Metrics for ENA, Section 1.4, Mentioned, A

analyze3.0ms (0%)

Memory

6.8MiB live, 6.8MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	49.6%	50.4%	0%	0%	0%	0
0%	0%	49.6%	50.4%	0%	0%	0%	1
0%	0%	49.6%	50.4%	0%	0%	0%	2
50%	24.8%	24.8%	50.4%	0%	0%	0%	3
75%	37.2%	12.4%	50.4%	0%	0%	0%	4
87.5%	43.4%	6.2%	50.4%	0%	0%	0%	5
93.8%	46.5%	3.1%	50.4%	0%	0%	0%	6
96.9%	48.1%	1.6%	50.4%	0%	0%	0%	7
98.4%	48.8%	0.8%	50.4%	0%	0%	0%	8
99.2%	49.2%	0.4%	50.4%	0%	0%	0%	9
99.6%	49.4%	0.2%	50.4%	0%	0%	0%	10
99.8%	49.5%	0.1%	50.4%	0%	0%	0%	11
99.9%	49.6%	0%	50.4%	0%	0%	0%	12

Compiler

Compiled 12 to 10 computations (16.7% saved)

sample2.7s (33.1%)

Memory

39.4MiB live, 3 165.0MiB allocated

Samples

2.0s	5 720×	2	valid
483.0ms	2 449×	1	valid
6.0ms	87×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.8s

ival-cos: 1.3s (69.8% of total)

const: 229.0ms (12.5% of total)

ival-sub: 126.0ms (6.9% of total)

adjust: 100.0ms (5.5% of total)

ival-<=: 70.0ms (3.8% of total)

exact: 13.0ms (0.7% of total)

ival-and: 11.0ms (0.6% of total)

ival-assert: 3.0ms (0.2% of total)

Bogosity

preprocess19.0ms (0.2%)

Memory

-31.1MiB live, 32.6MiB allocated

Algorithm

2×	egg-herbie

Rules

24×	`+-lowering-+.f64`
24×	`+-lowering-+.f32`
22×	`sub-neg`
18×	`--lowering--.f32`
18×	`--lowering--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	17	12
2	36	12
3	56	12
4	88	12
5	104	12
6	110	12
0	4	4
1	8	4
2	12	4
3	17	4
4	23	4
5	31	4
6	41	4
7	52	4
8	55	4
0	55	4

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(- 1 (cos x))

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

Call 2

Inputs
(- 1 (cos x))
(- 1 (cos (neg x)))
(neg (- 1 (cos (neg x))))

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

Symmetry

(abs x)

explain147.0ms (1.8%)

Memory

25.3MiB live, 260.7MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
139	1	(4.16159740757327e-162)	-	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(cos.f64 x)`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	cancellation	140	0

Confusion

	Predicted +	Predicted -
+	139	0
-	1	116

Precision

0.9928571428571429

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	139	0	0
-	1	0	116

Precision?

0.9928571428571429

Recall?

1.0

Freqs

test

number	freq
0	116
1	140

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

68.0ms	340×	2	valid
25.0ms	170×	1	valid
0.0ms	2×	0	valid

Compiler

Compiled 30 to 20 computations (33.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 75.0ms

ival-cos: 49.0ms (65.4% of total)

ival-sub: 19.0ms (25.3% of total)

adjust: 6.0ms (8% of total)

exact: 1.0ms (1.3% of total)

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

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

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	49.9%	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0.1%)

Memory

10.5MiB live, 10.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Rules

24×	`+-lowering-+.f64`
24×	`+-lowering-+.f32`
18×	`--lowering--.f32`
18×	`--lowering--.f64`
16×	`sub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	8
1	8	8
2	12	8
3	17	8
4	23	8
5	31	8
6	41	8
7	52	8
8	55	8
0	55	8

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(- 1 (cos x))
1
(cos x)
x

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

localize160.0ms (2%)

Memory

-19.4MiB live, 61.4MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	49.9%	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Samples

146.0ms	170×	2	valid
7.0ms	85×	1	valid
0.0ms	1×	0	valid

Compiler

Compiled 10 to 6 computations (40% saved)

Precisions

Click to see histograms. Total time spent on operations: 144.0ms

ival-cos: 104.0ms (72.2% of total)

ival-sub: 36.0ms (25% of total)

adjust: 3.0ms (2.1% of total)

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

exact: 0.0ms (0% of total)

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

series1.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Counts

2 → 24

Calls

Call 1

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

Outputs
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>

Calls

6 calls:

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

rewrite350.0ms (4.3%)

Memory

6.5MiB live, 555.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 830×	`-lowering-.f32`
4 830×	`-lowering-.f64`
4 620×	`/-lowering-/.f32`
4 620×	`/-lowering-/.f64`
3 866×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	21	6
2	140	6
3	1151	6
0	9229	6

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 314

Calls

Call 1

Inputs
(- 1 (cos x))
(cos x)

Outputs
(+.f64 #s(literal 1 binary64) (cos.f64 x))
(+.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x)))
(+.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (cos.f64 x))))
(+.f64 (cos.f64 x) #s(literal 1 binary64))
(+.f64 (neg.f64 (cos.f64 x)) #s(literal 1 binary64))
(+.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)))))
(+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x)))) #s(literal -1 binary64)))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(-.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x)))
(-.f64 #s(literal 0 binary64) (-.f64 (cos.f64 x) #s(literal 1 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)))) (neg.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 6 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 4 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))))
(-.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (-.f64 (cos.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (cos.f64 x) #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)))) (neg.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 6 binary64))))) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))) (/.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 9 binary64)) (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 6 binary64))))) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))) (/.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 6 binary64)) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (/.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))) (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (/.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 6 binary64)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (/.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 6 binary64)))))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 9 binary64)) (.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 6 binary64)))))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 6 binary64)) (.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))))
(-.f64 (/.f64 (.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))) (pow.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) #s(literal 2 binary64))) (/.f64 (.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (pow.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) #s(literal 2 binary64))))
(-.f64 (/.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (pow.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64))) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64))))
(-.f64 (/.f64 (pow.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) #s(literal -3 binary64)) (+.f64 (pow.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) #s(literal -2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))))))) (/.f64 (.f64 (pow.f64 (cos.f64 x) #s(literal 9 binary64)) (pow.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) #s(literal -3 binary64))) (+.f64 (pow.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) #s(literal -2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))) #s(literal 2 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))))))))
(-.f64 (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -3 binary64)) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -2 binary64)) (+.f64 (pow.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (cos.f64 x))))))) (/.f64 (pow.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 3 binary64)) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -2 binary64)) (+.f64 (pow.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (cos.f64 x))))))))
(-.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (-.f64 (neg.f64 (cos.f64 x)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (neg.f64 (cos.f64 x)) #s(literal 1 binary64))))
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(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 3/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64))) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 3/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 3/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64))) (neg.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 3/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64))) (neg.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) #s(literal 1 binary64)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (/.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (sin.f64 x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (/.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (neg.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (neg.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
(*.f64 (/.f64 (neg.f64 (sin.f64 x)) #s(literal -1 binary64)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))))))
(.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (/.f64 (sin.f64 x) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))))))
(.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))))
(.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (cos.f64 x)))
(.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)))))
(.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))))) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(exp.f64 (log.f64 (cos.f64 x)))
(exp.f64 (*.f64 (log.f64 (cos.f64 x)) #s(literal 1 binary64)))
(cos.f64 x)
(pow.f64 (cos.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (cos.f64 x))
(*.f64 (cos.f64 x) #s(literal 1 binary64))

simplify961.0ms (11.7%)

Memory

3.5MiB live, 985.3MiB allocated

Algorithm

1×	egg-herbie

Rules

32 720×	`accelerator-lowering-fma.f32`
32 720×	`accelerator-lowering-fma.f64`
3 926×	`-lowering-.f32`
3 926×	`-lowering-.f64`
3 120×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	144
1	101	144
2	246	144
3	589	144
4	1230	144
5	1905	144
6	2165	144
7	2814	144
8	4054	144
9	5622	144
10	6523	144
11	6804	144
12	6843	144
13	6843	144
14	7276	144
15	7552	144
16	7593	144
17	7595	144
18	7595	144
19	7595	144
20	7595	144
21	7605	144
22	7605	144
23	7605	144
0	8510	132

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 24

Calls

Call 1

Inputs
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)

Outputs
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))) #s(literal 1 binary64))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)

eval85.0ms (1%)

Memory: -38.7MiB live, 94.3MiB allocated
Compiler: Compiled 10 753 to 912 computations (91.5% saved)

prune44.0ms (0.5%)

Memory

-0.4MiB live, 118.2MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	333	5	338
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	334	5	339

Accuracy

100.0%

Counts

339 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	49.8%	(-.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
▶	49.4%	(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
▶	100.0%	(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
▶	100.0%	(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
▶	99.8%	(.f64 #s(literal 1/2 binary64) (.f64 x x))

Compiler

Compiled 92 to 56 computations (39.1% saved)

simplify269.0ms (3.3%)

Memory

30.0MiB live, 544.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
✓	cost-diff	256	(-.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 #s(literal 1/2 binary64) (.f64 x x))
✓	cost-diff	192	(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
✓	cost-diff	0	(fma.f64 x (*.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))
✓	cost-diff	0	(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))

Rules

10 902×	`accelerator-lowering-fma.f32`
10 902×	`accelerator-lowering-fma.f64`
2 078×	`+-lowering-+.f64`
2 078×	`+-lowering-+.f32`
1 960×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	101
1	67	101
2	177	101
3	347	101
4	588	101
5	1691	101
6	2720	101
7	3900	101
8	5217	101
9	6187	101
10	7067	101
0	8068	93

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (* x x) (+ (* (* x x) (+ (* x (* x 1/720)) -1/24)) 1/2))
(* x x)
x
(+ (* (* x x) (+ (* x (* x 1/720)) -1/24)) 1/2)
(+ (* x (* x 1/720)) -1/24)
(* x 1/720)
1/720
-1/24
1/2
(- 1 1)
1
(* 1/2 (* x x))
1/2
(* x x)
x
(- 1 (+ (* (* x x) -1/2) 1))
1
(+ (* (* x x) -1/2) 1)
(* x x)
x
-1/2
(* (* x x) (+ (* (* x x) -1/24) 1/2))
(* x x)
x
(+ (* (* x x) -1/24) 1/2)
-1/24
1/2

Outputs
(* (* x x) (+ (* (* x x) (+ (* x (* x 1/720)) -1/24)) 1/2))
(.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))
(* x x)
(*.f64 x x)
x
(+ (* (* x x) (+ (* x (* x 1/720)) -1/24)) 1/2)
(fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))
(+ (* x (* x 1/720)) -1/24)
(fma.f64 x (*.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))
(* x 1/720)
(*.f64 x #s(literal 1/720 binary64))
1/720
#s(literal 1/720 binary64)
-1/24
#s(literal -1/24 binary64)
1/2
#s(literal 1/2 binary64)
(- 1 1)
#s(literal 0 binary64)
1
#s(literal 1 binary64)
(* 1/2 (* x x))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(* x x)
(*.f64 x x)
x
(- 1 (+ (* (* x x) -1/2) 1))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
1
#s(literal 1 binary64)
(+ (* (* x x) -1/2) 1)
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(* x x)
(*.f64 x x)
x
-1/2
#s(literal -1/2 binary64)
(* (* x x) (+ (* (* x x) -1/24) 1/2))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* x x)
(*.f64 x x)
x
(+ (* (* x x) -1/24) 1/2)
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
-1/24
#s(literal -1/24 binary64)
1/2
#s(literal 1/2 binary64)

localize178.0ms (2.2%)

Memory

-15.1MiB live, 374.4MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	49.9%	(-.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 #s(literal 1/2 binary64) (.f64 x x))
✓	accuracy	100.0%	(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
✓	accuracy	100.0%	(fma.f64 x (*.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))
✓	accuracy	100.0%	(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.6%	(*.f64 x #s(literal 1/720 binary64))

Samples

76.0ms	170×	2	valid
27.0ms	85×	1	valid
0.0ms	1×	0	valid

Compiler

Compiled 100 to 23 computations (77% saved)

Precisions

Click to see histograms. Total time spent on operations: 70.0ms

ival-mult: 28.0ms (40.1% of total)

ival-add: 13.0ms (18.6% of total)

adjust: 12.0ms (17.2% of total)

const: 10.0ms (14.3% of total)

ival-sub: 6.0ms (8.6% of total)

exact: 1.0ms (1.4% of total)

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

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

series6.0ms (0.1%)

Memory

11.9MiB live, 11.9MiB allocated

Counts

11 → 120

Calls

Call 1

Inputs
#<alt (* (* x x) (+ (* (* x x) (+ (* x (* x 1/720)) -1/24)) 1/2))>
#<alt (* x x)>
#<alt (+ (* (* x x) (+ (* x (* x 1/720)) -1/24)) 1/2)>
#<alt (+ (* x (* x 1/720)) -1/24)>
#<alt (- 1 1)>
#<alt (* 1/2 (* x x))>
#<alt (- 1 (+ (* (* x x) -1/2) 1))>
#<alt (+ (* (* x x) -1/2) 1)>
#<alt (* (* x x) (+ (* (* x x) -1/24) 1/2))>
#<alt (+ (* (* x x) -1/24) 1/2)>
#<alt (* x 1/720)>

Outputs
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* 1/720 (pow x 6))>
#<alt (* (pow x 6) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* 1/720 (pow x 6))>
#<alt (* (pow x 6) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt 1/2>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))>
#<alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))>
#<alt (* 1/720 (pow x 4))>
#<alt (* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* 1/720 (pow x 4))>
#<alt (* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))>
#<alt -1/24>
#<alt (- (* 1/720 (pow x 2)) 1/24)>
#<alt (- (* 1/720 (pow x 2)) 1/24)>
#<alt (- (* 1/720 (pow x 2)) 1/24)>
#<alt (* 1/720 (pow x 2))>
#<alt (* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* 1/720 (pow x 2))>
#<alt (* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* -1/24 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* -1/24 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (* -1/24 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* -1/24 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* 1/720 x)>
#<alt (* 1/720 x)>
#<alt (* 1/720 x)>
#<alt (* 1/720 x)>
#<alt (* 1/720 x)>
#<alt (* 1/720 x)>
#<alt (* 1/720 x)>
#<alt (* 1/720 x)>
#<alt (* 1/720 x)>
#<alt (* 1/720 x)>
#<alt (* 1/720 x)>
#<alt (* 1/720 x)>

Calls

30 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(* (* x x) (+ (* (* x x) -1/24) 1/2))
1.0ms	x	@	inf	(* (* x x) (+ (* (* x x) (+ (* x (* x 1/720)) -1/24)) 1/2))
0.0ms	x	@	0	(* (* x x) (+ (* (* x x) (+ (* x (* x 1/720)) -1/24)) 1/2))
0.0ms	x	@	-inf	(* x 1/720)
0.0ms	x	@	inf	(* 1/2 (* x x))

rewrite372.0ms (4.5%)

Memory

11.2MiB live, 531.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 238×	`accelerator-lowering-fma.f32`
6 238×	`accelerator-lowering-fma.f64`
4 762×	`-lowering-.f32`
4 762×	`-lowering-.f64`
3 994×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	79
1	130	79
2	1006	79
0	8282	71

Stop Event

1×	iter limit
1×	node limit

Counts

11 → 480

Calls

Call 1

Inputs
(* (* x x) (+ (* (* x x) (+ (* x (* x 1/720)) -1/24)) 1/2))
(* x x)
(+ (* (* x x) (+ (* x (* x 1/720)) -1/24)) 1/2)
(+ (* x (* x 1/720)) -1/24)
(- 1 1)
(* 1/2 (* x x))
(- 1 (+ (* (* x x) -1/2) 1))
(+ (* (* x x) -1/2) 1)
(* (* x x) (+ (* (* x x) -1/24) 1/2))
(+ (* (* x x) -1/24) 1/2)
(* x 1/720)

Outputs
(+.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (.f64 (.f64 x x) (*.f64 x x))))
(+.f64 (.f64 (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (.f64 (.f64 x x) (.f64 x x))) (.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(-.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) (.f64 x (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))))) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) (.f64 (*.f64 x x) #s(literal -1/2 binary64)))))
(fma.f64 x (.f64 x #s(literal 1/2 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (.f64 (.f64 x x) (.f64 x x))))
(fma.f64 x (.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))))) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 x (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) (.f64 x x)) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 x (neg.f64 (.f64 x #s(literal -1/2 binary64))) (.f64 (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (.f64 (.f64 x x) (.f64 x x))))
(fma.f64 (.f64 x x) (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 (.f64 x x) #s(literal 1/2 binary64) (.f64 (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (.f64 (.f64 x x) (.f64 x x))))
(fma.f64 (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))) (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (.f64 x x) (.f64 (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (.f64 (.f64 x x) (.f64 x x))))
(fma.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/2 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (.f64 (.f64 x x) (*.f64 x x))))
(fma.f64 #s(literal -1/2 binary64) (neg.f64 (.f64 x x)) (.f64 (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (.f64 (.f64 x x) (.f64 x x))))
(fma.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) #s(literal -1 binary64) (.f64 (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (.f64 (.f64 x x) (*.f64 x x))))
(fma.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) #s(literal 1 binary64) (.f64 (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (.f64 (.f64 x x) (*.f64 x x))))
(fma.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64))) (.f64 (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (.f64 (.f64 x x) (*.f64 x x))))
(fma.f64 (+.f64 #s(literal 1 binary64) (.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64)))) (.f64 (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (.f64 (.f64 x x) (.f64 x x))))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) x (.f64 (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (.f64 (.f64 x x) (.f64 x x))))
(fma.f64 (.f64 x #s(literal -1/2 binary64)) (neg.f64 x) (.f64 (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (.f64 (.f64 x x) (.f64 x x))))
(fma.f64 (.f64 x (.f64 x x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (fma.f64 (.f64 x x) #s(literal 1/2 binary64) #s(literal -1 binary64))))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))) (.f64 (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (.f64 (.f64 x x) (*.f64 x x))))
(fma.f64 (+.f64 #s(literal -1 binary64) (.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -2 binary64) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) (.f64 (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (.f64 (.f64 x x) (.f64 x x))))
(fma.f64 (fma.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (+.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))) (.f64 (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (.f64 (.f64 x x) (.f64 x x))))
(fma.f64 #s(literal -1 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (.f64 (.f64 x x) (*.f64 x x))))
(fma.f64 (.f64 (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/2 binary64))) #s(literal 1 binary64))) (.f64 (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (.f64 (.f64 x x) (.f64 x x))))
(fma.f64 (.f64 (.f64 x x) (.f64 x x)) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 (neg.f64 x) (.f64 x #s(literal -1/2 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (.f64 (.f64 x x) (.f64 x x))))
(fma.f64 (neg.f64 (.f64 x x)) #s(literal -1/2 binary64) (.f64 (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (.f64 (.f64 x x) (.f64 x x))))
(fma.f64 (.f64 (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))) x) x (.f64 (.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 (neg.f64 (.f64 x #s(literal -1/2 binary64))) x (.f64 (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (.f64 (.f64 x x) (.f64 x x))))
(/.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))))) (.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)))))) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 (.f64 (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) #s(literal 1/2 binary64))))) (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) (.f64 (.f64 x x) #s(literal -1/2 binary64))) (.f64 (.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64))) (.f64 (*.f64 x x) #s(literal -1/2 binary64))))))
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(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
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(/.f64 (.f64 (fma.f64 #s(literal 1/191102976 binary64) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal -1/64 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal -1/13824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1/8 binary64)) (+.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64)) #s(literal 1/4 binary64)) (.f64 (*.f64 x x) #s(literal 1/48 binary64)))))
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(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/4 binary64)))) (neg.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))))
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(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))) (fma.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))) (.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal -1/2 binary64)))))))
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(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
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(.f64 (neg.f64 (fma.f64 #s(literal -1/13824 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64)) #s(literal 1/4 binary64)) (.f64 (*.f64 x x) #s(literal 1/48 binary64))))))
(.f64 (neg.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))))
(.f64 (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/576 binary64) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))))
(*.f64 x #s(literal 1/720 binary64))
(*.f64 #s(literal 1/720 binary64) x)

simplify311.0ms (3.8%)

Memory

-22.6MiB live, 426.8MiB allocated

Algorithm

1×	egg-herbie

Rules

9 364×	`accelerator-lowering-fma.f32`
9 364×	`accelerator-lowering-fma.f64`
3 304×	`-lowering-.f32`
3 304×	`-lowering-.f64`
1 466×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	796
1	100	796
2	230	796
3	563	796
4	1461	796
5	4358	796
6	6765	796
0	8078	734

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

Inputs
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* 1/720 (pow x 6))
(* (pow x 6) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* 1/720 (pow x 6))
(* (pow x 6) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(* 1/720 (pow x 4))
(* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* 1/720 (pow x 4))
(* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
-1/24
(- (* 1/720 (pow x 2)) 1/24)
(- (* 1/720 (pow x 2)) 1/24)
(- (* 1/720 (pow x 2)) 1/24)
(* 1/720 (pow x 2))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* 1/720 (pow x 2))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* -1/2 (pow x 2)))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* -1/24 (pow x 4))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* -1/24 (pow x 4))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* -1/24 (pow x 2)))
(* -1/24 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* -1/24 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* 1/720 x)
(* 1/720 x)
(* 1/720 x)
(* 1/720 x)
(* 1/720 x)
(* 1/720 x)
(* 1/720 x)
(* 1/720 x)
(* 1/720 x)
(* 1/720 x)
(* 1/720 x)
(* 1/720 x)

Outputs
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))
(* 1/720 (pow x 6))
(.f64 x (.f64 x (.f64 #s(literal 1/720 binary64) (.f64 x (.f64 x (.f64 x x))))))
(* (pow x 6) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) (.f64 x (.f64 x (*.f64 x x))))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal -1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) #s(literal 1/720 binary64)))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal -1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) #s(literal 1/720 binary64)))
(* 1/720 (pow x 6))
(.f64 x (.f64 x (.f64 #s(literal 1/720 binary64) (.f64 x (.f64 x (.f64 x x))))))
(* (pow x 6) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64)) (.f64 x (.f64 x (*.f64 x x))))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal -1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) #s(literal 1/720 binary64)))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal -1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) #s(literal 1/720 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)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))
(* 1/720 (pow x 4))
(.f64 #s(literal 1/720 binary64) (.f64 x (.f64 x (.f64 x x))))
(* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))))
(* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))
(* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))
(* 1/720 (pow x 4))
(.f64 #s(literal 1/720 binary64) (.f64 x (.f64 x (.f64 x x))))
(* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))))
(* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))
(* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))
-1/24
#s(literal -1/24 binary64)
(- (* 1/720 (pow x 2)) 1/24)
(fma.f64 (*.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))
(- (* 1/720 (pow x 2)) 1/24)
(fma.f64 (*.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))
(- (* 1/720 (pow x 2)) 1/24)
(fma.f64 (*.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))
(* 1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/720 binary64))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))
(* 1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/720 binary64))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(* -1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(* -1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
(* -1/24 (pow x 4))
(.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (.f64 x x))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
(* -1/24 (pow x 4))
(.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (.f64 x x))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(* -1/24 (pow x 2))
(.f64 x (.f64 x #s(literal -1/24 binary64)))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(* -1/24 (pow x 2))
(.f64 x (.f64 x #s(literal -1/24 binary64)))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(fma.f64 x (*.f64 x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(* 1/720 x)
(*.f64 x #s(literal 1/720 binary64))
(* 1/720 x)
(*.f64 x #s(literal 1/720 binary64))
(* 1/720 x)
(*.f64 x #s(literal 1/720 binary64))
(* 1/720 x)
(*.f64 x #s(literal 1/720 binary64))
(* 1/720 x)
(*.f64 x #s(literal 1/720 binary64))
(* 1/720 x)
(*.f64 x #s(literal 1/720 binary64))
(* 1/720 x)
(*.f64 x #s(literal 1/720 binary64))
(* 1/720 x)
(*.f64 x #s(literal 1/720 binary64))
(* 1/720 x)
(*.f64 x #s(literal 1/720 binary64))
(* 1/720 x)
(*.f64 x #s(literal 1/720 binary64))
(* 1/720 x)
(*.f64 x #s(literal 1/720 binary64))
(* 1/720 x)
(*.f64 x #s(literal 1/720 binary64))

eval107.0ms (1.3%)

Memory: -6.9MiB live, 186.8MiB allocated
Compiler: Compiled 19 503 to 1 287 computations (93.4% saved)

prune86.0ms (1%)

Memory

32.3MiB live, 146.5MiB allocated

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	694	1	695
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	695	5	700

Accuracy

100.0%

Counts

700 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	49.8%	(-.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
✓	100.0%	(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
✓	100.0%	(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
✓	99.8%	(.f64 #s(literal 1/2 binary64) (.f64 x x))
▶	49.4%	#s(literal 0 binary64)

Compiler

Compiled 44 to 27 computations (38.6% saved)

simplify3.0ms (0%)

Memory

6.9MiB live, 6.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	1
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0
#s(literal 0 binary64)

localize8.0ms (0.1%)

Memory

-32.8MiB live, 12.4MiB allocated

Samples

4.0ms

256×

valid

Compiler

Compiled 3 to 4 computations (-33.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

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

exact: 0.0ms (0% of total)

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

series0.0ms (0%)

Memory

0.0MiB live, 0.0MiB allocated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

rewrite7.0ms (0.1%)

Memory

9.6MiB live, 9.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
0	0	0

Stop Event

1×	saturated
1×	saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

simplify3.0ms (0%)

Memory

4.1MiB live, 4.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
0	0	0

Stop Event

1×	saturated
1×	saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune3.0ms (0%)

Memory

6.2MiB live, 6.2MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	4	4
Total	5	5

Accuracy

100.0%

Counts

5 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	49.8%	(-.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
✓	100.0%	(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
✓	100.0%	(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
✓	99.8%	(.f64 #s(literal 1/2 binary64) (.f64 x x))
✓	49.4%	#s(literal 0 binary64)

Compiler

Compiled 91 to 47 computations (48.4% saved)

regimes10.0ms (0.1%)

Memory

-19.4MiB live, 18.8MiB allocated

Counts

7 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(-.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(-.f64 #s(literal 1 binary64) (cos.f64 x))

Outputs
(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))

Calls

3 calls:

5.0ms	x
2.0ms	(-.f64 #s(literal 1 binary64) (cos.f64 x))
2.0ms	(cos.f64 x)

Results

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

Compiler

Compiled 10 to 7 computations (30% saved)

regimes6.0ms (0.1%)

Memory

15.9MiB live, 15.9MiB allocated

Counts

5 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(-.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))

Outputs
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))

Calls

3 calls:

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

Results

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

Compiler

Compiled 10 to 7 computations (30% saved)

regimes6.0ms (0.1%)

Memory

14.3MiB live, 14.3MiB allocated

Counts

4 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(-.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))

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

Calls

3 calls:

2.0ms	x
2.0ms	(-.f64 #s(literal 1 binary64) (cos.f64 x))
1.0ms	(cos.f64 x)

Results

Accuracy	Segments	Branch
99.8%	1	`x`
99.8%	1	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
99.8%	1	`(cos.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes5.0ms (0.1%)

Memory

-27.9MiB live, 11.2MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

2 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))

Outputs
#s(literal 0 binary64)

Calls

3 calls:

2.0ms	(cos.f64 x)
1.0ms	x
1.0ms	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Results

Accuracy	Segments	Branch
49.4%	1	`x`
49.4%	1	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
49.4%	1	`(cos.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

simplify7.0ms (0.1%)

Memory

16.8MiB live, 16.8MiB allocated

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	31
1	17	31

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
#s(literal 0 binary64)

Outputs
(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
#s(literal 0 binary64)

soundness2.3s (27.7%)

Memory

11.0MiB live, 372.0MiB allocated

Rules

32 720×	`accelerator-lowering-fma.f32`
32 720×	`accelerator-lowering-fma.f64`
6 238×	`accelerator-lowering-fma.f32`
6 238×	`accelerator-lowering-fma.f64`
4 762×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	79
1	130	79
2	1006	79
0	8282	71
0	41	144
1	101	144
2	246	144
3	589	144
4	1230	144
5	1905	144
6	2165	144
7	2814	144
8	4054	144
9	5622	144
10	6523	144
11	6804	144
12	6843	144
13	6843	144
14	7276	144
15	7552	144
16	7593	144
17	7595	144
18	7595	144
19	7595	144
20	7595	144
21	7605	144
22	7605	144
23	7605	144
0	8510	132

Stop Event

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

Compiler

Compiled 71 to 37 computations (47.9% saved)

preprocess55.0ms (0.7%)

Memory: -15.2MiB live, 100.3MiB allocated
Remove: (abs x)
Compiler: Compiled 160 to 84 computations (47.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	8	13
1	17	12
2	36	12
3	56	12
4	88	12
5	104	12
6	110	12
0	4	4
1	8	4
2	12	4
3	17	4
4	23	4
5	31	4
6	41	4
7	52	4
8	55	4
0	55	4

Iter	Nodes	Cost
0	8	13
1	17	12
2	36	12
3	56	12
4	88	12
5	104	12
6	110	12
0	4	4
1	8	4
2	12	4
3	17	4
4	23	4
5	31	4
6	41	4
7	52	4
8	55	4
0	55	4

analyze3.0ms (0%)

sample2.7s (33.1%)

preprocess19.0ms (0.2%)

explain147.0ms (1.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.1%)

localize160.0ms (2%)

series1.0ms (0%)

rewrite350.0ms (4.3%)

simplify961.0ms (11.7%)

eval85.0ms (1%)

prune44.0ms (0.5%)

simplify269.0ms (3.3%)

localize178.0ms (2.2%)

series6.0ms (0.1%)

rewrite372.0ms (4.5%)

simplify311.0ms (3.8%)

eval107.0ms (1.3%)

prune86.0ms (1%)

simplify3.0ms (0%)

localize8.0ms (0.1%)

series0.0ms (0%)

rewrite7.0ms (0.1%)

simplify3.0ms (0%)

eval0.0ms (0%)

prune3.0ms (0%)

regimes10.0ms (0.1%)

regimes6.0ms (0.1%)

regimes6.0ms (0.1%)

regimes5.0ms (0.1%)

simplify7.0ms (0.1%)

soundness2.3s (27.7%)

preprocess55.0ms (0.7%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	13
1	17	12
2	36	12
3	56	12
4	88	12
5	104	12
6	110	12
0	4	4
1	8	4
2	12	4
3	17	4
4	23	4
5	31	4
6	41	4
7	52	4
8	55	4
0	55	4