
1	51	240
2	106	240
3	227	240
4	522	240
5	1554	240
6	1723	240
7	1945	240
8	2231	240
9	2616	240
10	3071	240
11	3638	240
12	3891	240
13	4055	240
14	4163	240
15	4278	240
16	4412	240
17	5141	240
18	6166	240
19	6603	240
20	6817	240
21	6926	240
22	7033	240
23	7157	240
24	7277	240
25	7379	240
26	7481	240
27	7583	240
28	7627	240
0	8324	222

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

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

eval53.0ms (0.4%)

Memory: 7.4MiB live, 124.5MiB allocated
Compiler: Compiled 17 315 to 1 234 computations (92.9% saved)

prune40.0ms (0.3%)

Memory

-3.8MiB live, 113.8MiB allocated

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	409	1	410
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	409	3	412

Accuracy

100.0%

Counts

412 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

▶

100.0%

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

✓

99.5%

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

✓

99.4%

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

Compiler

Compiled 24 to 17 computations (29.2% saved)

simplify6.0ms (0%)

Memory

11.6MiB live, 11.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x #s(literal 1/45 binary64))
✓	cost-diff	0	(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
✓	cost-diff	1088	(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))

Rules

42×	`lower-*.f32`
40×	`lower-*.f64`
24×	`lower-fma.f32`
22×	`lower-fma.f64`
22×	`lower-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	31
0	13	31
1	22	29
2	34	29
3	55	29
4	61	29
5	62	29
0	62	29

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize52.0ms (0.4%)

Memory

-14.2MiB live, 69.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
✓	accuracy	100.0%	(fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
✓	accuracy	99.6%	(*.f64 x #s(literal 1/45 binary64))

Samples

41.0ms

256×

valid

Compiler

Compiled 36 to 11 computations (69.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

const: 6.0ms (44.3% of total)

ival-div: 3.0ms (22.1% of total)

ival-mult: 3.0ms (22.1% of total)

ival-add: 1.0ms (7.4% of total)

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

exact: 0.0ms (0% of total)

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

series1.0ms (0%)

Memory

2.6MiB live, 2.6MiB allocated

Counts

4 → 48

Calls

Call 1

Inputs
#<alt (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))>
#<alt (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))>
#<alt (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))>
#<alt (*.f64 x #s(literal 1/45 binary64))>

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

12 calls:

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

rewrite305.0ms (2.1%)

Memory

0.4MiB live, 595.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 538×	`lower-*.f32`
4 536×	`lower-*.f64`
3 828×	`lower-fma.f32`
3 826×	`lower-fma.f64`
3 558×	`lower-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	27
0	13	27
1	52	25
2	291	25
3	2610	25
0	8719	25

Stop Event

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

Counts

4 → 570

Calls

Call 1

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

Outputs
(exp.f64 (.f64 (neg.f64 (log.f64 (.f64 x (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))) #s(literal -1 binary64)))
(+.f64 (.f64 x #s(literal 1/3 binary64)) (.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x x))))
(+.f64 (.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x x))) (.f64 x #s(literal 1/3 binary64)))
(+.f64 (.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/3 binary64))) (.f64 #s(literal 1 binary64) (.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x x)))))
(+.f64 (.f64 #s(literal 1 binary64) (.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/3 binary64))))
(+.f64 (.f64 (neg.f64 x) #s(literal -1/3 binary64)) (.f64 (neg.f64 x) (.f64 (.f64 x x) #s(literal -1/45 binary64))))
(+.f64 (.f64 (neg.f64 x) (.f64 (.f64 x x) #s(literal -1/45 binary64))) (.f64 (neg.f64 x) #s(literal -1/3 binary64)))
(+.f64 (.f64 #s(literal -1/3 binary64) (neg.f64 x)) (.f64 (.f64 (.f64 x x) #s(literal -1/45 binary64)) (neg.f64 x)))
(+.f64 (.f64 (.f64 (.f64 x x) #s(literal -1/45 binary64)) (neg.f64 x)) (.f64 #s(literal -1/3 binary64) (neg.f64 x)))
(-.f64 #s(literal 0 binary64) (.f64 x (fma.f64 (.f64 x x) #s(literal -1/45 binary64) #s(literal -1/3 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))) (.f64 x (fma.f64 (*.f64 x x) #s(literal -1/45 binary64) #s(literal -1/3 binary64))))
(fma.f64 x #s(literal 1/3 binary64) (.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x x))))
(fma.f64 x (.f64 x (.f64 x #s(literal 1/45 binary64))) (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 x (.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/45 binary64)))) (.f64 x #s(literal 1/3 binary64)))
(fma.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/3 binary64)) (.f64 #s(literal 1 binary64) (.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x x)))))
(fma.f64 #s(literal 1 binary64) (.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x x))) (.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/3 binary64))))
(fma.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x x)) (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 (.f64 x #s(literal 1/45 binary64)) (.f64 x x) (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 #s(literal 1/3 binary64) x (.f64 #s(literal 1/45 binary64) (.f64 x (*.f64 x x))))
(fma.f64 (.f64 x (.f64 x #s(literal 1/45 binary64))) x (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 (neg.f64 x) #s(literal -1/3 binary64) (.f64 (neg.f64 x) (.f64 (*.f64 x x) #s(literal -1/45 binary64))))
(fma.f64 (neg.f64 x) (.f64 (.f64 x x) #s(literal -1/45 binary64)) (*.f64 (neg.f64 x) #s(literal -1/3 binary64)))
(fma.f64 (.f64 x x) (.f64 x #s(literal 1/45 binary64)) (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/45 binary64) (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 #s(literal -1/3 binary64) (neg.f64 x) (.f64 (.f64 (*.f64 x x) #s(literal -1/45 binary64)) (neg.f64 x)))
(fma.f64 (.f64 (.f64 x x) #s(literal -1/45 binary64)) (neg.f64 x) (*.f64 #s(literal -1/3 binary64) (neg.f64 x)))
(fma.f64 (.f64 x #s(literal 1/3 binary64)) #s(literal 1 binary64) (.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x x))))
(fma.f64 (.f64 #s(literal 1/45 binary64) (.f64 x (.f64 x x))) #s(literal 1 binary64) (.f64 x #s(literal 1/3 binary64)))
(neg.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal -1/45 binary64) #s(literal -1/3 binary64))))
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64)) (.f64 x (fma.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 (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64)) (.f64 x (fma.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal 1/2025 binary64))) #s(literal -1/9 binary64)))))
(/.f64 (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))))
(/.f64 (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)) (neg.f64 (.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64)) (.f64 x (fma.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) (neg.f64 (/.f64 (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64)) (.f64 x (fma.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal 1/2025 binary64))) #s(literal -1/9 binary64))))))
(/.f64 (fma.f64 (.f64 x x) #s(literal -1/45 binary64) #s(literal -1/3 binary64)) (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
(/.f64 (fma.f64 (.f64 x x) #s(literal -1/45 binary64) #s(literal -1/3 binary64)) (.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)))
(/.f64 (fma.f64 (*.f64 x x) #s(literal -1/45 binary64) #s(literal -1/3 binary64)) (neg.f64 (/.f64 #s(literal 1 binary64) x)))
(/.f64 (neg.f64 x) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/45 binary64) #s(literal -1/3 binary64))))
(/.f64 (fma.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) x) (fma.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64))))
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(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/9 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 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 (pow.f64 (/.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64)) (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/756680642578125 binary64)) #s(literal 1/19683 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/8303765625 binary64) #s(literal 1/729 binary64)) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/2460375 binary64)))))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64)) (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/8303765625 binary64)) #s(literal -1/729 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64)) #s(literal -1/27 binary64))))
(.f64 (exp.f64 (log.f64 #s(literal -1 binary64))) (exp.f64 (log.f64 (fma.f64 (.f64 x x) #s(literal -1/45 binary64) #s(literal -1/3 binary64)))))
(.f64 (exp.f64 (log.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/91125 binary64)) #s(literal 1/27 binary64)))) (exp.f64 (neg.f64 (log.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/2025 binary64)) #s(literal 1/135 binary64)) #s(literal 1/9 binary64))))))
(.f64 (exp.f64 (log.f64 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/2025 binary64))) #s(literal -1/9 binary64)))) (exp.f64 (neg.f64 (log.f64 (fma.f64 x (*.f64 x #s(literal 1/45 binary64)) #s(literal -1/3 binary64))))))
(/.f64 #s(literal 1/45 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 x #s(literal 1/45 binary64)) #s(literal 1 binary64))
(/.f64 (neg.f64 (*.f64 x #s(literal 1/45 binary64))) #s(literal -1 binary64))
(/.f64 #s(literal -1/45 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 #s(literal 1/45 binary64) (neg.f64 x)) #s(literal -1 binary64))
(/.f64 (*.f64 (neg.f64 x) #s(literal 1/45 binary64)) #s(literal -1 binary64))
(/.f64 (neg.f64 (*.f64 #s(literal 1/45 binary64) (neg.f64 x))) #s(literal 1 binary64))
(/.f64 (neg.f64 (*.f64 (neg.f64 x) #s(literal 1/45 binary64))) #s(literal 1 binary64))
(*.f64 x #s(literal 1/45 binary64))
(*.f64 #s(literal 1/45 binary64) x)
(.f64 (.f64 x #s(literal 1/45 binary64)) #s(literal 1 binary64))

simplify431.0ms (3%)

Memory

8.2MiB live, 478.0MiB allocated

Algorithm

1×	egg-herbie

Rules

10 646×	`lower-fma.f64`
10 646×	`lower-fma.f32`
2 998×	`lower-*.f64`
2 998×	`lower-*.f32`
2 052×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	356
1	135	356
2	320	356
3	749	356
4	1734	356
5	3937	356
6	7320	356
0	8093	332

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

eval93.0ms (0.6%)

Memory: 10.8MiB live, 170.8MiB allocated
Compiler: Compiled 18 255 to 1 922 computations (89.5% saved)

prune63.0ms (0.4%)

Memory

27.4MiB live, 142.6MiB allocated

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	617	1	618
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	618	3	621

Accuracy

100.0%

Counts

621 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(/.f64 x #s(literal 3 binary64))
✓	99.5%	(.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
✓	99.4%	(*.f64 #s(literal 1/3 binary64) x)

Compiler

Compiled 17 to 12 computations (29.4% saved)

simplify6.0ms (0%)

Memory

-37.6MiB live, 6.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 x #s(literal 3 binary64))

Rules

2×	`lift-/.f64`
2×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	5
0	4	5
0	4	5

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize11.0ms (0.1%)

Memory

20.8MiB live, 20.8MiB allocated

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 x #s(literal 3 binary64))

Samples

6.0ms

256×

valid

Compiler

Compiled 7 to 5 computations (28.6% saved)

Precisions

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

ival-div: 2.0ms (85.5% of total)

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

exact: 0.0ms (0% of total)

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

series0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Counts

1 → 12

Calls

Call 1

Inputs
#<alt (/.f64 x #s(literal 3 binary64))>

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)>

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(/ x 3)
0.0ms	x	@	-inf	(/ x 3)
0.0ms	x	@	inf	(/ x 3)

rewrite183.0ms (1.3%)

Memory

10.3MiB live, 242.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

3 406×	`lower-fma.f64`
3 406×	`lower-fma.f32`
2 330×	`lower-*.f64`
2 330×	`lower-*.f32`
1 942×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	3
0	4	3
1	14	3
2	39	3
3	141	3
4	646	3
5	6446	3
0	8369	3

Stop Event

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

Counts

1 → 341

Calls

Call 1

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

Outputs
(exp.f64 (log.f64 (*.f64 x #s(literal 1/3 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 x #s(literal 1/3 binary64))) #s(literal 1 binary64)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x #s(literal 1/3 binary64)))) #s(literal 2 binary64)))
(exp.f64 (.f64 (-.f64 #s(literal 0 binary64) (log.f64 (.f64 (*.f64 x x) #s(literal 1/9 binary64)))) #s(literal -1/2 binary64)))
(exp.f64 (.f64 (.f64 (neg.f64 (log.f64 (*.f64 x #s(literal 1/3 binary64)))) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (fma.f64 (neg.f64 (log.f64 (.f64 x #s(literal 1/3 binary64)))) #s(literal -1/2 binary64) (.f64 (neg.f64 (log.f64 (*.f64 x #s(literal 1/3 binary64)))) #s(literal -1/2 binary64))))
(+.f64 #s(literal 0 binary64) (*.f64 x #s(literal 1/3 binary64)))
(+.f64 (*.f64 x #s(literal 1/3 binary64)) #s(literal 0 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 x #s(literal 1/3 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 #s(literal -3 binary64) (.f64 x x))) (*.f64 x #s(literal 1/3 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 x #s(literal -3 binary64))) (.f64 x #s(literal 1/3 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 (.f64 x x) #s(literal 1/9 binary64))) (*.f64 x #s(literal 1/3 binary64)))
(fma.f64 x #s(literal 1/3 binary64) #s(literal 0 binary64))
(fma.f64 x #s(literal -1/3 binary64) #s(literal 0 binary64))
(fma.f64 x (pow.f64 (pow.f64 #s(literal 3 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 x (*.f64 (pow.f64 #s(literal 3 binary64) #s(literal -1/2 binary64)) (pow.f64 #s(literal 3 binary64) #s(literal -1/2 binary64))) #s(literal 0 binary64))
(fma.f64 (neg.f64 x) #s(literal 1/3 binary64) #s(literal 0 binary64))
(fma.f64 (neg.f64 x) #s(literal -1/3 binary64) #s(literal 0 binary64))
(fma.f64 (neg.f64 x) (*.f64 (pow.f64 #s(literal -3 binary64) #s(literal -1/2 binary64)) (pow.f64 #s(literal -3 binary64) #s(literal -1/2 binary64))) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/3 binary64)) #s(literal 0 binary64))
(fma.f64 #s(literal 1/3 binary64) x #s(literal 0 binary64))
(fma.f64 #s(literal 1/3 binary64) (neg.f64 x) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (*.f64 x #s(literal 1/3 binary64)) #s(literal 0 binary64))
(fma.f64 #s(literal -1/3 binary64) x #s(literal 0 binary64))
(fma.f64 #s(literal -1/3 binary64) (neg.f64 x) #s(literal 0 binary64))
(fma.f64 (*.f64 x #s(literal 1/3 binary64)) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 (*.f64 x #s(literal 1/3 binary64)) #s(literal -1 binary64) #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal -1/3 binary64) (*.f64 x (neg.f64 x))) #s(literal 0 binary64))
(fma.f64 (neg.f64 (.f64 x (.f64 x x))) (/.f64 #s(literal -1/3 binary64) (*.f64 x x)) #s(literal 0 binary64))
(fma.f64 (neg.f64 (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 #s(literal -3 binary64) (.f64 x x))) #s(literal 0 binary64))
(fma.f64 (neg.f64 (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 3 binary64) (.f64 x x))) #s(literal 0 binary64))
(fma.f64 (neg.f64 (.f64 x (.f64 x x))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1/3 binary64)) #s(literal 0 binary64))
(fma.f64 (neg.f64 (.f64 x (.f64 x x))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/3 binary64)) #s(literal 0 binary64))
(fma.f64 (neg.f64 (.f64 x (.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -3 binary64)) #s(literal 0 binary64))
(fma.f64 (neg.f64 (.f64 x (.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 3 binary64)) #s(literal 0 binary64))
(fma.f64 (*.f64 x x) (/.f64 #s(literal -1/3 binary64) (neg.f64 x)) #s(literal 0 binary64))
(fma.f64 (*.f64 x (neg.f64 x)) (/.f64 #s(literal -1/3 binary64) x) #s(literal 0 binary64))
(fma.f64 (.f64 x (neg.f64 x)) (/.f64 #s(literal 1 binary64) (.f64 x #s(literal -3 binary64))) #s(literal 0 binary64))
(fma.f64 (.f64 x (neg.f64 x)) (/.f64 #s(literal 1 binary64) (.f64 x #s(literal 3 binary64))) #s(literal 0 binary64))
(fma.f64 (.f64 x (neg.f64 x)) (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/3 binary64)) #s(literal 0 binary64))
(fma.f64 (.f64 x (neg.f64 x)) (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/3 binary64)) #s(literal 0 binary64))
(fma.f64 (*.f64 x (neg.f64 x)) (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -3 binary64)) #s(literal 0 binary64))
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simplify5.0ms (0%)

Memory

5.5MiB live, 5.5MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`lower-*.f64`
4×	`lower-*.f32`
2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	36
1	4	36
0	4	36

Stop Event

1×	iter limit
1×	saturated

Counts

12 → 12

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)

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)

eval69.0ms (0.5%)

Memory: -24.1MiB live, 54.2MiB allocated
Compiler: Compiled 3 904 to 559 computations (85.7% saved)

prune39.0ms (0.3%)

Memory

0.5MiB live, 77.9MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	353	0	353
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	353	3	356

Accuracy

100.0%

Counts

356 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(/.f64 x #s(literal 3 binary64))
✓	99.5%	(.f64 x (fma.f64 x (.f64 x #s(literal 1/45 binary64)) #s(literal 1/3 binary64)))
✓	99.4%	(*.f64 #s(literal 1/3 binary64) x)

Compiler

Compiled 50 to 28 computations (44% saved)

regimes4.0ms (0%)

Memory

8.4MiB live, 8.4MiB allocated

Counts

5 → 1

Calls

Call 1

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	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)

regimes3.0ms (0%)

Memory

6.8MiB live, 6.8MiB allocated

Counts

3 → 1

Calls

Call 1

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

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

Calls

2 calls:

2.0ms	x
1.0ms	(-.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%)

Memory

5.2MiB live, 5.2MiB allocated

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

2 calls:

1.0ms	x
1.0ms	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (tan.f64 x)))

Results

Accuracy	Segments	Branch
99.4%	1	`x`
99.4%	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)

simplify5.0ms (0%)

Memory

10.2MiB live, 10.2MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	16	16

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness561.0ms (3.9%)

Memory

-19.5MiB live, 334.6MiB allocated

Rules

18 970×	`lower-fma.f64`
18 970×	`lower-fma.f32`
10 646×	`lower-fma.f64`
10 646×	`lower-fma.f32`
7 308×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	356
1	135	356
2	320	356
3	749	356
4	1734	356
5	3937	356
6	7320	356
0	8093	332
0	7	20
0	12	20
1	39	20
2	213	20
3	1647	20
0	8175	20
0	67	324
1	179	324
2	458	318
3	1321	318
4	2085	318
5	3083	318
6	3670	318
7	3941	318
8	5080	318
9	7268	318
0	8431	300

Stop Event

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

Compiler

Compiled 65 to 45 computations (30.8% saved)

preprocess70.0ms (0.5%)

Memory: 20.4MiB live, 97.0MiB allocated
Remove: (negabs x)
Compiler: Compiled 146 to 100 computations (31.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	8	21
1	21	19
2	54	16
3	131	16
4	204	16
5	228	16
6	230	16
0	6	8
0	10	8
1	14	8
2	22	8
3	31	8
4	43	8
5	63	8
6	102	8
7	134	8
8	192	8
9	225	8
10	247	8
0	247	8

Iter	Nodes	Cost
0	6	19
0	10	19
1	14	19
2	22	19
3	31	19
4	43	19
5	63	19
6	102	19
7	134	19
8	192	19
9	225	19
10	247	19
0	247	19

Iter	Nodes	Cost
0	8	21
1	21	19
2	54	16
3	131	16
4	204	16
5	228	16
6	230	16
0	6	8
0	10	8
1	14	8
2	22	8
3	31	8
4	43	8
5	63	8
6	102	8
7	134	8
8	192	8
9	225	8
10	247	8
0	247	8

Iter	Nodes	Cost
0	6	19
0	10	19
1	14	19
2	22	19
3	31	19
4	43	19
5	63	19
6	102	19
7	134	19
8	192	19
9	225	19
10	247	19
0	247	19

analyze8.0ms (0.1%)

sample9.3s (65.1%)

preprocess30.0ms (0.2%)

explain826.0ms (5.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify24.0ms (0.2%)

localize398.0ms (2.8%)

series4.0ms (0%)

rewrite273.0ms (1.9%)

simplify630.0ms (4.4%)

eval40.0ms (0.3%)

prune36.0ms (0.2%)

simplify5.0ms (0%)

localize37.0ms (0.3%)

series4.0ms (0%)

rewrite330.0ms (2.3%)

simplify350.0ms (2.4%)

eval53.0ms (0.4%)

prune40.0ms (0.3%)

simplify6.0ms (0%)

localize52.0ms (0.4%)

series1.0ms (0%)

rewrite305.0ms (2.1%)

simplify431.0ms (3%)

eval93.0ms (0.6%)

prune63.0ms (0.4%)

simplify6.0ms (0%)

localize11.0ms (0.1%)

series0.0ms (0%)

rewrite183.0ms (1.3%)

simplify5.0ms (0%)

eval69.0ms (0.5%)

prune39.0ms (0.3%)

regimes4.0ms (0%)

regimes3.0ms (0%)

regimes2.0ms (0%)

simplify5.0ms (0%)

soundness561.0ms (3.9%)

preprocess70.0ms (0.5%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	21
1	21	19
2	54	16
3	131	16
4	204	16
5	228	16
6	230	16
0	6	8
0	10	8
1	14	8
2	22	8
3	31	8
4	43	8
5	63	8
6	102	8
7	134	8
8	192	8
9	225	8
10	247	8
0	247	8

Iter	Nodes	Cost
0	6	19
0	10	19
1	14	19
2	22	19
3	31	19
4	43	19
5	63	19
6	102	19
7	134	19
8	192	19
9	225	19
10	247	19
0	247	19