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 (40.9% of total)

...c/correct-round.rkt:119:19: 1.0ms (40.9% 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)

sample1.6s (24.2%)

Results

1.3s	8211×	1	valid
4.0ms	45×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 981.0ms

ival-cos: 340.0ms (34.7% of total)

...c/correct-round.rkt:119:19: 256.0ms (26.1% of total)

ival-sub: 140.0ms (14.3% of total)

ival-<=: 123.0ms (12.5% of total)

backward-pass: 100.0ms (10.2% of total)

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

const: 10.0ms (1% of total)

Bogosity

preprocess20.0ms (0.3%)

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)

explain84.0ms (1.2%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
130	2	(9.168059517616894e-162)	-	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
0	0	-	-	`x`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(cos.f64 x)`

Results

60.0ms	502×	1	valid
0.0ms	10×	0	valid

Compiler

Compiled 25 to 14 computations (44% saved)

Precisions

Click to see histograms. Total time spent on operations: 32.0ms

ival-cos: 18.0ms (56.5% of total)

ival-sub: 6.0ms (18.8% of total)

backward-pass: 6.0ms (18.8% of total)

const: 1.0ms (3.1% 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
▶	55.5%	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Compiler

Compiled 5 to 4 computations (20% saved)

simplify6.0ms (0.1%)

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

localize40.0ms (0.6%)

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	55.5%	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Results

33.0ms	251×	1	valid
0.0ms	5×	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 (60.3% of total)

ival-sub: 3.0ms (18.1% of total)

backward-pass: 3.0ms (18.1% 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)

rewrite337.0ms (5%)

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	143	6
3	1225	6
0	9463	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 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))) (.f64 (+.f64 #s(literal 1 binary64) (cos.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 (+.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 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (pow.f64 (cos.f64 x) #s(literal 3 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))

simplify212.0ms (3.1%)

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	116
2	303	116
3	800	116
4	1851	116
5	2818	116
6	3365	116
7	4402	116
8	7643	116
0	8048	116

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 (.f64 x 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 (.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 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 (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 (.f64 x 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 (.f64 x 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)

eval24.0ms (0.4%)

Compiler: Compiled 6196 to 516 computations (91.7% saved)

prune33.0ms (0.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	173	6	179
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	174	6	180

Accuracy

100.0%

Counts

180 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	55.1%	(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64))))
▶	53.2%	(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
	100.0%	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64))))
▶	100.0%	(.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)))))))
▶	99.8%	(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))))
▶	98.6%	(.f64 #s(literal 1/2 binary64) (.f64 x x))

Compiler

Compiled 116 to 78 computations (32.8% saved)

simplify210.0ms (3.1%)

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

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

Rules

2126×	`+-lowering-+.f64`
2126×	`+-lowering-+.f32`
1782×	`--lowering--.f32`
1782×	`--lowering--.f64`
1696×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	124
1	67	112
2	215	112
3	501	112
4	1113	112
5	3208	112
6	5082	112
7	7273	112
0	8261	112

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize228.0ms (3.4%)

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal -1/24 binary64))))
✓	accuracy	100.0%	(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))))
✓	accuracy	99.7%	(.f64 (.f64 x x) #s(literal -1/24 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64)))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 (.f64 x x) #s(literal -1/2 binary64))
✓	accuracy	55.5%	(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64))))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 #s(literal 1/2 binary64) (.f64 x x))
✓	accuracy	100.0%	(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
✓	accuracy	100.0%	(.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)))))))
✓	accuracy	100.0%	(+.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))))

Results

186.0ms	251×	1	valid
1.0ms	5×	0	valid

Compiler

Compiled 156 to 23 computations (85.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 114.0ms

ival-mult: 53.0ms (46.4% of total)

ival-add: 28.0ms (24.5% of total)

...c/correct-round.rkt:119:19: 14.0ms (12.3% of total)

backward-pass: 13.0ms (11.4% of total)

ival-sub: 5.0ms (4.4% of total)

const: 1.0ms (0.9% of total)

series12.0ms (0.2%)

Counts

16 → 180

Calls

Call 1

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

Calls

45 calls:

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

rewrite380.0ms (5.6%)

Algorithm

1×	batch-egg-rewrite

Rules

4184×	`-lowering-.f32`
4184×	`-lowering-.f64`
3792×	`/-lowering-/.f32`
3792×	`/-lowering-/.f64`
2028×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	107
1	130	94
2	1129	94
0	8339	94

Stop Event

1×	iter limit
1×	node limit

Counts

16 → 413

Calls

Call 1

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

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

simplify218.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

2700×	`-lowering-.f32`
2700×	`-lowering-.f64`
1566×	`+-lowering-+.f64`
1566×	`+-lowering-+.f32`
1242×	`fnmadd-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	66	1291
1	173	1054
2	465	1054
3	1395	1032
4	4380	1032
0	8465	1032

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

Calls

Call 1

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

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 (.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 x (.f64 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 x (.f64 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 #s(literal -1/2 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (+.f64 #s(literal 1/720 binary64) (/.f64 #s(literal -1/24 binary64) (.f64 x x))) (/.f64 #s(literal -1/2 binary64) (.f64 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 #s(literal -1/2 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (+.f64 #s(literal 1/720 binary64) (/.f64 #s(literal -1/24 binary64) (.f64 x x))) (/.f64 #s(literal -1/2 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 (*.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 x (*.f64 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 x (*.f64 x #s(literal 1/720 binary64))))))))
(* 1/720 (pow x 5))
(.f64 x (.f64 x (.f64 #s(literal 1/720 binary64) (.f64 x (*.f64 x x)))))
(* (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 (.f64 x (.f64 x (.f64 x 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 #s(literal -1/2 binary64) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 x (.f64 x (*.f64 x 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 #s(literal -1/2 binary64) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 x (.f64 x (*.f64 x x))) x))
(* 1/720 (pow x 5))
(.f64 x (.f64 x (.f64 #s(literal 1/720 binary64) (.f64 x (*.f64 x x)))))
(* -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 (.f64 x (.f64 x (.f64 x 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 #s(literal -1/2 binary64) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 x (.f64 x (*.f64 x 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 #s(literal -1/2 binary64) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 x (.f64 x (*.f64 x 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 x (.f64 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 x (.f64 x #s(literal 1/720 binary64)))))))
(* 1/720 (pow x 4))
(.f64 x (.f64 #s(literal 1/720 binary64) (.f64 x (.f64 x x))))
(* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 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 #s(literal 1/720 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (.f64 x 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 #s(literal 1/720 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (.f64 x x))))) (*.f64 x x))))
(* 1/720 (pow x 4))
(.f64 x (.f64 #s(literal 1/720 binary64) (.f64 x (.f64 x x))))
(* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 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 #s(literal 1/720 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (.f64 x 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 #s(literal 1/720 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (.f64 x 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 x (.f64 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 x (.f64 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 x (.f64 x #s(literal 1/720 binary64))))))
(* 1/720 (pow x 4))
(.f64 x (.f64 #s(literal 1/720 binary64) (.f64 x (.f64 x x))))
(* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 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 x (.f64 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 x (.f64 x #s(literal 1/720 binary64))))))
(* 1/720 (pow x 4))
(.f64 x (.f64 #s(literal 1/720 binary64) (.f64 x (.f64 x x))))
(* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 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 x (.f64 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 x (.f64 x #s(literal 1/720 binary64))))))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(+ 1 (* -1/2 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(+ 1 (* -1/2 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* -1/2 (pow x 2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))))
(* -1/24 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -1/24 binary64))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))))
(* -1/24 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -1/24 binary64))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))))
(* 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 (* -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 (* -1/24 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal -1/24 binary64))))
(* -1/24 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal -1/24 binary64)))
(* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal -1/24 binary64))))
(* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal -1/24 binary64))))
(* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal -1/24 binary64))))
(* -1/24 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal -1/24 binary64)))
(* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal -1/24 binary64))))
(* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal -1/24 binary64))))
(* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal -1/24 binary64))))
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 (* -1/24 (pow x 2)))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))
(+ 1/2 (* -1/24 (pow x 2)))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))
(* -1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/24 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))
(* -1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/24 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))
(* -1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/24 binary64))
(* -1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/24 binary64))
(* -1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/24 binary64))
(* -1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/24 binary64))
(* -1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/24 binary64))
(* -1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/24 binary64))
(* -1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/24 binary64))
(* -1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/24 binary64))
(* -1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/24 binary64))
(* -1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/24 binary64))
(* -1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/24 binary64))
(* -1/24 (pow x 2))
(.f64 (.f64 x 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)))
-1/24
#s(literal -1/24 binary64)
(- (* 1/720 (pow x 2)) 1/24)
(+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64))))
(- (* 1/720 (pow x 2)) 1/24)
(+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64))))
(- (* 1/720 (pow x 2)) 1/24)
(+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64))))
(* 1/720 (pow x 2))
(.f64 x (.f64 x #s(literal 1/720 binary64)))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64))))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64))))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64))))
(* 1/720 (pow x 2))
(.f64 x (.f64 x #s(literal 1/720 binary64)))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64))))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64))))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64))))

eval87.0ms (1.3%)

Compiler: Compiled 18067 to 1712 computations (90.5% saved)

prune60.0ms (0.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	660	5	665
Fresh	1	0	1
Picked	3	2	5
Done	0	0	0
Total	664	7	671

Accuracy

100.0%

Counts

671 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	55.1%	(-.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))
✓	55.1%	(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64))))
▶	100.0%	(.f64 (+.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)))))) (.f64 x x))
▶	98.6%	(.f64 (.f64 x #s(literal 1/2 binary64)) x)
▶	99.8%	(.f64 x (.f64 x (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))))))
✓	99.8%	(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))))
▶	53.2%	#s(literal 0 binary64)

Compiler

Compiled 126 to 85 computations (32.5% saved)

simplify186.0ms (2.7%)

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

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

Rules

1792×	`+-lowering-+.f64`
1792×	`+-lowering-+.f32`
1512×	`--lowering--.f32`
1512×	`--lowering--.f64`
1290×	`-lowering-.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	134
1	66	121
2	178	121
3	422	121
4	905	121
5	3013	121
6	5937	121
0	8171	121

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize222.0ms (3.3%)

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 x (.f64 x (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))))))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64))))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))))
✓	accuracy	99.7%	(.f64 (.f64 x x) #s(literal -1/24 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(.f64 x (.f64 x #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(*.f64 x #s(literal 1/2 binary64))
✓	accuracy	55.5%	(-.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))
✓	accuracy	100.0%	(.f64 (.f64 x #s(literal 1/2 binary64)) x)
✓	accuracy	100.0%	(*.f64 x #s(literal 1/2 binary64))
✓	accuracy	100.0%	(.f64 (+.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)))))) (.f64 x x))
✓	accuracy	99.8%	(.f64 (.f64 x x) #s(literal 1/720 binary64))
✓	accuracy	99.8%	(.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64)))))
✓	accuracy	99.4%	(.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (*.f64 x x) #s(literal 1/720 binary64))))

Results

173.0ms	252×	1	valid
1.0ms	4×	0	valid

Compiler

Compiled 176 to 25 computations (85.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 92.0ms

ival-mult: 42.0ms (45.8% of total)

...c/correct-round.rkt:119:19: 16.0ms (17.4% of total)

backward-pass: 13.0ms (14.2% of total)

ival-add: 10.0ms (10.9% of total)

ival-div: 7.0ms (7.6% of total)

ival-sub: 3.0ms (3.3% of total)

const: 1.0ms (1.1% of total)

series5.0ms (0.1%)

Counts

15 → 180

Calls

Call 1

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

Outputs
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* 1/720 (pow x 6))>
#<alt (* (pow x 6) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* 1/720 (pow x 6))>
#<alt (* (pow x 6) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))>
#<alt 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 (* -1/24 x)>
#<alt (* x (- (* 1/720 (pow x 2)) 1/24))>
#<alt (* x (- (* 1/720 (pow x 2)) 1/24))>
#<alt (* x (- (* 1/720 (pow x 2)) 1/24))>
#<alt (* 1/720 (pow x 3))>
#<alt (* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* 1/720 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720)))>
#<alt (* -1 (* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720)))>
#<alt (* -1 (* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720)))>
#<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 (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt 1>
#<alt (+ 1 (* 1/2 (pow x 2)))>
#<alt (+ 1 (* 1/2 (pow x 2)))>
#<alt (+ 1 (* 1/2 (pow x 2)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 (pow x 2))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 (pow x 2))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (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 2>
#<alt (+ 2 (* 1/6 (pow x 2)))>
#<alt (+ 2 (* (pow x 2) (+ 1/6 (* 1/72 (pow x 2)))))>
#<alt (+ 2 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/72 (* 1/864 (pow x 2)))))))>
#<alt (/ -24 (pow x 2))>
#<alt (* -1 (/ (+ 24 (* 288 (/ 1 (pow x 2)))) (pow x 2)))>
#<alt (/ (- (* -1 (/ (+ 288 (* 3456 (/ 1 (pow x 2)))) (pow x 2))) 24) (pow x 2))>
#<alt (/ (- (* -1 (/ (+ 3456 (* 41472 (/ 1 (pow x 2)))) (pow x 4))) (+ 24 (* 288 (/ 1 (pow x 2))))) (pow x 2))>
#<alt (/ -24 (pow x 2))>
#<alt (* -1 (/ (+ 24 (* 288 (/ 1 (pow x 2)))) (pow x 2)))>
#<alt (/ (- (* -1 (/ (+ 288 (* 3456 (/ 1 (pow x 2)))) (pow x 2))) 24) (pow x 2))>
#<alt (/ (- (* -1 (/ (+ 3456 (* 41472 (/ 1 (pow x 2)))) (pow x 4))) (+ 24 (* 288 (/ 1 (pow x 2))))) (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))>
#<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))>

Calls

45 calls:

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

rewrite380.0ms (5.6%)

Algorithm

1×	batch-egg-rewrite

Rules

4608×	`-lowering-.f32`
4608×	`-lowering-.f64`
3888×	`/-lowering-/.f32`
3888×	`/-lowering-/.f64`
1710×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	23	105
1	142	92
2	1132	91
0	8323	91

Stop Event

1×	iter limit
1×	node limit

Counts

15 → 545

Calls

Call 1

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

Outputs
(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64))))))))
(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64)))))) (.f64 x x)))
(+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64))))))) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(+.f64 (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64)))))) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (.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 x (*.f64 x #s(literal 1/720 binary64))))))))
(fma.f64 #s(literal 1/2 binary64) (.f64 x x) (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64)))))) (*.f64 x x)))
(fma.f64 x (.f64 #s(literal 1/2 binary64) x) (.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 x (*.f64 x #s(literal 1/720 binary64))))))))
(fma.f64 x (.f64 #s(literal 1/2 binary64) x) (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64)))))) (*.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 x (*.f64 x #s(literal 1/720 binary64))))))))
(fma.f64 (.f64 x x) #s(literal 1/2 binary64) (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64)))))) (*.f64 x x)))
(fma.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64)))))) (.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(fma.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64)))))) (.f64 x x) (.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 x (*.f64 x #s(literal 1/720 binary64))))))))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64)))))) (*.f64 x x)))
(fma.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x #s(literal 1/720 binary64))))))))
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(-.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x)))) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/13824 binary64) (.f64 x (.f64 x x)))))) (/.f64 (.f64 #s(literal -1/48 binary64) (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/13824 binary64) (.f64 x (.f64 x x)))))))
(neg.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64))))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64)))))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64))))) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (+.f64 (neg.f64 (.f64 x (.f64 x #s(literal -1/24 binary64)))) #s(literal -1/2 binary64)))
(/.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64))))) #s(literal -1 binary64))
(/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/13824 binary64) (.f64 x (*.f64 x x))))))
(/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x))) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x)))))
(/.f64 (neg.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))) (neg.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/13824 binary64) (.f64 x (*.f64 x x)))))))
(/.f64 (neg.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x)))) (neg.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x))))))
(/.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x))))) (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x)))) (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64))))))
(/.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) #s(literal 1/2 binary64))) (.f64 (.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) #s(literal 1/2 binary64))) (.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))))) (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/13824 binary64) (.f64 x (.f64 x x))))) (+.f64 #s(literal 1/16 binary64) (-.f64 (.f64 (.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) #s(literal 1/2 binary64))) (.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))) (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))))))
(/.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/16 binary64) (.f64 (.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) #s(literal 1/2 binary64))) (.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))))) (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/13824 binary64) (.f64 x (.f64 x x))))) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))))
(/.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/13824 binary64) (.f64 x (.f64 x x)))))) (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x)))) (+.f64 #s(literal 1/4 binary64) (+.f64 (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 #s(literal -1/48 binary64) (.f64 x x))))))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64))))) #s(literal 1 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64)))) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64)))) (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal -1/24 binary64))))) #s(literal -1/2 binary64))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal -1/24 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal -1/24 binary64))))) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal -1/24 binary64))))))
(.f64 #s(literal -1 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal -1/24 binary64))))) #s(literal 1 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal -1/24 binary64))))) #s(literal -1 binary64))
(.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/13824 binary64) (.f64 x (.f64 x x)))))))
(.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (*.f64 x x))))))
(.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal -1/24 binary64)))) #s(literal -1/2 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/13824 binary64) (.f64 x (.f64 x x)))))) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/13824 binary64) (.f64 x (.f64 x x)))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) #s(literal 1/2 binary64))))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x)))) #s(literal -1 binary64)))
(.f64 (pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64)))) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal -1/24 binary64)))) #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64)))) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal -1/24 binary64)))) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal -1/13824 binary64) (.f64 x (.f64 x x)))))) #s(literal 1 binary64)) (pow.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (.f64 x x))))) #s(literal 1 binary64)) (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))) #s(literal 1 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)
(.f64 x (.f64 x #s(literal -1/24 binary64)))
(.f64 #s(literal -1/24 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal -1/24 binary64))
(.f64 (.f64 x #s(literal -1/24 binary64)) x)

simplify257.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

2478×	`-lowering-.f32`
2478×	`-lowering-.f64`
1980×	`fma-lowering-fma.f32`
1980×	`fma-lowering-fma.f64`
1592×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	95	1344
1	257	1118
2	748	1110
3	2139	1110
4	5803	1110
0	8082	1110

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

Calls

Call 1

Inputs
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* 1/720 (pow x 6))
(* (pow x 6) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* 1/720 (pow x 6))
(* (pow x 6) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
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)))))
(* -1/24 x)
(* x (- (* 1/720 (pow x 2)) 1/24))
(* x (- (* 1/720 (pow x 2)) 1/24))
(* x (- (* 1/720 (pow x 2)) 1/24))
(* 1/720 (pow x 3))
(* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* 1/720 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720)))
(* -1 (* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720)))
(* -1 (* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720)))
(* 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))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
1
(+ 1 (* 1/2 (pow x 2)))
(+ 1 (* 1/2 (pow x 2)))
(+ 1 (* 1/2 (pow x 2)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/2 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/2 (/ 1 (pow x 2))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/2 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1/2 (/ 1 (pow x 2))))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* (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))
2
(+ 2 (* 1/6 (pow x 2)))
(+ 2 (* (pow x 2) (+ 1/6 (* 1/72 (pow x 2)))))
(+ 2 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/72 (* 1/864 (pow x 2)))))))
(/ -24 (pow x 2))
(* -1 (/ (+ 24 (* 288 (/ 1 (pow x 2)))) (pow x 2)))
(/ (- (* -1 (/ (+ 288 (* 3456 (/ 1 (pow x 2)))) (pow x 2))) 24) (pow x 2))
(/ (- (* -1 (/ (+ 3456 (* 41472 (/ 1 (pow x 2)))) (pow x 4))) (+ 24 (* 288 (/ 1 (pow x 2))))) (pow x 2))
(/ -24 (pow x 2))
(* -1 (/ (+ 24 (* 288 (/ 1 (pow x 2)))) (pow x 2)))
(/ (- (* -1 (/ (+ 288 (* 3456 (/ 1 (pow x 2)))) (pow x 2))) 24) (pow x 2))
(/ (- (* -1 (/ (+ 3456 (* 41472 (/ 1 (pow x 2)))) (pow x 4))) (+ 24 (* 288 (/ 1 (pow x 2))))) (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))
(* -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))

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

eval91.0ms (1.3%)

Compiler: Compiled 20173 to 1998 computations (90.1% saved)

prune70.0ms (1%)

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	737	2	739
Fresh	0	0	0
Picked	1	4	5
Done	0	2	2
Total	738	8	746

Accuracy

100.0%

Counts

746 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(/.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal -1/24 binary64))))))
✓	55.1%	(-.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))
✓	55.1%	(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64))))
✓	100.0%	(.f64 (+.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)))))) (.f64 x x))
▶	25.0%	(.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 #s(literal -1/24 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))
✓	98.6%	(.f64 (.f64 x #s(literal 1/2 binary64)) x)
✓	99.8%	(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))))
✓	53.2%	#s(literal 0 binary64)

Compiler

Compiled 88 to 58 computations (34.1% saved)

simplify140.0ms (2.1%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64))))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64)))))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	128	(/.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (+.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 x (.f64 x x))
✓	cost-diff	0	(.f64 x (.f64 x (*.f64 x x)))
✓	cost-diff	256	(.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 #s(literal -1/24 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))

Rules

1822×	`fnmadd-define`
1798×	`sum3-define`
1380×	`-lowering-.f32`
1380×	`-lowering-.f64`
1204×	`/-lowering-/.f32`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	16	73
1	40	65
2	100	65
3	288	65
4	771	65
5	1905	61
6	3592	61
7	5857	61
0	8079	61

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize101.0ms (1.5%)

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64)))))
✓	accuracy	99.9%	(/.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (+.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	99.9%	(.f64 x (.f64 x (*.f64 x x)))
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	99.8%	(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
✓	accuracy	26.0%	(.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 #s(literal -1/24 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))

Results

77.0ms

256×

valid

Compiler

Compiled 91 to 17 computations (81.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 35.0ms

ival-mult: 22.0ms (63.1% of total)

ival-div: 5.0ms (14.3% of total)

...c/correct-round.rkt:119:19: 4.0ms (11.5% of total)

ival-sub: 1.0ms (2.9% of total)

ival-add: 1.0ms (2.9% of total)

const: 1.0ms (2.9% of total)

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

series6.0ms (0.1%)

Counts

10 → 120

Calls

Call 1

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

Outputs
#<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 (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<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 2>
#<alt (+ 2 (* 1/6 (pow x 2)))>
#<alt (+ 2 (* (pow x 2) (+ 1/6 (* 1/72 (pow x 2)))))>
#<alt (+ 2 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/72 (* 1/864 (pow x 2)))))))>
#<alt (/ -24 (pow x 2))>
#<alt (* -1 (/ (+ 24 (* 288 (/ 1 (pow x 2)))) (pow x 2)))>
#<alt (/ (- (* -1 (/ (+ 288 (* 3456 (/ 1 (pow x 2)))) (pow x 2))) 24) (pow x 2))>
#<alt (/ (- (* -1 (/ (+ 3456 (* 41472 (/ 1 (pow x 2)))) (pow x 4))) (+ 24 (* 288 (/ 1 (pow x 2))))) (pow x 2))>
#<alt (/ -24 (pow x 2))>
#<alt (* -1 (/ (+ 24 (* 288 (/ 1 (pow x 2)))) (pow x 2)))>
#<alt (/ (- (* -1 (/ (+ 288 (* 3456 (/ 1 (pow x 2)))) (pow x 2))) 24) (pow x 2))>
#<alt (/ (- (* -1 (/ (+ 3456 (* 41472 (/ 1 (pow x 2)))) (pow x 4))) (+ 24 (* 288 (/ 1 (pow x 2))))) (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 (/ -1/2 (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 (* -1/24 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 (* -1/24 (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))>

Calls

30 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(* (* x (* x (* x x))) (- -1/24 (/ -1/2 (* x x))))
1.0ms	x	@	inf	(* (* x (* x (* x x))) (- -1/24 (/ -1/2 (* x x))))
0.0ms	x	@	0	(* x (* x x))
0.0ms	x	@	-inf	(* x (* x x))
0.0ms	x	@	-inf	(* x -1/24)

rewrite286.0ms (4.2%)

Algorithm

1×	batch-egg-rewrite

Rules

4250×	`-lowering-.f32`
4250×	`-lowering-.f64`
3026×	`/-lowering-/.f32`
3026×	`/-lowering-/.f64`
1026×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	56
1	91	48
2	657	48
3	7290	48
0	8100	48

Stop Event

1×	iter limit
1×	node limit

Counts

10 → 393

Calls

Call 1

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

Outputs
(+.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 (.f64 x x) #s(literal 1/2 binary64))) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal -1/24 binary64)))))
(+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal -1/24 binary64)))) (/.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 (.f64 x x) #s(literal 1/2 binary64))))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/24 binary64) (/.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 (*.f64 x x) #s(literal 1/2 binary64))))
(fma.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (.f64 x x))) (/.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 (*.f64 x x) #s(literal 1/2 binary64))))
(/.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x)))))
(/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (+.f64 #s(literal -1/24 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (.f64 x (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/576 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x (.f64 x (.f64 x x)))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/576 binary64) (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal -1/24 binary64)))) (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal -1/13824 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))))))
(/.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(/.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/576 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x (.f64 x (.f64 x x))))))) (-.f64 #s(literal -1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))))
(/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal -1/13824 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (+.f64 #s(literal 1/576 binary64) (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal -1/24 binary64)))))
(/.f64 (neg.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/576 binary64) (/.f64 #s(literal -1/4 binary64) (.f64 x (.f64 x (.f64 x x)))))))) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1/24 binary64)))
(/.f64 (neg.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal -1/13824 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/576 binary64) (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal -1/24 binary64))))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal -1/24 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 (.f64 x x) #s(literal 1/2 binary64))) #s(literal 3 binary64))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal -1/24 binary64)))) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal -1/24 binary64))))) (-.f64 (.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 (.f64 x x) #s(literal 1/2 binary64))) (/.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 (.f64 x x) #s(literal 1/2 binary64)))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal -1/24 binary64)))) (/.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 (*.f64 x x) #s(literal 1/2 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal -1/24 binary64)))) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal -1/24 binary64))))) (.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 (.f64 x x) #s(literal 1/2 binary64))) (/.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 (.f64 x x) #s(literal 1/2 binary64))))) (-.f64 (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal -1/24 binary64)))) (/.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 (.f64 x x) #s(literal 1/2 binary64)))))
(/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/13824 binary64) (/.f64 (/.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/576 binary64) (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1/24 binary64))))))
(/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal -1/576 binary64) (/.f64 (/.f64 #s(literal 1/4 binary64) x) (.f64 x (.f64 x x))))) (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 1/24 binary64)))
(/.f64 (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))))) (-.f64 #s(literal 0 binary64) (*.f64 x x))) #s(literal -1 binary64))
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(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64)))) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1/576 binary64))))
(.f64 (+.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/576 binary64))) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (*.f64 x #s(literal -1/24 binary64))) #s(literal -1/2 binary64))))
(.f64 (pow.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64))))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 #s(literal -1/24 binary64) (+.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) #s(literal -1/2 binary64)))))) #s(literal 1 binary64)))
(.f64 (pow.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/576 binary64))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))) #s(literal 1 binary64)))
(.f64 (pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64)))) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal -1/24 binary64)))) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64)))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 #s(literal -1/24 binary64) (+.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) #s(literal -1/2 binary64)))))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/576 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))))
(.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64)))) #s(literal 1/2 binary64)) (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal -1/24 binary64)))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64))))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal -1/24 binary64))))) #s(literal -1/2 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64)))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 #s(literal -1/24 binary64) (+.f64 (.f64 x (*.f64 x #s(literal -1/24 binary64))) #s(literal -1/2 binary64)))))))
(.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/576 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64)))))
(.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/576 binary64))) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/576 binary64)))) (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal -1/24 binary64)))))
(.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64))))) (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 x x) (.f64 #s(literal -1/24 binary64) (+.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) #s(literal -1/2 binary64)))) (.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/576 binary64))) (.f64 (+.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) #s(literal -1/2 binary64)) (+.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) #s(literal -1/2 binary64))))))) (+.f64 #s(literal 1/16 binary64) (.f64 (.f64 (.f64 x x) (.f64 #s(literal -1/24 binary64) (+.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) #s(literal -1/2 binary64)))) (-.f64 (.f64 (.f64 x x) (.f64 #s(literal -1/24 binary64) (+.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) #s(literal -1/2 binary64)))) #s(literal 1/4 binary64)))))
(.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64))))) (-.f64 #s(literal 1/16 binary64) (.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/576 binary64))) (.f64 (+.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) #s(literal -1/2 binary64)) (+.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) #s(literal -1/2 binary64)))))) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) (+.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) #s(literal -1/2 binary64)))))
(.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/576 binary64))) (-.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64)))))) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x #s(literal -1/24 binary64)) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64))))))))
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) #s(literal -1/2 binary64))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(neg.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(/.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -2 binary64))
(/.f64 (/.f64 #s(literal -1/2 binary64) x) x)
(/.f64 (/.f64 #s(literal -1/2 binary64) x) (neg.f64 (-.f64 #s(literal 0 binary64) x)))
(/.f64 (/.f64 #s(literal 1/2 binary64) x) (-.f64 #s(literal 0 binary64) x))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x #s(literal -1/2 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) x))
(pow.f64 (/.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal -1 binary64))
(.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
(.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x)))
(.f64 #s(literal 1/2 binary64) (.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal 1 binary64)))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1/2 binary64))
(.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal -1 binary64))
(*.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 #s(literal -1/2 binary64) x) (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1/2 binary64) x))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(literal 1/2 binary64))
(.f64 (pow.f64 (/.f64 (.f64 x x) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)))
(*.f64 x #s(literal -1/24 binary64))
(*.f64 #s(literal -1/24 binary64) x)
(/.f64 #s(literal -1/24 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) #s(literal 1 binary64))
(/.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal -1 binary64))
(.f64 x (.f64 x #s(literal -1/24 binary64)))
(.f64 (.f64 x x) #s(literal -1/24 binary64))
(.f64 #s(literal -1/24 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal -1/24 binary64)) x)
(.f64 (.f64 x (*.f64 x #s(literal -1/24 binary64))) #s(literal 1 binary64))

simplify200.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

1888×	`-lowering-.f32`
1888×	`-lowering-.f64`
1308×	`fma-lowering-fma.f32`
1308×	`fma-lowering-fma.f64`
1228×	`fnmadd-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	62	724
1	154	582
2	440	574
3	1103	574
4	2348	574
5	5190	574
0	8014	574

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

Inputs
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* -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))
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(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))
2
(+ 2 (* 1/6 (pow x 2)))
(+ 2 (* (pow x 2) (+ 1/6 (* 1/72 (pow x 2)))))
(+ 2 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/72 (* 1/864 (pow x 2)))))))
(/ -24 (pow x 2))
(* -1 (/ (+ 24 (* 288 (/ 1 (pow x 2)))) (pow x 2)))
(/ (- (* -1 (/ (+ 288 (* 3456 (/ 1 (pow x 2)))) (pow x 2))) 24) (pow x 2))
(/ (- (* -1 (/ (+ 3456 (* 41472 (/ 1 (pow x 2)))) (pow x 4))) (+ 24 (* 288 (/ 1 (pow x 2))))) (pow x 2))
(/ -24 (pow x 2))
(* -1 (/ (+ 24 (* 288 (/ 1 (pow x 2)))) (pow x 2)))
(/ (- (* -1 (/ (+ 288 (* 3456 (/ 1 (pow x 2)))) (pow x 2))) 24) (pow x 2))
(/ (- (* -1 (/ (+ 3456 (* 41472 (/ 1 (pow x 2)))) (pow x 4))) (+ 24 (* 288 (/ 1 (pow x 2))))) (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))
(/ -1/2 (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))
(* -1/24 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)
(* -1/24 (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))

Outputs
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64))))
(* (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 (* -1/24 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64))))
(* -1/24 (pow x 4))
(.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (.f64 x x))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64))))
(* -1/24 (pow x 4))
(.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (.f64 x x))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64))))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x 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 (* -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 (* -1/24 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64))))
(* -1/24 (pow x 4))
(.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (.f64 x x))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64))))
(* -1/24 (pow x 4))
(.f64 #s(literal -1/24 binary64) (.f64 x (.f64 x (.f64 x x))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64))))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64))))
2
#s(literal 2 binary64)
(+ 2 (* 1/6 (pow x 2)))
(+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))
(+ 2 (* (pow x 2) (+ 1/6 (* 1/72 (pow x 2)))))
(+.f64 #s(literal 2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) #s(literal 1/72 binary64))))))
(+ 2 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/72 (* 1/864 (pow x 2)))))))
(+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/72 binary64) (.f64 (.f64 x x) #s(literal 1/864 binary64)))))))
(/ -24 (pow x 2))
(/.f64 #s(literal -24 binary64) (*.f64 x x))
(* -1 (/ (+ 24 (* 288 (/ 1 (pow x 2)))) (pow x 2)))
(/.f64 (+.f64 #s(literal -24 binary64) (/.f64 #s(literal -288 binary64) (.f64 x x))) (.f64 x x))
(/ (- (* -1 (/ (+ 288 (* 3456 (/ 1 (pow x 2)))) (pow x 2))) 24) (pow x 2))
(/.f64 (+.f64 #s(literal -24 binary64) (/.f64 (-.f64 #s(literal -288 binary64) (/.f64 #s(literal 3456 binary64) (.f64 x x))) (.f64 x x))) (*.f64 x x))
(/ (- (* -1 (/ (+ 3456 (* 41472 (/ 1 (pow x 2)))) (pow x 4))) (+ 24 (* 288 (/ 1 (pow x 2))))) (pow x 2))
(/.f64 (+.f64 #s(literal -24 binary64) (.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 (/.f64 (+.f64 #s(literal 3456 binary64) (/.f64 #s(literal 41472 binary64) (.f64 x x))) (.f64 x x)) #s(literal 288 binary64)))) (*.f64 x x))
(/ -24 (pow x 2))
(/.f64 #s(literal -24 binary64) (*.f64 x x))
(* -1 (/ (+ 24 (* 288 (/ 1 (pow x 2)))) (pow x 2)))
(/.f64 (+.f64 #s(literal -24 binary64) (/.f64 #s(literal -288 binary64) (.f64 x x))) (.f64 x x))
(/ (- (* -1 (/ (+ 288 (* 3456 (/ 1 (pow x 2)))) (pow x 2))) 24) (pow x 2))
(/.f64 (+.f64 #s(literal -24 binary64) (/.f64 (-.f64 #s(literal -288 binary64) (/.f64 #s(literal 3456 binary64) (.f64 x x))) (.f64 x x))) (*.f64 x x))
(/ (- (* -1 (/ (+ 3456 (* 41472 (/ 1 (pow x 2)))) (pow x 4))) (+ 24 (* 288 (/ 1 (pow x 2))))) (pow x 2))
(/.f64 (+.f64 #s(literal -24 binary64) (.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 (/.f64 (+.f64 #s(literal 3456 binary64) (/.f64 #s(literal 41472 binary64) (.f64 x x))) (.f64 x x)) #s(literal 288 binary64)))) (*.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 (* -1/24 (pow x 2)))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))
(+ 1/2 (* -1/24 (pow x 2)))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))
(* -1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/24 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))
(* -1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/24 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))
(/ -1/2 (pow x 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/ -1/2 (pow x 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/ -1/2 (pow x 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/ -1/2 (pow x 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/ -1/2 (pow x 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/ -1/2 (pow x 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/ -1/2 (pow x 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/ -1/2 (pow x 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/ -1/2 (pow x 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/ -1/2 (pow x 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/ -1/2 (pow x 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/ -1/2 (pow x 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(* -1/24 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))
(* -1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/24 binary64))
(* -1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/24 binary64))
(* -1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/24 binary64))
(* -1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/24 binary64))
(* -1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/24 binary64))
(* -1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/24 binary64))
(* -1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/24 binary64))
(* -1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/24 binary64))
(* -1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/24 binary64))
(* -1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/24 binary64))
(* -1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/24 binary64))
(* -1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/24 binary64))

eval84.0ms (1.2%)

Compiler: Compiled 13324 to 1384 computations (89.6% saved)

prune60.0ms (0.9%)

Pruning

8 alts after pruning (0 fresh and 8 done)

	Pruned	Kept	Total
New	579	0	579
Fresh	0	0	0
Picked	0	2	2
Done	0	6	6
Total	579	8	587

Accuracy

100.0%

Counts

587 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.7%	(/.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal -1/24 binary64))))))
✓	55.1%	(-.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))
✓	55.1%	(-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64))))
✓	100.0%	(.f64 (+.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)))))) (.f64 x x))
✓	25.0%	(.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 #s(literal -1/24 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))
✓	98.6%	(.f64 (.f64 x #s(literal 1/2 binary64)) x)
✓	99.8%	(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))))
✓	53.2%	#s(literal 0 binary64)

Compiler

Compiled 220 to 111 computations (49.5% saved)

regimes14.0ms (0.2%)

Counts

14 → 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 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64))))
(-.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))))
(/.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal -1/24 binary64))))))
(.f64 x (.f64 x (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))))))
(.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 #s(literal -1/24 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 x 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 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64)))))) (.f64 x x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64))))

Outputs
(.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)))))))

Calls

3 calls:

5.0ms	x
4.0ms	(cos.f64 x)
3.0ms	(-.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)

regimes4.0ms (0.1%)

Counts

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

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

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
99.8%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0%)

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

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

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
98.6%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes4.0ms (0.1%)

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:

3.0ms

Results

Accuracy	Segments	Branch
98.6%	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:

2.0ms

Results

Accuracy	Segments	Branch
53.2%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

20×	`*-commutative_binary64`
6×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	39
1	32	39

Stop Event

1×

saturated

Calls

Call 1

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

soundness1.0s (15.2%)

Rules

4184×	`-lowering-.f32`
4184×	`-lowering-.f64`
3792×	`/-lowering-/.f32`
3792×	`/-lowering-/.f64`
2028×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	107
1	130	94
2	1129	94
0	8339	94
0	41	140
1	109	116
2	303	116
3	800	116
4	1851	116
5	2818	116
6	3365	116
7	4402	116
8	7643	116
0	8048	116

Stop Event

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

Compiler

Compiled 94 to 55 computations (41.5% saved)

preprocess39.0ms (0.6%)

Remove: (abs x)
Compiler: Compiled 184 to 104 computations (43.5% saved)

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

analyze4.0ms (0.1%)

sample1.6s (24.2%)

preprocess20.0ms (0.3%)

explain84.0ms (1.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify6.0ms (0.1%)

localize40.0ms (0.6%)

series1.0ms (0%)

rewrite337.0ms (5%)

simplify212.0ms (3.1%)

eval24.0ms (0.4%)

prune33.0ms (0.5%)

simplify210.0ms (3.1%)

localize228.0ms (3.4%)

series12.0ms (0.2%)

rewrite380.0ms (5.6%)

simplify218.0ms (3.2%)

eval87.0ms (1.3%)

prune60.0ms (0.9%)

simplify186.0ms (2.7%)

localize222.0ms (3.3%)

series5.0ms (0.1%)

rewrite380.0ms (5.6%)

simplify257.0ms (3.8%)

eval91.0ms (1.3%)

prune70.0ms (1%)

simplify140.0ms (2.1%)

localize101.0ms (1.5%)

series6.0ms (0.1%)

rewrite286.0ms (4.2%)

simplify200.0ms (2.9%)

eval84.0ms (1.2%)

prune60.0ms (0.9%)

regimes14.0ms (0.2%)

regimes4.0ms (0.1%)

regimes3.0ms (0%)

regimes4.0ms (0.1%)

regimes2.0ms (0%)

simplify8.0ms (0.1%)

soundness1.0s (15.2%)

preprocess39.0ms (0.6%)

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