Metrics for ENA, Section 1.4, Mentioned, A

analyze4.0ms (0.1%)

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 9 computations (25% saved)

Precisions

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

ival-cos: 1.0ms (42.2% of total)

...c/correct-round.rkt:119:19: 1.0ms (42.2% of total)

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

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

const: 0.0ms (0% of total)

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

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

sample1.8s (34.7%)

Results

1.4s	8226×	1	valid
19.0ms	30×	0	valid

Precisions

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

...c/correct-round.rkt:119:19: 339.0ms (33.6% of total)

ival-cos: 324.0ms (32.1% of total)

ival-sub: 118.0ms (11.7% of total)

backward-pass: 105.0ms (10.4% of total)

ival-<=: 102.0ms (10.1% of total)

const: 11.0ms (1.1% of total)

ival-and: 11.0ms (1.1% of total)

Bogosity

preprocess21.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

52×	`fmsub-define`
48×	`fnmsub-define`
48×	`fnmadd-define`
42×	`sum3-define`
32×	`sum3-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	17	12
2	36	12
3	57	12
4	114	12
5	177	12
6	220	12
7	229	12
0	4	4
1	8	4
2	12	4
3	18	4
4	26	4
5	39	4
6	56	4
7	70	4
8	82	4
9	83	4
0	83	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)

explain83.0ms (1.6%)

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
130	-	-	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
0	-	-	`x`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(cos.f64 x)`

Results

59.0ms	510×	1	valid
0.0ms	2×	0	valid

Compiler

Compiled 25 to 14 computations (44% saved)

Precisions

Click to see histograms. Total time spent on operations: 31.0ms

ival-cos: 18.0ms (57.7% of total)

ival-sub: 6.0ms (19.2% of total)

backward-pass: 6.0ms (19.2% of total)

const: 1.0ms (3.2% of total)

eval0.0ms (0%)

Compiler: Compiled 5 to 4 computations (20% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.2%	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Compiler

Compiled 5 to 4 computations (20% saved)

simplify11.0ms (0.2%)

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

32×	`sum3-define`
24×	`+-lowering-+.f64`
24×	`+-lowering-+.f32`
18×	`--lowering--.f32`
18×	`--lowering--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	8
1	8	8
2	12	8
3	18	8
4	26	8
5	39	8
6	56	8
7	70	8
8	82	8
9	83	8
0	83	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

localize38.0ms (0.7%)

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	54.2%	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Results

31.0ms	255×	1	valid
0.0ms	1×	0	valid

Compiler

Compiled 10 to 5 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-cos: 10.0ms (59.6% of total)

ival-sub: 3.0ms (17.9% of total)

backward-pass: 3.0ms (17.9% of total)

const: 1.0ms (6% of total)

series1.0ms (0%)

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	@	-inf	(- 1 (cos x))
0.0ms	x	@	0	(cos x)
0.0ms	x	@	inf	(- 1 (cos x))
0.0ms	x	@	inf	(cos x)

rewrite289.0ms (5.7%)

Algorithm

1×	batch-egg-rewrite

Rules

3692×	`-lowering-.f32`
3692×	`-lowering-.f64`
2386×	`/-lowering-/.f32`
2386×	`/-lowering-/.f64`
1832×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	21	6
2	142	6
3	1218	6
0	9408	6

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 155

Calls

Call 1

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

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

simplify201.0ms (4%)

Algorithm

1×	egg-herbie

Rules

2004×	`-lowering-.f32`
2004×	`-lowering-.f64`
1558×	`fma-lowering-fma.f32`
1558×	`fma-lowering-fma.f64`
1502×	`fmsub-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	41	140
1	109	132
2	302	132
3	796	132
4	1881	132
5	2840	132
6	3376	132
7	4413	132
8	7649	132
0	8052	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 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64))))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 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 (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 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)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/24 binary64)))))))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 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)

eval23.0ms (0.5%)

Compiler: Compiled 6196 to 524 computations (91.5% saved)

prune24.0ms (0.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	174	5	179
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	175	5	180

Accuracy

100.0%

Counts

180 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.7%	(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
▶	100.0%	(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64))))))
▶	100.0%	(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))))))))
▶	99.9%	(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64))))))
▶	99.7%	(.f64 #s(literal 1/2 binary64) (.f64 x x))

Compiler

Compiled 128 to 80 computations (37.5% saved)

simplify98.0ms (1.9%)

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64))))
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64)))))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64))))))
✓	cost-diff	0	(.f64 x (.f64 x #s(literal -1/24 binary64)))
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64))))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal -1/24 binary64)))))
✓	cost-diff	0	(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64))))))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 #s(literal 1/2 binary64) (.f64 x x))
✓	cost-diff	128	(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
✓	cost-diff	0	(.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64)))))))
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))))))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/720 binary64) (.f64 (*.f64 x x) #s(literal -1/40320 binary64)))))))))
✓	cost-diff	0	(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))))))))

Rules

2878×	`fma-define`
2152×	`fma-lowering-fma.f32`
2152×	`fma-lowering-fma.f64`
660×	`sum3-define`
636×	`distribute-lft-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	29	243
1	96	218
2	337	218
3	832	218
4	1782	218
5	3083	218
6	3280	218
7	3305	218
8	3305	218
9	3701	218
10	3701	218
0	3701	218

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

Outputs
(* x (* x (+ 1/2 (* (* x x) (+ -1/24 (* x (* x (+ 1/720 (* (* x x) -1/40320)))))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))))))))
x
(* x (+ 1/2 (* (* x x) (+ -1/24 (* x (* x (+ 1/720 (* (* x x) -1/40320))))))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/720 binary64) (.f64 (*.f64 x x) #s(literal -1/40320 binary64))))))))))
(+ 1/2 (* (* x x) (+ -1/24 (* x (* x (+ 1/720 (* (* x x) -1/40320)))))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64)))))))))
1/2
#s(literal 1/2 binary64)
(* (* x x) (+ -1/24 (* x (* x (+ 1/720 (* (* x x) -1/40320))))))
(.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))))))
(* x x)
(*.f64 x x)
(+ -1/24 (* x (* x (+ 1/720 (* (* x x) -1/40320)))))
(+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))))
-1/24
#s(literal -1/24 binary64)
(* x (* x (+ 1/720 (* (* x x) -1/40320))))
(.f64 x (.f64 x (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64)))))
(* x (+ 1/720 (* (* x x) -1/40320)))
(.f64 x (+.f64 #s(literal 1/720 binary64) (.f64 (*.f64 x x) #s(literal -1/40320 binary64))))
(+ 1/720 (* (* x x) -1/40320))
(+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64)))
1/720
#s(literal 1/720 binary64)
(* (* x x) -1/40320)
(.f64 (.f64 x x) #s(literal -1/40320 binary64))
-1/40320
#s(literal -1/40320 binary64)
(- 1 1)
#s(literal 0 binary64)
1
#s(literal 1 binary64)
(* 1/2 (* x x))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
1/2
#s(literal 1/2 binary64)
(* x x)
(*.f64 x x)
x
(* x (* x (+ 1/2 (* x (* x -1/24)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))))
x
(* x (+ 1/2 (* x (* x -1/24))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal -1/24 binary64))))
(+ 1/2 (* x (* x -1/24)))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))
1/2
#s(literal 1/2 binary64)
(* x (* x -1/24))
(.f64 (.f64 x x) #s(literal -1/24 binary64))
(* x -1/24)
(*.f64 x #s(literal -1/24 binary64))
-1/24
#s(literal -1/24 binary64)
(* (* x x) (+ 1/2 (* (* x x) (+ -1/24 (* (* x x) 1/720)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64)))))))
(* x x)
(*.f64 x x)
x
(+ 1/2 (* (* x x) (+ -1/24 (* (* x x) 1/720))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64))))))
1/2
#s(literal 1/2 binary64)
(* (* x x) (+ -1/24 (* (* x x) 1/720)))
(.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64)))))
(+ -1/24 (* (* x x) 1/720))
(+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64)))
-1/24
#s(literal -1/24 binary64)
(* (* x x) 1/720)
(.f64 (.f64 x x) #s(literal 1/720 binary64))
1/720
#s(literal 1/720 binary64)

localize159.0ms (3.1%)

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64))))))
✓	accuracy	99.8%	(.f64 (.f64 x x) #s(literal 1/720 binary64))
✓	accuracy	99.7%	(.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64))))
✓	accuracy	100.0%	(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64))))))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal -1/24 binary64)))))
✓	accuracy	99.8%	(.f64 x (.f64 x #s(literal -1/24 binary64)))
✓	accuracy	99.4%	(*.f64 x #s(literal -1/24 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	99.8%	(.f64 (.f64 x x) #s(literal -1/40320 binary64))
✓	accuracy	99.8%	(.f64 x (.f64 x (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64)))))
✓	accuracy	99.7%	(.f64 x (+.f64 #s(literal 1/720 binary64) (.f64 (*.f64 x x) #s(literal -1/40320 binary64))))
✓	accuracy	99.7%	(.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64)))))))

Results

99.0ms	255×	0	valid
1.0ms	1×	3	valid

Compiler

Compiled 247 to 29 computations (88.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 63.0ms

ival-mult: 44.0ms (69.4% of total)

...c/correct-round.rkt:119:19: 10.0ms (15.8% of total)

ival-add: 7.0ms (11% of total)

const: 1.0ms (1.6% of total)

ival-sub: 1.0ms (1.6% of total)

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

series12.0ms (0.2%)

Counts

19 → 216

Calls

Call 1

Inputs
#<alt (* x (* x (+ 1/2 (* (* x x) (+ -1/24 (* x (* x (+ 1/720 (* (* x x) -1/40320)))))))))>
#<alt (* x (+ 1/2 (* (* x x) (+ -1/24 (* x (* x (+ 1/720 (* (* x x) -1/40320))))))))>
#<alt (+ 1/2 (* (* x x) (+ -1/24 (* x (* x (+ 1/720 (* (* x x) -1/40320)))))))>
#<alt (* (* x x) (+ -1/24 (* x (* x (+ 1/720 (* (* x x) -1/40320))))))>
#<alt (- 1 1)>
#<alt (* 1/2 (* x x))>
#<alt (* x x)>
#<alt (* x (* x (+ 1/2 (* x (* x -1/24)))))>
#<alt (* x (+ 1/2 (* x (* x -1/24))))>
#<alt (+ 1/2 (* x (* x -1/24)))>
#<alt (* x (* x -1/24))>
#<alt (* (* x x) (+ 1/2 (* (* x x) (+ -1/24 (* (* x x) 1/720)))))>
#<alt (+ 1/2 (* (* x x) (+ -1/24 (* (* x x) 1/720))))>
#<alt (* (* x x) (+ -1/24 (* (* x x) 1/720)))>
#<alt (* x (+ 1/720 (* (* x x) -1/40320)))>
#<alt (* x (* x (+ 1/720 (* (* x x) -1/40320))))>
#<alt (* (* x x) -1/40320)>
#<alt (* x -1/24)>
#<alt (* (* x 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) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))>
#<alt (* -1/40320 (pow x 8))>
#<alt (* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* (pow x 8) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* -1/40320 (pow x 8))>
#<alt (* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* (pow x 8) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))>
#<alt (* -1/40320 (pow x 7))>
#<alt (* (pow x 7) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 7) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* (pow x 7) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* -1/40320 (pow x 7))>
#<alt (* -1 (* (pow x 7) (- 1/40320 (* 1/720 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 7) (- (+ 1/40320 (/ 1/24 (pow x 4))) (* 1/720 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 7) (- (+ 1/40320 (/ 1/24 (pow x 4))) (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))>
#<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) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))>
#<alt (* -1/40320 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* (pow x 6) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* -1/40320 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* (pow x 6) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* -1/24 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))>
#<alt (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))>
#<alt (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))>
#<alt (* -1/40320 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* -1/40320 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<alt (* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))>
#<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 (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 (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 x)>
#<alt (* x (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* -1/24 (pow x 3))>
#<alt (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* -1/24 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))>
#<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 (* -1/24 (pow x 2))>
#<alt (* -1/24 (pow x 2))>
#<alt (* -1/24 (pow x 2))>
#<alt (* -1/24 (pow x 2))>
#<alt (* -1/24 (pow x 2))>
#<alt (* -1/24 (pow x 2))>
#<alt (* -1/24 (pow x 2))>
#<alt (* -1/24 (pow x 2))>
#<alt (* -1/24 (pow x 2))>
#<alt (* -1/24 (pow x 2))>
#<alt (* -1/24 (pow x 2))>
#<alt (* -1/24 (pow x 2))>
#<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 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 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))>
#<alt (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))>
#<alt (* (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 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 1/720 (* 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 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* 1/720 x)>
#<alt (* x (+ 1/720 (* -1/40320 (pow x 2))))>
#<alt (* x (+ 1/720 (* -1/40320 (pow x 2))))>
#<alt (* x (+ 1/720 (* -1/40320 (pow x 2))))>
#<alt (* -1/40320 (pow x 3))>
#<alt (* (pow x 3) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 3) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 3) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* -1/40320 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/40320 (* 1/720 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- 1/40320 (* 1/720 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- 1/40320 (* 1/720 (/ 1 (pow x 2))))))>
#<alt (* 1/720 (pow x 2))>
#<alt (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2))))>
#<alt (* -1/40320 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* -1/40320 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* -1/40320 (pow x 2))>
#<alt (* -1/24 x)>
#<alt (* -1/24 x)>
#<alt (* -1/24 x)>
#<alt (* -1/24 x)>
#<alt (* -1/24 x)>
#<alt (* -1/24 x)>
#<alt (* -1/24 x)>
#<alt (* -1/24 x)>
#<alt (* -1/24 x)>
#<alt (* -1/24 x)>
#<alt (* -1/24 x)>
#<alt (* -1/24 x)>
#<alt (* 1/720 (pow x 2))>
#<alt (* 1/720 (pow x 2))>
#<alt (* 1/720 (pow x 2))>
#<alt (* 1/720 (pow x 2))>
#<alt (* 1/720 (pow x 2))>
#<alt (* 1/720 (pow x 2))>
#<alt (* 1/720 (pow x 2))>
#<alt (* 1/720 (pow x 2))>
#<alt (* 1/720 (pow x 2))>
#<alt (* 1/720 (pow x 2))>
#<alt (* 1/720 (pow x 2))>
#<alt (* 1/720 (pow x 2))>

Calls

54 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(* x -1/24)
1.0ms	x	@	inf	(* x (* x (+ 1/2 (* (* x x) (+ -1/24 (* x (* x (+ 1/720 (* (* x x) -1/40320)))))))))
1.0ms	x	@	inf	(* x x)
0.0ms	x	@	inf	(* (* x x) (+ -1/24 (* x (* x (+ 1/720 (* (* x x) -1/40320))))))
0.0ms	x	@	inf	(* x (* x (+ 1/2 (* x (* x -1/24)))))

rewrite370.0ms (7.3%)

Algorithm

1×	batch-egg-rewrite

Rules

4308×	`-lowering-.f32`
4308×	`-lowering-.f64`
3008×	`/-lowering-/.f32`
3008×	`/-lowering-/.f64`
2334×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	29	195
1	171	174
2	1526	174
0	8646	174

Stop Event

1×	iter limit
1×	node limit

Counts

19 → 429

Calls

Call 1

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

Outputs
(+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))) (.f64 x (.f64 x x)))))
(+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64)))))))))
(+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 (.f64 (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))) (.f64 x (.f64 x x))) x))
(+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))))) (.f64 x x)))
(+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64)))))))) (.f64 x (.f64 x #s(literal 1/2 binary64))))
(+.f64 (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))))) (.f64 x x)) (.f64 x (.f64 x #s(literal 1/2 binary64))))
(fma.f64 x (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))) (.f64 x (*.f64 x x)))))
(fma.f64 x (.f64 x #s(literal 1/2 binary64)) (.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (*.f64 x x) #s(literal -1/40320 binary64)))))))))
(fma.f64 x (.f64 x #s(literal 1/2 binary64)) (.f64 (.f64 (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))) (.f64 x (*.f64 x x))) x))
(fma.f64 x (.f64 x #s(literal 1/2 binary64)) (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))))) (*.f64 x x)))
(fma.f64 #s(literal 1/2 binary64) (.f64 x x) (.f64 x (.f64 (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))) (.f64 x (*.f64 x x)))))
(fma.f64 #s(literal 1/2 binary64) (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (*.f64 x x) #s(literal -1/40320 binary64)))))))))
(fma.f64 #s(literal 1/2 binary64) (.f64 x x) (.f64 (.f64 (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))) (.f64 x (*.f64 x x))) x))
(fma.f64 #s(literal 1/2 binary64) (.f64 x x) (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))))) (*.f64 x x)))
(fma.f64 (.f64 x x) #s(literal 1/2 binary64) (.f64 x (.f64 (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))) (.f64 x (*.f64 x x)))))
(fma.f64 (.f64 x x) #s(literal 1/2 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (*.f64 x x) #s(literal -1/40320 binary64)))))))))
(fma.f64 (.f64 x x) #s(literal 1/2 binary64) (.f64 (.f64 (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))) (.f64 x (*.f64 x x))) x))
(fma.f64 (.f64 x x) #s(literal 1/2 binary64) (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))))) (*.f64 x x)))
(fma.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))))) (.f64 x (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))))) (.f64 x x) (.f64 x (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) x (.f64 x (.f64 (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))) (.f64 x (*.f64 x x)))))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) x (.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (*.f64 x x) #s(literal -1/40320 binary64)))))))))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) x (.f64 (.f64 (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))) (.f64 x (*.f64 x x))) x))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) x (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))))) (*.f64 x x)))
(/.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))))) (.f64 (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))) (.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64)))))))))))) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))))) (-.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (*.f64 x x) #s(literal -1/40320 binary64))))))) #s(literal 1/2 binary64)))))
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(/.f64 (neg.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))) (.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64)))))))))))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (*.f64 x x) #s(literal -1/40320 binary64))))))))))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) (pow.f64 (.f64 x (.f64 (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))) (.f64 x (.f64 x x)))) #s(literal 3 binary64))) (+.f64 (.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/2 binary64)))) (-.f64 (.f64 (.f64 x (.f64 (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))) (.f64 x (.f64 x x)))) (.f64 x (.f64 (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))) (.f64 x (.f64 x x))))) (.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))) (.f64 x (*.f64 x x))))))))
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(fma.f64 x (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))))) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) x (.f64 (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))) (.f64 x (*.f64 x x))))
(fma.f64 (.f64 x x) (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64)))))) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))) (.f64 x (.f64 x x)) (*.f64 x #s(literal 1/2 binary64)))
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simplify209.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

3034×	`-lowering-.f32`
3034×	`-lowering-.f64`
1788×	`+-lowering-+.f64`
1788×	`+-lowering-+.f32`
1752×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	102	1826
1	287	1771
2	815	1749
3	2631	1749
4	7602	1749
0	8236	1749

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 216

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))))
(* -1/40320 (pow x 8))
(* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 8) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* -1/40320 (pow x 8))
(* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 8) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* 1/2 x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(* -1/40320 (pow x 7))
(* (pow x 7) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 7) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 7) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* -1/40320 (pow x 7))
(* -1 (* (pow x 7) (- 1/40320 (* 1/720 (/ 1 (pow x 2))))))
(* -1 (* (pow x 7) (- (+ 1/40320 (/ 1/24 (pow x 4))) (* 1/720 (/ 1 (pow x 2))))))
(* -1 (* (pow x 7) (- (+ 1/40320 (/ 1/24 (pow x 4))) (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
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) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(* -1/40320 (pow x 6))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* -1/40320 (pow x 6))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* -1/24 (pow x 2))
(* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))
(* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))
(* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))
(* -1/40320 (pow x 6))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* -1/40320 (pow x 6))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(* 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))
(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 (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 x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(* x (+ 1/2 (* -1/24 (pow x 2))))
(* x (+ 1/2 (* -1/24 (pow x 2))))
(* -1/24 (pow x 3))
(* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* -1/24 (pow x 3))
(* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))
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))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* 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)))))
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 (pow x 2))
(* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))
(* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))
(* (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 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 4) (- 1/720 (* 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 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* 1/720 x)
(* x (+ 1/720 (* -1/40320 (pow x 2))))
(* x (+ 1/720 (* -1/40320 (pow x 2))))
(* x (+ 1/720 (* -1/40320 (pow x 2))))
(* -1/40320 (pow x 3))
(* (pow x 3) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 3) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 3) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* -1/40320 (pow x 3))
(* -1 (* (pow x 3) (- 1/40320 (* 1/720 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/40320 (* 1/720 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/40320 (* 1/720 (/ 1 (pow x 2))))))
(* 1/720 (pow x 2))
(* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2))))
(* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2))))
(* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2))))
(* -1/40320 (pow x 4))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* -1/40320 (pow x 4))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* (pow x 4) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(* -1/40320 (pow x 2))
(* -1/40320 (pow x 2))
(* -1/40320 (pow x 2))
(* -1/40320 (pow x 2))
(* -1/40320 (pow x 2))
(* -1/40320 (pow x 2))
(* -1/40320 (pow x 2))
(* -1/40320 (pow x 2))
(* -1/40320 (pow x 2))
(* -1/40320 (pow x 2))
(* -1/40320 (pow x 2))
(* -1/40320 (pow x 2))
(* -1/24 x)
(* -1/24 x)
(* -1/24 x)
(* -1/24 x)
(* -1/24 x)
(* -1/24 x)
(* -1/24 x)
(* -1/24 x)
(* -1/24 x)
(* -1/24 x)
(* -1/24 x)
(* -1/24 x)
(* 1/720 (pow x 2))
(* 1/720 (pow x 2))
(* 1/720 (pow x 2))
(* 1/720 (pow x 2))
(* 1/720 (pow x 2))
(* 1/720 (pow x 2))
(* 1/720 (pow x 2))
(* 1/720 (pow x 2))
(* 1/720 (pow x 2))
(* 1/720 (pow x 2))
(* 1/720 (pow x 2))
(* 1/720 (pow x 2))

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 (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64))))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64))))))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64)))))))))
(* -1/40320 (pow x 8))
(*.f64 #s(literal -1/40320 binary64) (pow.f64 x #s(literal 8 binary64)))
(* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal 1/720 binary64) (.f64 x x))))
(* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (/.f64 #s(literal 1/720 binary64) (.f64 x x)) (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
(* (pow x 8) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (+.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal 1/720 binary64) (.f64 x x))) (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
(* -1/40320 (pow x 8))
(*.f64 #s(literal -1/40320 binary64) (pow.f64 x #s(literal 8 binary64)))
(* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal 1/720 binary64) (.f64 x x))))
(* (pow x 8) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (/.f64 #s(literal 1/720 binary64) (.f64 x x)) (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
(* (pow x 8) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (+.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal 1/720 binary64) (.f64 x x))) (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal -1/24 binary64)))))
(* x (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (*.f64 x #s(literal 1/720 binary64)))))))
(* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/720 binary64) (.f64 (*.f64 x x) #s(literal -1/40320 binary64)))))))))
(* -1/40320 (pow x 7))
(*.f64 #s(literal -1/40320 binary64) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (+.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal 1/720 binary64) (.f64 x x))) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(.f64 (+.f64 (/.f64 #s(literal 1/720 binary64) (.f64 x x)) (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x (*.f64 x x)))))) (pow.f64 x #s(literal 7 binary64)))
(* (pow x 7) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(.f64 (+.f64 (+.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal 1/720 binary64) (.f64 x x))) (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (*.f64 x x)))))) (pow.f64 x #s(literal 7 binary64)))
(* -1/40320 (pow x 7))
(*.f64 #s(literal -1/40320 binary64) (pow.f64 x #s(literal 7 binary64)))
(* -1 (* (pow x 7) (- 1/40320 (* 1/720 (/ 1 (pow x 2))))))
(.f64 (+.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal 1/720 binary64) (.f64 x x))) (pow.f64 x #s(literal 7 binary64)))
(* -1 (* (pow x 7) (- (+ 1/40320 (/ 1/24 (pow x 4))) (* 1/720 (/ 1 (pow x 2))))))
(.f64 (+.f64 (/.f64 #s(literal 1/720 binary64) (.f64 x x)) (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x (*.f64 x x)))))) (pow.f64 x #s(literal 7 binary64)))
(* -1 (* (pow x 7) (- (+ 1/40320 (/ 1/24 (pow x 4))) (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))
(.f64 (+.f64 (+.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal 1/720 binary64) (.f64 x x))) (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (*.f64 x x)))))) (pow.f64 x #s(literal 7 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64))))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64))))))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))))))
(* -1/40320 (pow x 6))
(*.f64 #s(literal -1/40320 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (+.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal 1/720 binary64) (.f64 x x))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(.f64 (+.f64 (/.f64 #s(literal 1/720 binary64) (.f64 x x)) (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x (*.f64 x x)))))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal 1/720 binary64) (.f64 x x))) (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
(* -1/40320 (pow x 6))
(*.f64 #s(literal -1/40320 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (+.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal 1/720 binary64) (.f64 x x))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(.f64 (+.f64 (/.f64 #s(literal 1/720 binary64) (.f64 x x)) (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x (*.f64 x x)))))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (+ (* 1/720 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal 1/720 binary64) (.f64 x x))) (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (*.f64 x x)))))))
(* -1/24 (pow x 2))
(.f64 x (.f64 x #s(literal -1/24 binary64)))
(* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))
(.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64)))))
(* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))
(.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64)))))))
(* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))
(.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64)))))))
(* -1/40320 (pow x 6))
(*.f64 #s(literal -1/40320 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) 1/40320))
(.f64 (+.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal 1/720 binary64) (.f64 x x))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (* 1/720 (/ 1 (pow x 2))) (+ 1/40320 (/ 1/24 (pow x 4)))))
(.f64 (+.f64 (/.f64 #s(literal 1/720 binary64) (.f64 x x)) (-.f64 #s(literal -1/40320 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x (*.f64 x x)))))) (pow.f64 x #s(literal 6 binary64)))
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(.f64 (.f64 x x) #s(literal -1/40320 binary64))
(* -1/40320 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/40320 binary64))
(* -1/40320 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/40320 binary64))
(* -1/40320 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/40320 binary64))
(* -1/40320 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/40320 binary64))
(* -1/40320 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/40320 binary64))
(* -1/40320 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/40320 binary64))
(* -1/40320 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/40320 binary64))
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))
(* -1/24 x)
(*.f64 x #s(literal -1/24 binary64))
(* 1/720 (pow x 2))
(.f64 x (.f64 x #s(literal 1/720 binary64)))
(* 1/720 (pow x 2))
(.f64 x (.f64 x #s(literal 1/720 binary64)))
(* 1/720 (pow x 2))
(.f64 x (.f64 x #s(literal 1/720 binary64)))
(* 1/720 (pow x 2))
(.f64 x (.f64 x #s(literal 1/720 binary64)))
(* 1/720 (pow x 2))
(.f64 x (.f64 x #s(literal 1/720 binary64)))
(* 1/720 (pow x 2))
(.f64 x (.f64 x #s(literal 1/720 binary64)))
(* 1/720 (pow x 2))
(.f64 x (.f64 x #s(literal 1/720 binary64)))
(* 1/720 (pow x 2))
(.f64 x (.f64 x #s(literal 1/720 binary64)))
(* 1/720 (pow x 2))
(.f64 x (.f64 x #s(literal 1/720 binary64)))
(* 1/720 (pow x 2))
(.f64 x (.f64 x #s(literal 1/720 binary64)))
(* 1/720 (pow x 2))
(.f64 x (.f64 x #s(literal 1/720 binary64)))
(* 1/720 (pow x 2))
(.f64 x (.f64 x #s(literal 1/720 binary64)))

eval150.0ms (3%)

Compiler: Compiled 24246 to 2015 computations (91.7% saved)

prune63.0ms (1.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	732	3	735
Fresh	0	0	0
Picked	4	1	5
Done	0	0	0
Total	736	4	740

Accuracy

100.0%

Counts

740 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64)))))) x)
▶	99.7%	(.f64 (.f64 x #s(literal 1/2 binary64)) x)
✓	99.9%	(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64))))))
▶	53.7%	#s(literal 0 binary64)

Compiler

Compiled 38 to 25 computations (34.2% saved)

simplify24.0ms (0.5%)

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Program
✓	cost-diff	(.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64))))
✓	cost-diff	(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64)))))
✓	cost-diff	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (*.f64 x x) #s(literal 1/720 binary64))))))
✓	cost-diff	(.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64)))))) x)
✓	cost-diff	(*.f64 x #s(literal 1/2 binary64))
✓	cost-diff	(.f64 (.f64 x #s(literal 1/2 binary64)) x)

Rules

460×	`fma-define`
408×	`fma-lowering-fma.f32`
408×	`fma-lowering-fma.f64`
242×	`-lowering-.f32`
242×	`-lowering-.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	86
1	39	78
2	129	78
3	323	78
4	515	78
5	630	78
6	635	78
0	635	78

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
0
(* (* x 1/2) x)
(* x 1/2)
x
1/2
(* (* x (+ 1/2 (* (* x x) (+ -1/24 (* (* x x) 1/720))))) x)
(* x (+ 1/2 (* (* x x) (+ -1/24 (* (* x x) 1/720)))))
x
(+ 1/2 (* (* x x) (+ -1/24 (* (* x x) 1/720))))
1/2
(* (* x x) (+ -1/24 (* (* x x) 1/720)))
(* x x)
(+ -1/24 (* (* x x) 1/720))
-1/24
(* (* x x) 1/720)
1/720

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

localize80.0ms (1.6%)

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64)))))) x)
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (*.f64 x x) #s(literal 1/720 binary64))))))
✓	accuracy	99.8%	(.f64 (.f64 x x) #s(literal 1/720 binary64))
✓	accuracy	99.7%	(.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64))))
✓	accuracy	100.0%	(.f64 (.f64 x #s(literal 1/2 binary64)) x)
✓	accuracy	100.0%	(*.f64 x #s(literal 1/2 binary64))

Results

62.0ms	255×	0	valid
1.0ms	1×	3	valid

Compiler

Compiled 88 to 15 computations (83% saved)

Precisions

Click to see histograms. Total time spent on operations: 30.0ms

ival-mult: 19.0ms (63.7% of total)

...c/correct-round.rkt:119:19: 8.0ms (26.8% of total)

ival-add: 3.0ms (10.1% of total)

const: 0.0ms (0% of total)

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

series2.0ms (0%)

Counts

7 → 84

Calls

Call 1

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

Outputs
#<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 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<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 (* 1/2 x)>
#<alt (* x (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* x (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* 1/720 (pow x 5))>
#<alt (* (pow x 5) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* 1/720 (pow x 5))>
#<alt (* -1 (* (pow x 5) (- (* 1/24 (/ 1 (pow x 2))) 1/720)))>
#<alt (* -1 (* (pow x 5) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4))))))>
#<alt (* -1 (* (pow x 5) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4))))))>
#<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 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))>
#<alt (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))>
#<alt (* (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 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 1/720 (* 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 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* 1/720 (pow x 2))>
#<alt (* 1/720 (pow x 2))>
#<alt (* 1/720 (pow x 2))>
#<alt (* 1/720 (pow x 2))>
#<alt (* 1/720 (pow x 2))>
#<alt (* 1/720 (pow x 2))>
#<alt (* 1/720 (pow x 2))>
#<alt (* 1/720 (pow x 2))>
#<alt (* 1/720 (pow x 2))>
#<alt (* 1/720 (pow x 2))>
#<alt (* 1/720 (pow x 2))>
#<alt (* 1/720 (pow x 2))>

Calls

21 calls:

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

rewrite302.0ms (5.9%)

Algorithm

1×	batch-egg-rewrite

Rules

4092×	`-lowering-.f32`
4092×	`-lowering-.f64`
2000×	`/-lowering-/.f32`
2000×	`/-lowering-/.f64`
1892×	`sum5-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	69
1	69	62
2	566	62
3	6457	62
0	8485	62

Stop Event

1×	iter limit
1×	node limit

Counts

7 → 225

Calls

Call 1

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

Outputs
(.f64 x (.f64 x #s(literal 1/2 binary64)))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal 1/2 binary64)) x)
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(*.f64 x #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) x)
(+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64))))))))
(+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64))))))) (.f64 x (.f64 x #s(literal 1/2 binary64))))
(+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal -1/24 binary64)))) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 #s(literal 1/720 binary64) (.f64 x (.f64 x x)))))))
(+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64))))) (.f64 (.f64 x x) (.f64 x (.f64 #s(literal 1/720 binary64) (.f64 x (.f64 x x))))))
(+.f64 (.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) (.f64 x x)) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 #s(literal 1/720 binary64) (.f64 x (.f64 x x))))) (.f64 x x)))
(+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64)))) (.f64 x x)) (.f64 (.f64 x (.f64 #s(literal 1/720 binary64) (.f64 x (.f64 x x)))) (.f64 x x)))
(fma.f64 x (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (*.f64 x #s(literal 1/720 binary64))))))))
(fma.f64 #s(literal 1/2 binary64) (.f64 x x) (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (*.f64 x #s(literal 1/720 binary64))))))))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) x (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (*.f64 x #s(literal 1/720 binary64))))))))
(fma.f64 (.f64 x x) #s(literal 1/2 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (*.f64 x #s(literal 1/720 binary64))))))))
(/.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (*.f64 x #s(literal 1/720 binary64))))))))
(/.f64 (+.f64 (pow.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64))))))) #s(literal 3 binary64))) (+.f64 (.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/2 binary64)))) (-.f64 (.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64))))))) (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64)))))))) (.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (*.f64 x #s(literal 1/720 binary64)))))))))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x #s(literal 1/2 binary64)))) (.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64))))))) (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64))))))))) (-.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64)))))))))
(/.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (.f64 (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64)))) (.f64 (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64)))))) (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64)))))))))) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64))))) (+.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (*.f64 x #s(literal 1/720 binary64))))) #s(literal -1/2 binary64)))))
(/.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64))))) (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal -1/720 binary64)) #s(literal 1/24 binary64)))))) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 (.f64 (*.f64 x x) #s(literal -1/720 binary64)) #s(literal 1/24 binary64)))))
(/.f64 (.f64 (.f64 x x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64))))))))
(/.f64 (.f64 x (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64)))))) (.f64 (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64)))))) (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64)))))))))) (+.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64)))))) (-.f64 (.f64 x (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64)))))) (*.f64 x #s(literal 1/2 binary64))))))
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(/.f64 (neg.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/373248000 binary64)))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/518400 binary64)) #s(literal -1/17280 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/518400 binary64)))) (.f64 x (.f64 x (.f64 x x)))) (.f64 #s(literal 1/576 binary64) (.f64 x (.f64 x (.f64 x x))))) (-.f64 (.f64 x (.f64 #s(literal 1/720 binary64) (.f64 x (.f64 x x)))) (.f64 x (.f64 x #s(literal -1/24 binary64)))))
(/.f64 (.f64 (.f64 x x) (+.f64 (neg.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/373248000 binary64)))) #s(literal 1/13824 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/518400 binary64)) #s(literal -1/17280 binary64))))))
(/.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/576 binary64) (neg.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/518400 binary64))))) (+.f64 #s(literal 1/24 binary64) (neg.f64 (.f64 (.f64 x x) #s(literal -1/720 binary64)))))
(/.f64 (.f64 (.f64 x x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64))))))
(/.f64 (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/518400 binary64)))) #s(literal -1/576 binary64))) (+.f64 (.f64 x (.f64 x #s(literal 1/720 binary64))) #s(literal 1/24 binary64)))
(/.f64 (.f64 (+.f64 (neg.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/373248000 binary64)))) #s(literal 1/13824 binary64)) (.f64 x x)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/518400 binary64)) #s(literal -1/17280 binary64))))))
(/.f64 (.f64 (+.f64 #s(literal -1/576 binary64) (neg.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/518400 binary64)))) (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (neg.f64 (.f64 (.f64 x x) #s(literal -1/720 binary64)))))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64))))))
(/.f64 (.f64 (+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/518400 binary64)))) #s(literal -1/576 binary64)) (.f64 x x)) (+.f64 (.f64 x (.f64 x #s(literal 1/720 binary64))) #s(literal 1/24 binary64)))
(.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64))))))
(.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64)))))
(.f64 (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64)))) (.f64 x x))
(.f64 (+.f64 #s(literal -1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/373248000 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/518400 binary64)) #s(literal -1/17280 binary64))))) (*.f64 x x)))
(.f64 (+.f64 #s(literal -1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/373248000 binary64)))) (/.f64 (.f64 x x) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/518400 binary64)) #s(literal -1/17280 binary64))))))
(.f64 (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/518400 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))) (*.f64 x x)))
(.f64 (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/518400 binary64))) (/.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))
(.f64 (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64))))) x)
(.f64 (+.f64 (.f64 #s(literal -1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/373248000 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/576 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 #s(literal 1/720 binary64) (.f64 x (.f64 x x)))) (-.f64 (.f64 x (.f64 #s(literal 1/720 binary64) (.f64 x (.f64 x x)))) (.f64 x (.f64 x #s(literal -1/24 binary64))))))))
(.f64 (.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64))))) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))))
(.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/518400 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))
(.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/373248000 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/518400 binary64)) #s(literal -1/17280 binary64))))))
(.f64 (/.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/518400 binary64)))) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/518400 binary64)))) (+.f64 #s(literal -1/24 binary64) (.f64 x (*.f64 x #s(literal 1/720 binary64)))))
(.f64 (/.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/518400 binary64)))) (+.f64 #s(literal -1/13824 binary64) (.f64 #s(literal -1/373248000 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (+.f64 (.f64 (*.f64 x x) #s(literal 1/518400 binary64)) #s(literal -1/17280 binary64)))))
(.f64 (/.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/373248000 binary64))))) (+.f64 #s(literal 1/191102976 binary64) (.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/518400 binary64)) #s(literal -1/17280 binary64))) (.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/518400 binary64)) #s(literal -1/17280 binary64))) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/518400 binary64)) #s(literal -1/17280 binary64))))))) (+.f64 #s(literal 1/331776 binary64) (.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/518400 binary64)) #s(literal -1/17280 binary64))) (-.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/518400 binary64)) #s(literal -1/17280 binary64))) #s(literal 1/576 binary64)))))
(.f64 (/.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/373248000 binary64))))) (-.f64 #s(literal 1/331776 binary64) (.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/518400 binary64)) #s(literal -1/17280 binary64))) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/518400 binary64)) #s(literal -1/17280 binary64)))))) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/518400 binary64)) #s(literal -1/17280 binary64)))))
(.f64 x (.f64 x #s(literal 1/720 binary64)))
(.f64 (.f64 x x) #s(literal 1/720 binary64))
(.f64 #s(literal 1/720 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal 1/720 binary64)) x)

simplify192.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

2622×	`-lowering-.f32`
2622×	`-lowering-.f64`
2038×	`sum5-define`
1860×	`fma-define`
1416×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	48	690
1	127	669
2	323	669
3	892	669
4	2646	658
5	7289	658
0	8227	658

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

Calls

Call 1

Inputs
(* 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 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 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)))))
(* 1/2 x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* x (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* 1/720 (pow x 5))
(* (pow x 5) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 5) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 5) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* 1/720 (pow x 5))
(* -1 (* (pow x 5) (- (* 1/24 (/ 1 (pow x 2))) 1/720)))
(* -1 (* (pow x 5) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4))))))
(* -1 (* (pow x 5) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4))))))
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 (pow x 2))
(* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))
(* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))
(* (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 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 4) (- 1/720 (* 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 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* 1/720 (pow x 2))
(* 1/720 (pow x 2))
(* 1/720 (pow x 2))
(* 1/720 (pow x 2))
(* 1/720 (pow x 2))
(* 1/720 (pow x 2))
(* 1/720 (pow x 2))
(* 1/720 (pow x 2))
(* 1/720 (pow x 2))
(* 1/720 (pow x 2))
(* 1/720 (pow x 2))
(* 1/720 (pow x 2))

Outputs
(* 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 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 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) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64)))))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64)))))))
(* 1/720 (pow x 6))
(*.f64 #s(literal 1/720 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal 1/720 binary64) (/.f64 #s(literal -1/24 binary64) (.f64 x x))))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal 1/720 binary64) (/.f64 #s(literal -1/24 binary64) (.f64 x x))) (/.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 x (.f64 x x)))))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal 1/720 binary64) (/.f64 #s(literal -1/24 binary64) (.f64 x x))) (/.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 x (.f64 x x)))))
(* 1/720 (pow x 6))
(*.f64 #s(literal 1/720 binary64) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal 1/720 binary64) (/.f64 #s(literal -1/24 binary64) (.f64 x x))))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal 1/720 binary64) (/.f64 #s(literal -1/24 binary64) (.f64 x x))) (/.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 x (.f64 x x)))))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal 1/720 binary64) (/.f64 #s(literal -1/24 binary64) (.f64 x x))) (/.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 x (.f64 x x)))))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal -1/24 binary64))))
(* x (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (*.f64 x x) #s(literal 1/720 binary64)))))))
(* x (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (*.f64 x x) #s(literal 1/720 binary64)))))))
(* 1/720 (pow x 5))
(.f64 (.f64 x x) (.f64 x (.f64 (*.f64 x x) #s(literal 1/720 binary64))))
(* (pow x 5) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(.f64 (+.f64 #s(literal 1/720 binary64) (/.f64 #s(literal -1/24 binary64) (.f64 x x))) (.f64 x (.f64 x (.f64 x (.f64 x x)))))
(* (pow x 5) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(.f64 (+.f64 (+.f64 #s(literal 1/720 binary64) (/.f64 #s(literal -1/24 binary64) (.f64 x x))) (/.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x (.f64 x x)))))
(* (pow x 5) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(.f64 (+.f64 (+.f64 #s(literal 1/720 binary64) (/.f64 #s(literal -1/24 binary64) (.f64 x x))) (/.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x (.f64 x x)))))
(* 1/720 (pow x 5))
(.f64 (.f64 x x) (.f64 x (.f64 (*.f64 x x) #s(literal 1/720 binary64))))
(* -1 (* (pow x 5) (- (* 1/24 (/ 1 (pow x 2))) 1/720)))
(.f64 (+.f64 #s(literal 1/720 binary64) (/.f64 #s(literal -1/24 binary64) (.f64 x x))) (.f64 x (.f64 x (.f64 x (.f64 x x)))))
(* -1 (* (pow x 5) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4))))))
(.f64 (+.f64 (+.f64 #s(literal 1/720 binary64) (/.f64 #s(literal -1/24 binary64) (.f64 x x))) (/.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x (.f64 x x)))))
(* -1 (* (pow x 5) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4))))))
(.f64 (+.f64 (+.f64 #s(literal 1/720 binary64) (/.f64 #s(literal -1/24 binary64) (.f64 x x))) (/.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x (.f64 x x)))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64))))))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64))))))
(* 1/720 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/720 binary64))))
(* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64)))))
(* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 x (.f64 x x)))))))
(* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 x (.f64 x x)))))))
(* 1/720 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/720 binary64))))
(* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64)))))
(* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 x (.f64 x x)))))))
(* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 x (.f64 x x)))))))
(* -1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/24 binary64))
(* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))
(.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64)))))
(* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))
(.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64)))))
(* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))
(.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64)))))
(* 1/720 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/720 binary64))))
(* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64)))))
(* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64)))))
(* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64)))))
(* 1/720 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/720 binary64))))
(* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64)))))
(* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64)))))
(* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64)))))
(* 1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/720 binary64))
(* 1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/720 binary64))
(* 1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/720 binary64))
(* 1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/720 binary64))
(* 1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/720 binary64))
(* 1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/720 binary64))
(* 1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/720 binary64))
(* 1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/720 binary64))
(* 1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/720 binary64))
(* 1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/720 binary64))
(* 1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/720 binary64))
(* 1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/720 binary64))

eval49.0ms (1%)

Compiler: Compiled 12437 to 966 computations (92.2% saved)

prune41.0ms (0.8%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	309	0	309
Fresh	0	0	0
Picked	0	3	3
Done	0	1	1
Total	309	4	313

Accuracy

100.0%

Counts

313 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64)))))) x)
✓	99.7%	(.f64 (.f64 x #s(literal 1/2 binary64)) x)
✓	99.9%	(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64))))))
✓	53.7%	#s(literal 0 binary64)

Compiler

Compiled 125 to 60 computations (52% saved)

regimes8.0ms (0.2%)

Counts

9 → 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 (.f64 x #s(literal 1/2 binary64)) x)
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64))))))
(.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64)))))) x)
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))))))))
(-.f64 #s(literal 1 binary64) (cos.f64 x))

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

Calls

3 calls:

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

regimes3.0ms (0.1%)

Counts

6 → 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 (.f64 x #s(literal 1/2 binary64)) x)
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64))))))

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
100.0%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes4.0ms (0.1%)

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 (.f64 x #s(literal 1/2 binary64)) x)
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64))))))

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

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
99.9%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
99.7%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

3 → 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))

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
99.7%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

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

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
53.7%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

24×	`*-commutative_binary64`
6×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	56
1	36	56

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness786.0ms (15.5%)

Rules

4308×	`-lowering-.f32`
4308×	`-lowering-.f64`
3008×	`/-lowering-/.f32`
3008×	`/-lowering-/.f64`
2334×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	29	195
1	171	174
2	1526	174
0	8646	174
0	41	140
1	109	132
2	302	132
3	796	132
4	1881	132
5	2840	132
6	3376	132
7	4413	132
8	7649	132
0	8052	132

Stop Event

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

Compiler

Compiled 147 to 77 computations (47.6% saved)

preprocess55.0ms (1.1%)

Remove: (abs x)
Compiler: Compiled 254 to 130 computations (48.8% saved)

ENA, Section 1.4, Mentioned, A

analyze4.0ms (0.1%)

sample1.8s (34.7%)

preprocess21.0ms (0.4%)

explain83.0ms (1.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify11.0ms (0.2%)

localize38.0ms (0.7%)

series1.0ms (0%)

rewrite289.0ms (5.7%)

simplify201.0ms (4%)

eval23.0ms (0.5%)

prune24.0ms (0.5%)

simplify98.0ms (1.9%)

localize159.0ms (3.1%)

series12.0ms (0.2%)

rewrite370.0ms (7.3%)

simplify209.0ms (4.1%)

eval150.0ms (3%)

prune63.0ms (1.2%)

simplify24.0ms (0.5%)

localize80.0ms (1.6%)

series2.0ms (0%)

rewrite302.0ms (5.9%)

simplify192.0ms (3.8%)

eval49.0ms (1%)

prune41.0ms (0.8%)

regimes8.0ms (0.2%)

regimes3.0ms (0.1%)

regimes4.0ms (0.1%)

regimes2.0ms (0%)

regimes2.0ms (0%)

regimes2.0ms (0%)

simplify8.0ms (0.2%)

soundness786.0ms (15.5%)

preprocess55.0ms (1.1%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	13
1	17	12
2	36	12
3	57	12
4	114	12
5	177	12
6	220	12
7	229	12
0	4	4
1	8	4
2	12	4
3	18	4
4	26	4
5	39	4
6	56	4
7	70	4
8	82	4
9	83	4
0	83	4

Iter	Nodes	Cost
0	8	13
1	17	12
2	36	12
3	57	12
4	114	12
5	177	12
6	220	12
7	229	12
0	4	4
1	8	4
2	12	4
3	18	4
4	26	4
5	39	4
6	56	4
7	70	4
8	82	4
9	83	4
0	83	4

Iter	Nodes	Cost
0	8	13
1	17	12
2	36	12
3	57	12
4	114	12
5	177	12
6	220	12
7	229	12
0	4	4
1	8	4
2	12	4
3	18	4
4	26	4
5	39	4
6	56	4
7	70	4
8	82	4
9	83	4
0	83	4