Metrics for ENA, Section 1.4, Mentioned, A

analyze7.0ms (0.2%)

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 (40.1% of total)

...c/correct-round.rkt:119:19: 1.0ms (40.1% 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)

sample1.9s (43.6%)

Results

1.6s	8199×	1	valid
5.0ms	57×	0	valid

Precisions

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

ival-cos: 379.0ms (36.8% of total)

...c/correct-round.rkt:119:19: 281.0ms (27.3% of total)

backward-pass: 140.0ms (13.6% of total)

ival-sub: 116.0ms (11.3% of total)

ival-<=: 90.0ms (8.7% of total)

ival-and: 12.0ms (1.2% of total)

const: 11.0ms (1.1% of total)

Bogosity

preprocess20.0ms (0.5%)

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)

explain95.0ms (2.2%)

FPErrors

Click to see full error table

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

Results

72.0ms

512×

valid

Compiler

Compiled 25 to 14 computations (44% saved)

Precisions

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

ival-cos: 16.0ms (53.7% of total)

ival-sub: 6.0ms (20.1% of total)

backward-pass: 6.0ms (20.1% of total)

const: 1.0ms (3.4% 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
▶	60.7%	(-.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

localize46.0ms (1.1%)

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	60.7%	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Results

39.0ms

256×

valid

Compiler

Compiled 10 to 5 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 26.0ms

ival-cos: 19.0ms (72.2% of total)

ival-sub: 3.0ms (11.4% of total)

backward-pass: 3.0ms (11.4% of total)

const: 1.0ms (3.8% 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	@	0	(cos x)
0.0ms	x	@	-inf	(- 1 (cos x))
0.0ms	x	@	inf	(- 1 (cos x))
0.0ms	x	@	inf	(cos x)

rewrite317.0ms (7.3%)

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))

simplify208.0ms (4.8%)

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)

eval23.0ms (0.5%)

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

prune29.0ms (0.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	176	3	179
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	177	3	180

Accuracy

100.0%

Counts

180 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	59.9%	(-.f64 #s(literal 1 binary64) #s(literal 1 binary64))
▶	100.0%	(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))))
▶	99.5%	(.f64 #s(literal 1/2 binary64) (.f64 x x))

Compiler

Compiled 22 to 15 computations (31.8% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

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

Rules

76×	`fma-define`
76×	`-lowering-.f32`
76×	`-lowering-.f64`
48×	`fma-lowering-fma.f32`
48×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	42
1	29	39
2	68	39
3	109	39
4	121	39
0	121	39

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize48.0ms (1.1%)

Localize:

Found 7 expressions of interest:

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

Results

34.0ms

256×

valid

Compiler

Compiled 54 to 12 computations (77.8% saved)

Precisions

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

ival-mult: 10.0ms (58.1% of total)

...c/correct-round.rkt:119:19: 4.0ms (23.2% of total)

ival-sub: 1.0ms (5.8% of total)

ival-add: 1.0ms (5.8% of total)

const: 1.0ms (5.8% of total)

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

series4.0ms (0.1%)

Counts

7 → 72

Calls

Call 1

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

Outputs
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* -1/24 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* -1/24 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* -1/24 (pow x 3))>
#<alt (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* -1/24 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (* -1/24 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* -1/24 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* -1/24 (pow x 2))>
#<alt (* -1/24 (pow x 2))>
#<alt (* -1/24 (pow x 2))>
#<alt (* -1/24 (pow x 2))>
#<alt (* -1/24 (pow x 2))>
#<alt (* -1/24 (pow x 2))>
#<alt (* -1/24 (pow x 2))>
#<alt (* -1/24 (pow x 2))>
#<alt (* -1/24 (pow x 2))>
#<alt (* -1/24 (pow x 2))>
#<alt (* -1/24 (pow x 2))>
#<alt (* -1/24 (pow x 2))>

Calls

18 calls:

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

rewrite384.0ms (8.8%)

Algorithm

1×	batch-egg-rewrite

Rules

3486×	`-lowering-.f32`
3486×	`-lowering-.f64`
2554×	`/-lowering-/.f32`
2554×	`/-lowering-/.f64`
1496×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	34
1	46	31
2	283	31
3	2411	31
0	8585	31

Stop Event

1×	iter limit
1×	node limit

Counts

7 → 281

Calls

Call 1

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

Outputs
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 x (.f64 #s(literal 1/2 binary64) x))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(.f64 (.f64 #s(literal 1/2 binary64) x) x)
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1 binary64)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(*.f64 x x)
(+.f64 (.f64 x (.f64 #s(literal 1/2 binary64) x)) (.f64 x (.f64 (.f64 x x) (.f64 x #s(literal -1/24 binary64)))))
(+.f64 (.f64 x (.f64 (.f64 x x) (.f64 x #s(literal -1/24 binary64)))) (.f64 x (.f64 #s(literal 1/2 binary64) x)))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 #s(literal 1/2 binary64) x)) (.f64 x (.f64 #s(literal 1/2 binary64) x))) (-.f64 (.f64 x (.f64 #s(literal 1/2 binary64) x)) (.f64 x (.f64 (.f64 x x) (.f64 x #s(literal -1/24 binary64)))))) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (.f64 x (.f64 x (.f64 x x)))) (-.f64 (.f64 x (.f64 #s(literal 1/2 binary64) x)) (.f64 x (.f64 (.f64 x x) (*.f64 x #s(literal -1/24 binary64)))))))
(-.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (.f64 x (.f64 x (.f64 x x)))) (-.f64 (.f64 x (.f64 (.f64 x x) (.f64 x #s(literal -1/24 binary64)))) (.f64 x (.f64 #s(literal 1/2 binary64) x)))) (/.f64 (.f64 (.f64 x (.f64 #s(literal 1/2 binary64) x)) (.f64 x (.f64 #s(literal 1/2 binary64) x))) (-.f64 (.f64 x (.f64 (.f64 x x) (.f64 x #s(literal -1/24 binary64)))) (.f64 x (*.f64 #s(literal 1/2 binary64) x)))))
(fma.f64 #s(literal 1/2 binary64) (.f64 x x) (.f64 x (.f64 (.f64 x x) (*.f64 x #s(literal -1/24 binary64)))))
(fma.f64 x (.f64 #s(literal 1/2 binary64) x) (.f64 x (.f64 (.f64 x x) (*.f64 x #s(literal -1/24 binary64)))))
(fma.f64 (.f64 x x) #s(literal 1/2 binary64) (.f64 x (.f64 (.f64 x x) (*.f64 x #s(literal -1/24 binary64)))))
(fma.f64 (.f64 x x) (.f64 x (.f64 x #s(literal -1/24 binary64))) (.f64 x (*.f64 #s(literal 1/2 binary64) x)))
(fma.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) (.f64 x x) (.f64 x (*.f64 #s(literal 1/2 binary64) x)))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 x (.f64 (.f64 x x) (*.f64 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 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/48 binary64)))) (.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))) (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/576 binary64))))))
(/.f64 (-.f64 #s(literal 0 binary64) (.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 (.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64)))))) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/48 binary64)))))
(/.f64 (.f64 (.f64 x x) (+.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 (.f64 x x) #s(literal 1/24 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/48 binary64)))) (.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64)))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))) (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/576 binary64)))))))
(/.f64 (neg.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64))))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/48 binary64))))))
(/.f64 (neg.f64 (.f64 (.f64 x x) (+.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) (neg.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)))))
(/.f64 (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (+.f64 (.f64 (.f64 x (.f64 #s(literal 1/2 binary64) x)) (.f64 x (.f64 #s(literal 1/2 binary64) x))) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 #s(literal 1/2 binary64) x)) (.f64 x (.f64 (.f64 x x) (.f64 x #s(literal -1/24 binary64))))))))
(/.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (.f64 x (.f64 x (.f64 x x)))) (-.f64 (.f64 (.f64 x (.f64 #s(literal 1/2 binary64) x)) (.f64 x (.f64 #s(literal 1/2 binary64) x))) (.f64 (.f64 x (.f64 (.f64 x x) (.f64 x #s(literal -1/24 binary64)))) (.f64 x (.f64 #s(literal 1/2 binary64) x))))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 #s(literal 1/2 binary64) x)) (.f64 x (.f64 #s(literal 1/2 binary64) x))) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (.f64 x (.f64 x (.f64 x x))))) (-.f64 (.f64 x (.f64 #s(literal 1/2 binary64) x)) (.f64 x (.f64 (.f64 x x) (*.f64 x #s(literal -1/24 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 #s(literal 1/2 binary64) x)) (.f64 x (.f64 #s(literal 1/2 binary64) x)))) (-.f64 (.f64 x (.f64 (.f64 x x) (.f64 x #s(literal -1/24 binary64)))) (.f64 x (*.f64 #s(literal 1/2 binary64) x))))
(/.f64 (.f64 x (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64))) (.f64 x (.f64 x x))))) (+.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 (.f64 x x) (.f64 x #s(literal -1/24 binary64))) (-.f64 (.f64 (.f64 x x) (.f64 x #s(literal -1/24 binary64))) (*.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (.f64 x (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64)))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))))
(/.f64 (.f64 (.f64 x x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64))))))
(/.f64 (.f64 (.f64 x x) (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/13824 binary64)) #s(literal -1/8 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/48 binary64))))))
(/.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/4 binary64) (neg.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/576 binary64))))) (+.f64 #s(literal -1/2 binary64) (neg.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)))))
(/.f64 (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) #s(literal -1/4 binary64))) (+.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) #s(literal -1/2 binary64)))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64))))))
(/.f64 (.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/13824 binary64)) #s(literal -1/8 binary64)) (.f64 x x)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/48 binary64))))))
(/.f64 (.f64 (+.f64 #s(literal -1/4 binary64) (neg.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/576 binary64)))) (.f64 x x)) (+.f64 #s(literal -1/2 binary64) (neg.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)))))
(/.f64 (.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) #s(literal -1/4 binary64)) (.f64 x x)) (+.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) #s(literal -1/2 binary64)))
(/.f64 (.f64 (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64))) (.f64 x (.f64 x x)))) x) (+.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 (.f64 x x) (.f64 x #s(literal -1/24 binary64))) (-.f64 (.f64 (.f64 x x) (.f64 x #s(literal -1/24 binary64))) (*.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (.f64 (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))))) x) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))))
(/.f64 (.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64))))) x) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/48 binary64)))))
(/.f64 (.f64 (.f64 x (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/576 binary64)))) x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))))
(/.f64 (neg.f64 (neg.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64)))))))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/48 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/576 binary64)))))) (neg.f64 (+.f64 #s(literal -1/2 binary64) (neg.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64))))))
(/.f64 (neg.f64 (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (neg.f64 (+.f64 (.f64 (.f64 x (.f64 #s(literal 1/2 binary64) x)) (.f64 x (.f64 #s(literal 1/2 binary64) x))) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 #s(literal 1/2 binary64) x)) (.f64 x (.f64 (.f64 x x) (.f64 x #s(literal -1/24 binary64)))))))))
(/.f64 (neg.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (neg.f64 (+.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (.f64 x (.f64 x (.f64 x x)))) (-.f64 (.f64 (.f64 x (.f64 #s(literal 1/2 binary64) x)) (.f64 x (.f64 #s(literal 1/2 binary64) x))) (.f64 (.f64 x (.f64 (.f64 x x) (.f64 x #s(literal -1/24 binary64)))) (.f64 x (.f64 #s(literal 1/2 binary64) x)))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x (.f64 #s(literal 1/2 binary64) x)) (.f64 x (.f64 #s(literal 1/2 binary64) x))) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (.f64 x (.f64 x (.f64 x x)))))) (neg.f64 (-.f64 (.f64 x (.f64 #s(literal 1/2 binary64) x)) (.f64 x (.f64 (.f64 x x) (*.f64 x #s(literal -1/24 binary64)))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 #s(literal 1/2 binary64) x)) (.f64 x (.f64 #s(literal 1/2 binary64) x))))) (neg.f64 (-.f64 (.f64 x (.f64 (.f64 x x) (.f64 x #s(literal -1/24 binary64)))) (.f64 x (*.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (neg.f64 (.f64 x (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64))) (.f64 x (.f64 x x)))))) (neg.f64 (+.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 (.f64 x x) (.f64 x #s(literal -1/24 binary64))) (-.f64 (.f64 (.f64 x x) (.f64 x #s(literal -1/24 binary64))) (*.f64 #s(literal 1/2 binary64) x))))))
(/.f64 (neg.f64 (.f64 x (.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))))))) (neg.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64))))))
(/.f64 (neg.f64 (.f64 (.f64 x x) #s(literal 1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64)))))))
(/.f64 (neg.f64 (.f64 (.f64 x x) (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/13824 binary64)) #s(literal -1/8 binary64)))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/48 binary64)))))))
(/.f64 (neg.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/4 binary64) (neg.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/576 binary64)))))) (neg.f64 (+.f64 #s(literal -1/2 binary64) (neg.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64))))))
(/.f64 (neg.f64 (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) #s(literal -1/4 binary64)))) (neg.f64 (+.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (.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 (neg.f64 (.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/13824 binary64)) #s(literal -1/8 binary64)) (.f64 x x))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/48 binary64)))))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal -1/4 binary64) (neg.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1/576 binary64)))) (.f64 x x))) (neg.f64 (+.f64 #s(literal -1/2 binary64) (neg.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64))))))
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(.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64)))) (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/48 binary64))) (.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/48 binary64))) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/48 binary64))))))) (+.f64 #s(literal 1/16 binary64) (.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/48 binary64))) (-.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/48 binary64))) #s(literal 1/4 binary64)))))
(.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64)))) (-.f64 #s(literal 1/16 binary64) (.f64 (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/48 binary64))) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/48 binary64)))))) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/48 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 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/13824 binary64)))) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (+.f64 (.f64 (*.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/48 binary64)))))
(.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))) (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal -1/191102976 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/16 binary64) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/576 binary64))))))))
(.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))) (-.f64 #s(literal 1/16 binary64) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/331776 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/576 binary64))))))
(.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/48 binary64)))) (+.f64 #s(literal 1/512 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal -1/2641807540224 binary64))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64))) (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/13824 binary64))) #s(literal 1/8 binary64))))))
(.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/576 binary64)) #s(literal -1/48 binary64)))) (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal -1/191102976 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x))) #s(literal 1/13824 binary64)))))
(exp.f64 (log.f64 (.f64 x (.f64 x #s(literal -1/24 binary64)))))
(exp.f64 (.f64 (log.f64 (.f64 x (*.f64 x #s(literal -1/24 binary64)))) #s(literal 1 binary64)))
(pow.f64 (.f64 x (.f64 x #s(literal -1/24 binary64))) #s(literal 1 binary64))
(.f64 x (.f64 x #s(literal -1/24 binary64)))
(.f64 x (pow.f64 (.f64 x #s(literal -1/24 binary64)) #s(literal 1 binary64)))
(.f64 x (exp.f64 (log.f64 (.f64 x #s(literal -1/24 binary64)))))
(.f64 (.f64 x x) #s(literal -1/24 binary64))
(.f64 (.f64 x x) (exp.f64 (log.f64 #s(literal -1/24 binary64))))
(.f64 #s(literal -1/24 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal -1/24 binary64)) x)
(.f64 (pow.f64 (.f64 x #s(literal -1/24 binary64)) #s(literal 1 binary64)) x)
(.f64 (exp.f64 (log.f64 (.f64 x #s(literal -1/24 binary64)))) x)
(.f64 (exp.f64 (log.f64 #s(literal -1/24 binary64))) (.f64 x x))
#s(literal 0 binary64)

simplify138.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

1988×	`-lowering-.f32`
1988×	`-lowering-.f64`
1448×	`times-frac`
1252×	`fma-define`
1192×	`fnmadd-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	29	438
1	74	336
2	185	336
3	545	336
4	1752	336
5	4955	336
0	8421	336

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

Inputs
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* -1/24 (pow x 4))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* -1/24 (pow x 4))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* 1/2 x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(* x (+ 1/2 (* -1/24 (pow x 2))))
(* x (+ 1/2 (* -1/24 (pow x 2))))
(* -1/24 (pow x 3))
(* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* -1/24 (pow x 3))
(* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* -1/24 (pow x 2)))
(* -1/24 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* -1/24 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))

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

eval45.0ms (1%)

Compiler: Compiled 11498 to 1077 computations (90.6% saved)

prune36.0ms (0.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	369	2	371
Fresh	0	0	0
Picked	2	1	3
Done	0	0	0
Total	371	3	374

Accuracy

100.0%

Counts

374 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(.f64 (.f64 #s(literal 1/2 binary64) x) x)
✓	100.0%	(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))))
▶	59.9%	#s(literal 0 binary64)

Compiler

Compiled 20 to 14 computations (30% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Rules

14×	`-lowering-.f32`
14×	`-lowering-.f64`
4×	`*-commutative`
2×	`associate-r`
2×	`square-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	5	11
1	9	10
2	11	10
0	11	10

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
0
(* (* 1/2 x) x)
(* 1/2 x)
1/2
x

Outputs
0
#s(literal 0 binary64)
(* (* 1/2 x) x)
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
1/2
#s(literal 1/2 binary64)
x

localize21.0ms (0.5%)

Localize:

Found 2 expressions of interest:

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

Results

15.0ms

256×

valid

Compiler

Compiled 13 to 6 computations (53.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-mult: 4.0ms (88.3% of total)

const: 0.0ms (0% of total)

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

series2.0ms (0%)

Counts

2 → 24

Calls

Call 1

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

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

Calls

6 calls:

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

rewrite185.0ms (4.3%)

Algorithm

1×	batch-egg-rewrite

Rules

2200×	`pow-lowering-pow.f64`
2200×	`pow-lowering-pow.f32`
1432×	`prod-exp`
1304×	`-lowering-.f32`
1304×	`-lowering-.f64`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	4	10
1	8	8
2	12	8
3	19	8
4	35	8
5	93	8
6	292	2
7	1854	2
8	1886	2
9	2020	2
10	3307	2
0	8651	2

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 2

Calls

Call 1

Inputs
(* (* 1/2 x) x)
(* 1/2 x)

Outputs
#s(literal 1/2 binary64)
#s(literal 1/2 binary64)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

14×	`-lowering-.f32`
14×	`-lowering-.f64`
4×	`*-commutative`
2×	`pow-lowering-pow.f64`
2×	`pow-lowering-pow.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	96
1	9	84
2	12	84
0	12	84

Stop Event

1×	iter limit
1×	saturated

Counts

24 → 24

Calls

Call 1

Inputs
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 (pow x 2))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)

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

eval2.0ms (0.1%)

Compiler: Compiled 125 to 5 computations (96% saved)

prune2.0ms (0.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	24	2	26
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	24	5	29

Accuracy

100.0%

Counts

29 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	(.f64 (.f64 #s(literal 1/2 binary64) x) x)
✓	100.0%	(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))))
▶	6.7%	(*.f64 #s(literal 1/2 binary64) x)
▶	3.9%	#s(literal 1/2 binary64)
✓	59.9%	#s(literal 0 binary64)

Compiler

Compiled 26 to 19 computations (26.9% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 1 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	6
1	4	6
0	4	6

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
1/2
(* 1/2 x)
1/2
x

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

localize15.0ms (0.4%)

Localize:

Found 1 expressions of interest:

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

Results

10.0ms

256×

valid

Compiler

Compiled 8 to 4 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-mult: 2.0ms (77.2% of total)

const: 0.0ms (0% of total)

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

series0.0ms (0%)

Counts

1 → 12

Calls

Call 1

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

Outputs
#<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)>

Calls

3 calls:

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

rewrite11.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated

Counts

1 → 2

Calls

Call 1

Inputs
(* 1/2 x)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated

Counts

12 → 12

Calls

Call 1

Inputs
(* 1/2 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)

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

eval1.0ms (0%)

Compiler: Compiled 43 to 4 computations (90.7% saved)

prune3.0ms (0.1%)

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	14	0	14
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	14	5	19

Accuracy

100.0%

Counts

19 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	(.f64 (.f64 #s(literal 1/2 binary64) x) x)
✓	100.0%	(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64)))))
✓	6.7%	(*.f64 #s(literal 1/2 binary64) x)
✓	3.9%	#s(literal 1/2 binary64)
✓	59.9%	#s(literal 0 binary64)

Compiler

Compiled 60 to 35 computations (41.7% saved)

regimes13.0ms (0.3%)

Counts

8 → 1

Calls

Call 1

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

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

Calls

3 calls:

7.0ms	(-.f64 #s(literal 1 binary64) (cos.f64 x))
3.0ms	x
2.0ms	(cos.f64 x)

Results

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

Compiler

Compiled 10 to 7 computations (30% saved)

regimes3.0ms (0.1%)

Counts

6 → 1

Calls

Call 1

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

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

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
99.5%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0.1%)

Counts

5 → 1

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
99.5%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0.1%)

Accuracy

Total -36.1b remaining (-140.7%)

Threshold costs -36.1b (-140.7%)

Counts

4 → 1

Calls

Call 1

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

Outputs
#s(literal 0 binary64)

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
59.9%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	19	22

Stop Event

1×

saturated

Calls

Call 1

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

soundness708.0ms (16.3%)

Rules

3486×	`-lowering-.f32`
3486×	`-lowering-.f64`
2554×	`/-lowering-/.f32`
2554×	`/-lowering-/.f64`
2004×	`-lowering-.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	34
1	46	31
2	283	31
3	2411	31
0	8585	31
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 59 to 37 computations (37.3% saved)

preprocess38.0ms (0.9%)

Remove: (abs x)
Compiler: Compiled 126 to 78 computations (38.1% 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

analyze7.0ms (0.2%)

sample1.9s (43.6%)

preprocess20.0ms (0.5%)

explain95.0ms (2.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify6.0ms (0.1%)

localize46.0ms (1.1%)

series1.0ms (0%)

rewrite317.0ms (7.3%)

simplify208.0ms (4.8%)

eval23.0ms (0.5%)

prune29.0ms (0.7%)

simplify8.0ms (0.2%)

localize48.0ms (1.1%)

series4.0ms (0.1%)

rewrite384.0ms (8.8%)

simplify138.0ms (3.2%)

eval45.0ms (1%)

prune36.0ms (0.8%)

simplify4.0ms (0.1%)

localize21.0ms (0.5%)

series2.0ms (0%)

rewrite185.0ms (4.3%)

simplify7.0ms (0.2%)

eval2.0ms (0.1%)

prune2.0ms (0.1%)

simplify4.0ms (0.1%)

localize15.0ms (0.4%)

series0.0ms (0%)

rewrite11.0ms (0.2%)

simplify4.0ms (0.1%)

eval1.0ms (0%)

prune3.0ms (0.1%)

regimes13.0ms (0.3%)

regimes3.0ms (0.1%)

regimes3.0ms (0.1%)

regimes3.0ms (0.1%)

simplify8.0ms (0.2%)

soundness708.0ms (16.3%)

preprocess38.0ms (0.9%)

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