Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50.4%	0.4%	49.2%	10
50.4%	0.2%	49.4%	11
50.4%	0.1%	49.5%	12
50.4%	0%	49.6%	13
50.4%	0%	49.6%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample4.4s (77.8%)

Results

3.2s	4315×	body	2048	valid
838.0ms	2051×	body	1024	valid
272.0ms	997×	body	512	valid
90.0ms	522×	body	256	valid
39.0ms	371×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 20 to 16 computations (20% saved)

preprocess32.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

624×	`fma-def_binary64`
581×	`fma-neg_binary64`
548×	`unswap-sqr_binary64`
284×	`cancel-sign-sub-inv_binary64`
199×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	20	13
2	36	13
3	60	13
4	122	13
5	272	13
6	697	13
7	1699	13
8	3110	13
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Outputs
(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
(+.f64 (+.f64 (exp.f64 x) -2) (exp.f64 (neg.f64 x)))
(+.f64 (exp.f64 x) (+.f64 -2 (exp.f64 (neg.f64 x))))
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify28.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

624×	`fma-def_binary64`
581×	`fma-neg_binary64`
548×	`unswap-sqr_binary64`
284×	`cancel-sign-sub-inv_binary64`
199×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	20	13
2	36	13
3	60	13
4	122	13
5	272	13
6	697	13
7	1699	13
8	3110	13

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Outputs
(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
(+.f64 (+.f64 (exp.f64 x) -2) (exp.f64 (neg.f64 x)))
(+.f64 (exp.f64 x) (+.f64 -2 (exp.f64 (neg.f64 x))))
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

26.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	26.2b	(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
▶	26.2b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Compiler

Compiled 53 to 38 computations (28.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (exp.f64 x) 2)
✓	5.0b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

series3.0ms (0%)

Counts

2 → 16

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
0.0ms	x	@	inf	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
0.0ms	x	@	-inf	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
0.0ms	x	@	0	(-.f64 (exp.f64 x) 2)
0.0ms	x	@	-inf	(-.f64 (exp.f64 x) 2)

rewrite44.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

815×	`log1p-expm1-u_binary64`
815×	`expm1-log1p-u_binary64`
95×	`add-sqr-sqrt_binary64`
91×	`add-log-exp_binary64`
89×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	181	17
2	2646	17

Stop Event

1×	node limit

Counts

2 → 78

Calls

Call 1

Inputs
(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
(-.f64 (exp.f64 x) 2)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 x) (-.f64 2 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (+.f64 (exp.f64 x) -2) 2) (+.f64 (exp.f64 x) (-.f64 -2 (exp.f64 x)))) (/.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) (-.f64 -2 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (exp.f64 x) (exp.f64 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2))) (pow.f64 (cbrt.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2))) 2) (cbrt.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2))) (sqrt.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (+.f64 (exp.f64 x) -2) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 (exp.f64 x) -2) 2) (.f64 (exp.f64 x) (-.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (pow.f64 (+.f64 (exp.f64 x) -2) 2) (pow.f64 (exp.f64 x) 2)) (/.f64 1 (+.f64 (exp.f64 x) (-.f64 -2 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 x) -2) 2) (.f64 (exp.f64 x) (-.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2)))) (+.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (+.f64 (exp.f64 x) -2) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (exp.f64 x) (-.f64 -2 (exp.f64 x))) (-.f64 (pow.f64 (+.f64 (exp.f64 x) -2) 2) (pow.f64 (exp.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (+.f64 (exp.f64 x) -2) 3)) (+.f64 (pow.f64 (+.f64 (exp.f64 x) -2) 2) (.f64 (exp.f64 x) (-.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (+.f64 (exp.f64 x) -2) 3)) (+.f64 (pow.f64 (exp.f64 x) 2) (-.f64 (pow.f64 (+.f64 (exp.f64 x) -2) 2) (.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 (exp.f64 x) -2) 2) (pow.f64 (exp.f64 x) 2)) (+.f64 (exp.f64 x) (-.f64 -2 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (+.f64 (exp.f64 x) -2) 3))) (neg.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 x) -2) 2) (.f64 (exp.f64 x) (-.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (+.f64 (exp.f64 x) -2) 2) (pow.f64 (exp.f64 x) 2))) (neg.f64 (+.f64 (exp.f64 x) (-.f64 -2 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 (+.f64 (pow.f64 (exp.f64 x) 3) -8) (exp.f64 x)) (.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2))) 1)) (.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2))) (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -4) (exp.f64 x)) (.f64 (+.f64 (exp.f64 x) 2) 1)) (.f64 (+.f64 (exp.f64 x) 2) (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2))) (.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 3) -8))) (.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (+.f64 (exp.f64 x) 2) (.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 2) -4))) (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (-.f64 2 (exp.f64 x)) 3)) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (.f64 (-.f64 2 (exp.f64 x)) (-.f64 2 (exp.f64 x))) (.f64 (exp.f64 x) (-.f64 2 (exp.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (exp.f64 x) 2) (.f64 (-.f64 2 (exp.f64 x)) (-.f64 2 (exp.f64 x)))) (+.f64 (exp.f64 x) (-.f64 2 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (exp.f64 x) 2) (pow.f64 (+.f64 (exp.f64 x) -2) 2)) (-.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (exp.f64 x) (+.f64 (exp.f64 x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (exp.f64 x) (neg.f64 (-.f64 2 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 (exp.f64 x) -2) (exp.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 (exp.f64 x) -2)) 2) (cbrt.f64 (+.f64 (exp.f64 x) -2)) (exp.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (cbrt.f64 (exp.f64 x)) (+.f64 (exp.f64 x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (cbrt.f64 (exp.f64 x)) (neg.f64 (-.f64 2 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 (exp.f64 x) -2)) (sqrt.f64 (+.f64 (exp.f64 x) -2)) (exp.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) (+.f64 (exp.f64 x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) (neg.f64 (-.f64 2 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (exp.f64 x) -2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -2 (exp.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (exp.f64 x) -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (+.f64 (exp.f64 x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (+.f64 (exp.f64 x) -2)) (pow.f64 (cbrt.f64 (+.f64 (exp.f64 x) -2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (+.f64 (exp.f64 x) -2)) 2) (cbrt.f64 (+.f64 (exp.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (+.f64 (exp.f64 x) -2)) (sqrt.f64 (+.f64 (exp.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (pow.f64 (exp.f64 x) 3) -8) (/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (pow.f64 (exp.f64 x) 2) -4) (/.f64 1 (+.f64 (exp.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2))) (+.f64 (pow.f64 (exp.f64 x) 3) -8)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (exp.f64 x) 2) (+.f64 (pow.f64 (exp.f64 x) 2) -4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (exp.f64 x) 3) -8) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (exp.f64 x) 3) -8) (+.f64 (pow.f64 (exp.f64 x) 2) (-.f64 4 (.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -4) (+.f64 (exp.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -4) (-.f64 (exp.f64 x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (exp.f64 x) 3) -8)) (neg.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -4)) (neg.f64 (+.f64 (exp.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (exp.f64 x) -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (exp.f64 x) -2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (exp.f64 x) -2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (exp.f64 x) -2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (exp.f64 x) -2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (exp.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (exp.f64 x) -2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (exp.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (exp.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 (exp.f64 x) -2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (exp.f64 x) -2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (cbrt.f64 (exp.f64 x)) -2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) -2)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (exp.f64 x) -2)))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 x) (-.f64 2 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (+.f64 (exp.f64 x) -2) 2) (+.f64 (exp.f64 x) (-.f64 -2 (exp.f64 x)))) (/.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) (-.f64 -2 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (exp.f64 x) (exp.f64 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2))) (pow.f64 (cbrt.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2))) 2) (cbrt.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2))) (sqrt.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (+.f64 (exp.f64 x) -2) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 (exp.f64 x) -2) 2) (*.f64 (exp.f64 x) (-.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (+.f64 (exp.f64 x) -2) 2) (pow.f64 (exp.f64 x) 2)) (/.f64 1 (+.f64 (exp.f64 x) (-.f64 -2 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 x) -2) 2) (*.f64 (exp.f64 x) (-.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2)))) (+.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (+.f64 (exp.f64 x) -2) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (exp.f64 x) (-.f64 -2 (exp.f64 x))) (-.f64 (pow.f64 (+.f64 (exp.f64 x) -2) 2) (pow.f64 (exp.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (+.f64 (exp.f64 x) -2) 3)) (+.f64 (pow.f64 (+.f64 (exp.f64 x) -2) 2) (*.f64 (exp.f64 x) (-.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (+.f64 (exp.f64 x) -2) 3)) (+.f64 (pow.f64 (exp.f64 x) 2) (-.f64 (pow.f64 (+.f64 (exp.f64 x) -2) 2) (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 (exp.f64 x) -2) 2) (pow.f64 (exp.f64 x) 2)) (+.f64 (exp.f64 x) (-.f64 -2 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (+.f64 (exp.f64 x) -2) 3))) (neg.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 x) -2) 2) (*.f64 (exp.f64 x) (-.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (+.f64 (exp.f64 x) -2) 2) (pow.f64 (exp.f64 x) 2))) (neg.f64 (+.f64 (exp.f64 x) (-.f64 -2 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (+.f64 (pow.f64 (exp.f64 x) 3) -8) (exp.f64 x)) (*.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (*.f64 (exp.f64 x) 2))) 1)) (*.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (*.f64 (exp.f64 x) 2))) (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -4) (exp.f64 x)) (*.f64 (+.f64 (exp.f64 x) 2) 1)) (*.f64 (+.f64 (exp.f64 x) 2) (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (*.f64 (exp.f64 x) 2))) (*.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 3) -8))) (*.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (*.f64 (exp.f64 x) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (+.f64 (exp.f64 x) 2) (*.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 2) -4))) (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (-.f64 2 (exp.f64 x)) 3)) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (*.f64 (-.f64 2 (exp.f64 x)) (-.f64 2 (exp.f64 x))) (*.f64 (exp.f64 x) (-.f64 2 (exp.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (exp.f64 x) 2) (*.f64 (-.f64 2 (exp.f64 x)) (-.f64 2 (exp.f64 x)))) (+.f64 (exp.f64 x) (-.f64 2 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (exp.f64 x) 2) (pow.f64 (+.f64 (exp.f64 x) -2) 2)) (-.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (exp.f64 x) (+.f64 (exp.f64 x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (exp.f64 x) (neg.f64 (-.f64 2 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 (exp.f64 x) -2) (exp.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 (exp.f64 x) -2)) 2) (cbrt.f64 (+.f64 (exp.f64 x) -2)) (exp.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (cbrt.f64 (exp.f64 x)) (+.f64 (exp.f64 x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (cbrt.f64 (exp.f64 x)) (neg.f64 (-.f64 2 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 (exp.f64 x) -2)) (sqrt.f64 (+.f64 (exp.f64 x) -2)) (exp.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) (+.f64 (exp.f64 x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) (neg.f64 (-.f64 2 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (exp.f64 x) -2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -2 (exp.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (exp.f64 x) -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (exp.f64 x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (exp.f64 x) -2)) (pow.f64 (cbrt.f64 (+.f64 (exp.f64 x) -2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (exp.f64 x) -2)) 2) (cbrt.f64 (+.f64 (exp.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (exp.f64 x) -2)) (sqrt.f64 (+.f64 (exp.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (exp.f64 x) 3) -8) (/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (*.f64 (exp.f64 x) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -4) (/.f64 1 (+.f64 (exp.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (*.f64 (exp.f64 x) 2))) (+.f64 (pow.f64 (exp.f64 x) 3) -8)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (exp.f64 x) 2) (+.f64 (pow.f64 (exp.f64 x) 2) -4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (exp.f64 x) 3) -8) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (*.f64 (exp.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (exp.f64 x) 3) -8) (+.f64 (pow.f64 (exp.f64 x) 2) (-.f64 4 (*.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -4) (+.f64 (exp.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -4) (-.f64 (exp.f64 x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (exp.f64 x) 3) -8)) (neg.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (*.f64 (exp.f64 x) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -4)) (neg.f64 (+.f64 (exp.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (exp.f64 x) -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (exp.f64 x) -2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (exp.f64 x) -2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (exp.f64 x) -2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (exp.f64 x) -2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (exp.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (exp.f64 x) -2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (exp.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (exp.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 (exp.f64 x) -2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (exp.f64 x) -2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (cbrt.f64 (exp.f64 x)) -2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) -2)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (exp.f64 x) -2)))))))

simplify30.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

749×	`unswap-sqr_binary64`
544×	`associate-l_binary64`
523×	`fma-def_binary64`
398×	`associate-r_binary64`
193×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	45	198
1	115	196
2	250	196
3	744	191
4	3163	191

Stop Event

1×	node limit

Counts

94 → 96

Calls

Call 1

Inputs
(pow.f64 x 2)
(+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (pow.f64 x 2)))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (*.f64 1/20160 (pow.f64 x 8)) (pow.f64 x 2))))
(-.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
(-.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
(-.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
(-.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
(-.f64 (+.f64 (exp.f64 (*.f64 -1 x)) (exp.f64 x)) 2)
(-.f64 (+.f64 (exp.f64 (*.f64 -1 x)) (exp.f64 x)) 2)
(-.f64 (+.f64 (exp.f64 (*.f64 -1 x)) (exp.f64 x)) 2)
(-.f64 (+.f64 (exp.f64 (*.f64 -1 x)) (exp.f64 x)) 2)
-1
(-.f64 x 1)
(-.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x) 1)
(-.f64 (+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 x (.f64 1/6 (pow.f64 x 3)))) 1)

Outputs
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2))
(fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (pow.f64 x 2)))
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 x x)))
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))
(fma.f64 x x (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4))))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (*.f64 1/20160 (pow.f64 x 8)) (pow.f64 x 2))))
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 1/20160 (pow.f64 x 8) (*.f64 x x))))
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
(fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))))
(-.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
(+.f64 (exp.f64 x) (-.f64 (exp.f64 (neg.f64 x)) 2))
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
(+.f64 (exp.f64 (neg.f64 x)) (+.f64 (exp.f64 x) -2))
(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))
(-.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
(+.f64 (exp.f64 x) (-.f64 (exp.f64 (neg.f64 x)) 2))
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
(+.f64 (exp.f64 (neg.f64 x)) (+.f64 (exp.f64 x) -2))
(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))
(-.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
(+.f64 (exp.f64 x) (-.f64 (exp.f64 (neg.f64 x)) 2))
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
(+.f64 (exp.f64 (neg.f64 x)) (+.f64 (exp.f64 x) -2))
(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))
(-.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
(+.f64 (exp.f64 x) (-.f64 (exp.f64 (neg.f64 x)) 2))
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
(+.f64 (exp.f64 (neg.f64 x)) (+.f64 (exp.f64 x) -2))
(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))
(-.f64 (+.f64 (exp.f64 (*.f64 -1 x)) (exp.f64 x)) 2)
(+.f64 (exp.f64 x) (-.f64 (exp.f64 (neg.f64 x)) 2))
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
(+.f64 (exp.f64 (neg.f64 x)) (+.f64 (exp.f64 x) -2))
(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))
(-.f64 (+.f64 (exp.f64 (*.f64 -1 x)) (exp.f64 x)) 2)
(+.f64 (exp.f64 x) (-.f64 (exp.f64 (neg.f64 x)) 2))
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
(+.f64 (exp.f64 (neg.f64 x)) (+.f64 (exp.f64 x) -2))
(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))
(-.f64 (+.f64 (exp.f64 (*.f64 -1 x)) (exp.f64 x)) 2)
(+.f64 (exp.f64 x) (-.f64 (exp.f64 (neg.f64 x)) 2))
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
(+.f64 (exp.f64 (neg.f64 x)) (+.f64 (exp.f64 x) -2))
(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))
(-.f64 (+.f64 (exp.f64 (*.f64 -1 x)) (exp.f64 x)) 2)
(+.f64 (exp.f64 x) (-.f64 (exp.f64 (neg.f64 x)) 2))
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
(+.f64 (exp.f64 (neg.f64 x)) (+.f64 (exp.f64 x) -2))
(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))
-1
(-.f64 x 1)
(+.f64 x -1)
(-.f64 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x) 1)
(+.f64 (fma.f64 1/2 (*.f64 x x) x) -1)
(+.f64 -1 (fma.f64 (*.f64 x x) 1/2 x))
(fma.f64 (fma.f64 x 1/2 1) x -1)
(fma.f64 x (fma.f64 x 1/2 1) -1)
(-.f64 (+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 x (.f64 1/6 (pow.f64 x 3)))) 1)
(+.f64 (+.f64 (fma.f64 1/2 (.f64 x x) x) (.f64 1/6 (pow.f64 x 3))) -1)
(+.f64 -1 (fma.f64 (*.f64 x x) 1/2 (fma.f64 1/6 (pow.f64 x 3) x)))
(+.f64 (fma.f64 (*.f64 x x) 1/2 x) (fma.f64 1/6 (pow.f64 x 3) -1))
(+.f64 x (fma.f64 (*.f64 x x) (fma.f64 x 1/6 1/2) -1))
(fma.f64 x (*.f64 x (fma.f64 x 1/6 1/2)) (+.f64 x -1))

prune73.0ms (1.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	95	3	98

Error

0.0b

Counts

98 → 3

Alt Table

Status	Error	Program
▶	0.8b	(fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))))
✓	26.2b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
	26.1b	(/.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2))) (.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 3) -8))) (.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2)))))

Status

Error

Program

▶

0.8b

(fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))))

✓

26.2b

(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

26.1b

(/.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (*.f64 (exp.f64 x) 2))) (*.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 3) -8))) (*.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (*.f64 (exp.f64 x) 2)))))

Compiler

Compiled 1537 to 897 computations (41.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))))
✓	0.0b	(*.f64 1/20160 (pow.f64 x 8))
✓	0.1b	(fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))
✓	0.1b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8))))

series6.0ms (0.1%)

Counts

4 → 36

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8))))
1.0ms	x	@	0	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8))))
1.0ms	x	@	-inf	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8))))
1.0ms	x	@	0	(fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))
1.0ms	x	@	inf	(fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))

rewrite57.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

260×	`prod-diff_binary64`
236×	`expm1-udef_binary64`
236×	`log1p-udef_binary64`
192×	`log-pow_binary64`
145×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	67
1	319	67
2	3293	67

Stop Event

1×	node limit

Counts

4 → 93

Calls

Call 1

Inputs
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8))))
(fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))
(*.f64 1/20160 (pow.f64 x 8))
(fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))) (.f64 1/12 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 1/12 (pow.f64 x 4)) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 1/12 (pow.f64 x 4)) 1) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1/12 (pow.f64 x 4) (.f64 1/360 (pow.f64 x 6))) (.f64 1/20160 (pow.f64 x 8)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))))) (pow.f64 (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))))) 2) (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))))) (sqrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 1/12 (pow.f64 x 4)) 3) (pow.f64 (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))) 3)) (fma.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/12 (pow.f64 x 4)) (-.f64 (pow.f64 (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))) 2) (.f64 (.f64 1/12 (pow.f64 x 4)) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/12 (pow.f64 x 4))) (pow.f64 (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))) 2)) (-.f64 (.f64 1/12 (pow.f64 x 4)) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))) (exp.f64 (.f64 1/12 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))))) (exp.f64 (.f64 1/12 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (.f64 1/12 (pow.f64 x 4))) (+.f64 1 (expm1.f64 (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8))))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 1/20160 (pow.f64 x 8)) (.f64 1/360 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/20160 (pow.f64 x 8)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 1/360 (pow.f64 x 6)) 1) (.f64 1/20160 (pow.f64 x 8)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))) (pow.f64 (cbrt.f64 (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))) 2) (cbrt.f64 (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))) (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 1/360 (pow.f64 x 6)) 3) (pow.f64 (.f64 1/20160 (pow.f64 x 8)) 3)) (fma.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/360 (pow.f64 x 6)) (-.f64 (.f64 1/406425600 (pow.f64 x 16)) (.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/20160 (pow.f64 x 8))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/360 (pow.f64 x 6)) (neg.f64 (.f64 1/406425600 (pow.f64 x 16)))) (-.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/20160 (pow.f64 x 8))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (pow.f64 (exp.f64 1/20160) (pow.f64 x 8)) (exp.f64 (.f64 1/360 (pow.f64 x 6)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (.f64 1/20160 (pow.f64 x 8)))) (exp.f64 (.f64 1/360 (pow.f64 x 6)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (.f64 1/360 (pow.f64 x 6))) (+.f64 1 (expm1.f64 (.f64 1/20160 (pow.f64 x 8))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 1/20160 (pow.f64 x 8)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/20160 (pow.f64 x 8)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 1/20160 (pow.f64 x 8)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 1/20160 (pow.f64 x 8))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 x 4) (sqrt.f64 1/20160)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 1/406425600 (pow.f64 x 16)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/20160) (pow.f64 x 8)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 1/20160 (pow.f64 x 8)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 1/20160 (pow.f64 x 8)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 1/20160 (pow.f64 x 8))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (fma.f64 8 (log.f64 x) (log.f64 1/20160)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (fma.f64 8 (log.f64 x) (log.f64 1/20160)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 1/20160 (pow.f64 x 8))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x x) (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 x x) 1) (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 x x (.f64 1/12 (pow.f64 x 4))) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))))) (pow.f64 (cbrt.f64 (fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))))) 2) (cbrt.f64 (fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 x (sqrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))))) (hypot.f64 x (sqrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 6) (pow.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))) 3)) (+.f64 (pow.f64 x 4) (-.f64 (pow.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))) 2) (.f64 (.f64 x x) (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (pow.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))) 2)) (-.f64 (.f64 x x) (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x (sqrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))))) (exp.f64 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))))) (exp.f64 (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (.f64 x x)) (+.f64 1 (expm1.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/20160 (pow.f64 x 8)))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))))))))))

simplify58.0ms (1%)

Algorithm

1×	egg-herbie

Rules

505×	`distribute-rgt-out_binary64`
413×	`unswap-sqr_binary64`
379×	`distribute-lft-out_binary64`
339×	`associate-l_binary64`
316×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	528
1	63	528
2	137	528
3	392	528
4	1768	528
5	4131	528
6	4472	528
7	4968	528

Stop Event

1×	node limit

Counts

129 → 109

Calls

Call 1

Inputs
(*.f64 1/12 (pow.f64 x 4))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/360 (pow.f64 x 6)))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/20160 (pow.f64 x 8))))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/20160 (pow.f64 x 8))))
(*.f64 1/20160 (pow.f64 x 8))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/20160 (pow.f64 x 8)))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/20160 (pow.f64 x 8))))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/20160 (pow.f64 x 8))))
(*.f64 1/20160 (pow.f64 x 8))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/20160 (pow.f64 x 8)))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/20160 (pow.f64 x 8))))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/20160 (pow.f64 x 8))))
(*.f64 1/360 (pow.f64 x 6))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/20160 (pow.f64 x 8)))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/20160 (pow.f64 x 8)))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/20160 (pow.f64 x 8)))
(*.f64 1/20160 (pow.f64 x 8))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/20160 (pow.f64 x 8)))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/20160 (pow.f64 x 8)))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/20160 (pow.f64 x 8)))
(*.f64 1/20160 (pow.f64 x 8))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/20160 (pow.f64 x 8)))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/20160 (pow.f64 x 8)))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/20160 (pow.f64 x 8)))
(pow.f64 x 2)
(+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (pow.f64 x 2)))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (*.f64 1/20160 (pow.f64 x 8)) (pow.f64 x 2))))
(*.f64 1/20160 (pow.f64 x 8))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/20160 (pow.f64 x 8)))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/20160 (pow.f64 x 8))))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (*.f64 1/20160 (pow.f64 x 8)) (pow.f64 x 2))))
(*.f64 1/20160 (pow.f64 x 8))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/20160 (pow.f64 x 8)))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/20160 (pow.f64 x 8))))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (*.f64 1/20160 (pow.f64 x 8)) (pow.f64 x 2))))

Outputs
(*.f64 1/12 (pow.f64 x 4))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/360 (pow.f64 x 6)))
(fma.f64 1/12 (pow.f64 x 4) (*.f64 1/360 (pow.f64 x 6)))
(fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4)))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/20160 (pow.f64 x 8))))
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8))))
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/20160 (pow.f64 x 8) (*.f64 1/360 (pow.f64 x 6))))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/20160 (pow.f64 x 8))))
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8))))
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/20160 (pow.f64 x 8) (*.f64 1/360 (pow.f64 x 6))))
(*.f64 1/20160 (pow.f64 x 8))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/20160 (pow.f64 x 8)))
(fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))
(fma.f64 1/20160 (pow.f64 x 8) (*.f64 1/360 (pow.f64 x 6)))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/20160 (pow.f64 x 8))))
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8))))
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/20160 (pow.f64 x 8) (*.f64 1/360 (pow.f64 x 6))))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/20160 (pow.f64 x 8))))
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8))))
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/20160 (pow.f64 x 8) (*.f64 1/360 (pow.f64 x 6))))
(*.f64 1/20160 (pow.f64 x 8))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/20160 (pow.f64 x 8)))
(fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))
(fma.f64 1/20160 (pow.f64 x 8) (*.f64 1/360 (pow.f64 x 6)))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/20160 (pow.f64 x 8))))
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8))))
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/20160 (pow.f64 x 8) (*.f64 1/360 (pow.f64 x 6))))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/20160 (pow.f64 x 8))))
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8))))
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/20160 (pow.f64 x 8) (*.f64 1/360 (pow.f64 x 6))))
(*.f64 1/360 (pow.f64 x 6))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/20160 (pow.f64 x 8)))
(fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))
(fma.f64 1/20160 (pow.f64 x 8) (*.f64 1/360 (pow.f64 x 6)))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/20160 (pow.f64 x 8)))
(fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))
(fma.f64 1/20160 (pow.f64 x 8) (*.f64 1/360 (pow.f64 x 6)))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/20160 (pow.f64 x 8)))
(fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))
(fma.f64 1/20160 (pow.f64 x 8) (*.f64 1/360 (pow.f64 x 6)))
(*.f64 1/20160 (pow.f64 x 8))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/20160 (pow.f64 x 8)))
(fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))
(fma.f64 1/20160 (pow.f64 x 8) (*.f64 1/360 (pow.f64 x 6)))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/20160 (pow.f64 x 8)))
(fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))
(fma.f64 1/20160 (pow.f64 x 8) (*.f64 1/360 (pow.f64 x 6)))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/20160 (pow.f64 x 8)))
(fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))
(fma.f64 1/20160 (pow.f64 x 8) (*.f64 1/360 (pow.f64 x 6)))
(*.f64 1/20160 (pow.f64 x 8))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/20160 (pow.f64 x 8)))
(fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))
(fma.f64 1/20160 (pow.f64 x 8) (*.f64 1/360 (pow.f64 x 6)))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/20160 (pow.f64 x 8)))
(fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))
(fma.f64 1/20160 (pow.f64 x 8) (*.f64 1/360 (pow.f64 x 6)))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/20160 (pow.f64 x 8)))
(fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))
(fma.f64 1/20160 (pow.f64 x 8) (*.f64 1/360 (pow.f64 x 6)))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2))
(fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (pow.f64 x 2)))
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 x x)))
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))
(fma.f64 1/360 (pow.f64 x 6) (fma.f64 1/12 (pow.f64 x 4) (*.f64 x x)))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (*.f64 1/20160 (pow.f64 x 8)) (pow.f64 x 2))))
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 1/20160 (pow.f64 x 8) (*.f64 x x))))
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
(fma.f64 1/360 (pow.f64 x 6) (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/20160 (pow.f64 x 8) (*.f64 x x))))
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))))
(fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (*.f64 1/20160 (pow.f64 x 8)))))
(fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))))
(*.f64 1/20160 (pow.f64 x 8))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/20160 (pow.f64 x 8)))
(fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))
(fma.f64 1/20160 (pow.f64 x 8) (*.f64 1/360 (pow.f64 x 6)))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/20160 (pow.f64 x 8))))
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8))))
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/20160 (pow.f64 x 8) (*.f64 1/360 (pow.f64 x 6))))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (*.f64 1/20160 (pow.f64 x 8)) (pow.f64 x 2))))
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 1/20160 (pow.f64 x 8) (*.f64 x x))))
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
(fma.f64 1/360 (pow.f64 x 6) (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/20160 (pow.f64 x 8) (*.f64 x x))))
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))))
(fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (*.f64 1/20160 (pow.f64 x 8)))))
(fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))))
(*.f64 1/20160 (pow.f64 x 8))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/20160 (pow.f64 x 8)))
(fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))
(fma.f64 1/20160 (pow.f64 x 8) (*.f64 1/360 (pow.f64 x 6)))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/20160 (pow.f64 x 8))))
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8))))
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/20160 (pow.f64 x 8) (*.f64 1/360 (pow.f64 x 6))))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (*.f64 1/20160 (pow.f64 x 8)) (pow.f64 x 2))))
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 1/20160 (pow.f64 x 8) (*.f64 x x))))
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
(fma.f64 1/360 (pow.f64 x 6) (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/20160 (pow.f64 x 8) (*.f64 x x))))
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))))
(fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (*.f64 1/20160 (pow.f64 x 8)))))
(fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))))

prune113.0ms (2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	109	3	112

Error

0.0b

Counts

112 → 3

Alt Table

Status

Error

Program

✓

0.8b

(fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))))

✓

26.2b

(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

▶

26.1b

(/.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (*.f64 (exp.f64 x) 2))) (*.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 3) -8))) (*.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (*.f64 (exp.f64 x) 2)))))

Compiler

Compiled 2554 to 1930 computations (24.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2))))
✓	0.0b	(pow.f64 (exp.f64 x) 2)
✓	0.1b	(pow.f64 (exp.f64 x) 3)
✓	5.7b	(+.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2))) (.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 3) -8)))

series10.0ms (0.2%)

Counts

4 → 32

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2))))
1.0ms	x	@	inf	(+.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2))) (.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 3) -8)))
1.0ms	x	@	-inf	(+.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2))) (.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 3) -8)))
1.0ms	x	@	0	(+.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2))) (.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 3) -8)))
1.0ms	x	@	-inf	(.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2))))

rewrite48.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

187×	`add-sqr-sqrt_binary64`
182×	`pow1_binary64`
180×	`*-un-lft-identity_binary64`
179×	`add-log-exp_binary64`
178×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	67
1	381	61

Stop Event

1×	node limit

Counts

4 → 120

Calls

Call 1

Inputs
(+.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2))) (.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 3) -8)))
(pow.f64 (exp.f64 x) 3)
(pow.f64 (exp.f64 x) 2)
(.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2))))

Outputs
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((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (exp.f64 x) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (exp.f64 x) (exp.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (exp.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (exp.f64 x) 2)) (cbrt.f64 (pow.f64 (exp.f64 x) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (exp.f64 x) 2)) (.f64 (cbrt.f64 (exp.f64 x)) (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (exp.f64 x) 4)) (cbrt.f64 (pow.f64 (exp.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (exp.f64 x)) (pow.f64 (exp.f64 x) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (exp.f64 x) 3/2) (sqrt.f64 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (exp.f64 x) 1) (exp.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (exp.f64 x) (cbrt.f64 (pow.f64 (exp.f64 x) 2))) (cbrt.f64 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (exp.f64 x) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (exp.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (exp.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (exp.f64 x) 6))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (exp.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (+.f64 x x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (exp.f64 x) 2)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (exp.f64 x) 3) (.f64 (fma.f64 (exp.f64 x) 2 4) (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (exp.f64 x) 3) (.f64 (exp.f64 x) (fma.f64 (exp.f64 x) 2 4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (fma.f64 (exp.f64 x) 2 4) (exp.f64 x)) (pow.f64 (exp.f64 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (exp.f64 x) (fma.f64 (exp.f64 x) 2 4)) (pow.f64 (exp.f64 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (+.f64 (pow.f64 (exp.f64 x) 2) 4) (exp.f64 x)) (.f64 (.f64 (exp.f64 x) 2) (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (pow.f64 (exp.f64 x) 3) 1) (.f64 (.f64 (fma.f64 (exp.f64 x) 2 4) (exp.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (pow.f64 (exp.f64 x) 3) 1) (.f64 (.f64 (exp.f64 x) (fma.f64 (exp.f64 x) 2 4)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 2) 4)) (.f64 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((x fma.f64 (pow.f64 (exp.f64 x) 3/2) (pow.f64 (exp.f64 x) 3/2) (.f64 (fma.f64 (exp.f64 x) 2 4) (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (exp.f64 x) 3/2) (pow.f64 (exp.f64 x) 3/2) (.f64 (exp.f64 x) (fma.f64 (exp.f64 x) 2 4)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (pow.f64 (exp.f64 x) 3) (.f64 (fma.f64 (exp.f64 x) 2 4) (exp.f64 x)))))))))

simplify36.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

448×	`associate-l_binary64`
446×	`distribute-rgt-out_binary64`
437×	`distribute-lft-out_binary64`
368×	`fma-def_binary64`
316×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	66	558
1	183	537
2	477	478
3	1488	476
4	3249	476

Stop Event

1×	node limit

Counts

152 → 152

Calls

Call 1

Inputs
(*.f64 7 (pow.f64 x 2))
(+.f64 (.f64 7 (pow.f64 x 2)) (.f64 11 (pow.f64 x 3)))
(+.f64 (.f64 133/12 (pow.f64 x 4)) (+.f64 (.f64 7 (pow.f64 x 2)) (*.f64 11 (pow.f64 x 3))))
(+.f64 (.f64 133/12 (pow.f64 x 4)) (+.f64 (.f64 35/4 (pow.f64 x 5)) (+.f64 (.f64 7 (pow.f64 x 2)) (.f64 11 (pow.f64 x 3)))))
(-.f64 (+.f64 4 (+.f64 (pow.f64 (exp.f64 x) 4) (pow.f64 (exp.f64 x) 2))) (*.f64 6 (exp.f64 x)))
(-.f64 (+.f64 4 (+.f64 (pow.f64 (exp.f64 x) 4) (pow.f64 (exp.f64 x) 2))) (*.f64 6 (exp.f64 x)))
(-.f64 (+.f64 4 (+.f64 (pow.f64 (exp.f64 x) 4) (pow.f64 (exp.f64 x) 2))) (*.f64 6 (exp.f64 x)))
(-.f64 (+.f64 4 (+.f64 (pow.f64 (exp.f64 x) 4) (pow.f64 (exp.f64 x) 2))) (*.f64 6 (exp.f64 x)))
(-.f64 (+.f64 4 (+.f64 (pow.f64 (exp.f64 x) 4) (pow.f64 (exp.f64 x) 2))) (*.f64 6 (exp.f64 x)))
(-.f64 (+.f64 4 (+.f64 (pow.f64 (exp.f64 x) 4) (pow.f64 (exp.f64 x) 2))) (*.f64 6 (exp.f64 x)))
(-.f64 (+.f64 4 (+.f64 (pow.f64 (exp.f64 x) 4) (pow.f64 (exp.f64 x) 2))) (*.f64 6 (exp.f64 x)))
(-.f64 (+.f64 4 (+.f64 (pow.f64 (exp.f64 x) 4) (pow.f64 (exp.f64 x) 2))) (*.f64 6 (exp.f64 x)))
1
(+.f64 1 (*.f64 3 x))
(+.f64 1 (+.f64 (.f64 9/2 (pow.f64 x 2)) (.f64 3 x)))
(+.f64 1 (+.f64 (.f64 9/2 (pow.f64 x 2)) (+.f64 (.f64 3 x) (*.f64 9/2 (pow.f64 x 3)))))
1
(+.f64 1 (*.f64 2 x))
(+.f64 1 (+.f64 (.f64 2 (pow.f64 x 2)) (.f64 2 x)))
(+.f64 1 (+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 (.f64 2 x) (*.f64 4/3 (pow.f64 x 3)))))
7
(+.f64 7 (*.f64 11 x))
(+.f64 7 (+.f64 (.f64 21/2 (pow.f64 x 2)) (.f64 11 x)))
(+.f64 7 (+.f64 (.f64 21/2 (pow.f64 x 2)) (+.f64 (.f64 11 x) (*.f64 47/6 (pow.f64 x 3)))))
(.f64 (exp.f64 x) (+.f64 4 (+.f64 (.f64 2 (exp.f64 x)) (pow.f64 (exp.f64 x) 2))))
(.f64 (exp.f64 x) (+.f64 4 (+.f64 (.f64 2 (exp.f64 x)) (pow.f64 (exp.f64 x) 2))))
(.f64 (exp.f64 x) (+.f64 4 (+.f64 (.f64 2 (exp.f64 x)) (pow.f64 (exp.f64 x) 2))))
(.f64 (exp.f64 x) (+.f64 4 (+.f64 (.f64 2 (exp.f64 x)) (pow.f64 (exp.f64 x) 2))))
(.f64 (exp.f64 x) (+.f64 4 (+.f64 (.f64 2 (exp.f64 x)) (pow.f64 (exp.f64 x) 2))))
(.f64 (exp.f64 x) (+.f64 4 (+.f64 (.f64 2 (exp.f64 x)) (pow.f64 (exp.f64 x) 2))))
(.f64 (exp.f64 x) (+.f64 4 (+.f64 (.f64 2 (exp.f64 x)) (pow.f64 (exp.f64 x) 2))))
(.f64 (exp.f64 x) (+.f64 4 (+.f64 (.f64 2 (exp.f64 x)) (pow.f64 (exp.f64 x) 2))))

Outputs
(*.f64 7 (pow.f64 x 2))
(.f64 7 (.f64 x x))
(+.f64 (.f64 7 (pow.f64 x 2)) (.f64 11 (pow.f64 x 3)))
(fma.f64 7 (.f64 x x) (.f64 11 (pow.f64 x 3)))
(.f64 (.f64 x x) (fma.f64 x 11 7))
(.f64 x (.f64 x (fma.f64 x 11 7)))
(+.f64 (.f64 133/12 (pow.f64 x 4)) (+.f64 (.f64 7 (pow.f64 x 2)) (*.f64 11 (pow.f64 x 3))))
(fma.f64 133/12 (pow.f64 x 4) (fma.f64 7 (.f64 x x) (.f64 11 (pow.f64 x 3))))
(fma.f64 133/12 (pow.f64 x 4) (.f64 (.f64 x x) (fma.f64 x 11 7)))
(fma.f64 133/12 (pow.f64 x 4) (.f64 x (.f64 x (fma.f64 x 11 7))))
(+.f64 (.f64 133/12 (pow.f64 x 4)) (+.f64 (.f64 35/4 (pow.f64 x 5)) (+.f64 (.f64 7 (pow.f64 x 2)) (.f64 11 (pow.f64 x 3)))))
(fma.f64 133/12 (pow.f64 x 4) (fma.f64 35/4 (pow.f64 x 5) (fma.f64 7 (.f64 x x) (.f64 11 (pow.f64 x 3)))))
(fma.f64 35/4 (pow.f64 x 5) (fma.f64 133/12 (pow.f64 x 4) (.f64 (.f64 x x) (fma.f64 x 11 7))))
(fma.f64 133/12 (pow.f64 x 4) (fma.f64 35/4 (pow.f64 x 5) (.f64 (.f64 x x) (fma.f64 x 11 7))))
(fma.f64 133/12 (pow.f64 x 4) (fma.f64 35/4 (pow.f64 x 5) (.f64 x (.f64 x (fma.f64 x 11 7)))))
(-.f64 (+.f64 4 (+.f64 (pow.f64 (exp.f64 x) 4) (pow.f64 (exp.f64 x) 2))) (*.f64 6 (exp.f64 x)))
(+.f64 4 (-.f64 (+.f64 (pow.f64 (exp.f64 x) 4) (pow.f64 (exp.f64 x) 2)) (*.f64 (exp.f64 x) 6)))
(+.f64 4 (+.f64 (pow.f64 (exp.f64 x) 4) (-.f64 (pow.f64 (exp.f64 x) 2) (*.f64 (exp.f64 x) 6))))
(+.f64 (+.f64 4 (pow.f64 (exp.f64 x) 4)) (*.f64 (exp.f64 x) (-.f64 (exp.f64 x) 6)))
(+.f64 (pow.f64 (exp.f64 x) 4) (+.f64 4 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) -6))))
(-.f64 (+.f64 4 (+.f64 (pow.f64 (exp.f64 x) 4) (pow.f64 (exp.f64 x) 2))) (*.f64 6 (exp.f64 x)))
(+.f64 4 (-.f64 (+.f64 (pow.f64 (exp.f64 x) 4) (pow.f64 (exp.f64 x) 2)) (*.f64 (exp.f64 x) 6)))
(+.f64 4 (+.f64 (pow.f64 (exp.f64 x) 4) (-.f64 (pow.f64 (exp.f64 x) 2) (*.f64 (exp.f64 x) 6))))
(+.f64 (+.f64 4 (pow.f64 (exp.f64 x) 4)) (*.f64 (exp.f64 x) (-.f64 (exp.f64 x) 6)))
(+.f64 (pow.f64 (exp.f64 x) 4) (+.f64 4 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) -6))))
(-.f64 (+.f64 4 (+.f64 (pow.f64 (exp.f64 x) 4) (pow.f64 (exp.f64 x) 2))) (*.f64 6 (exp.f64 x)))
(+.f64 4 (-.f64 (+.f64 (pow.f64 (exp.f64 x) 4) (pow.f64 (exp.f64 x) 2)) (*.f64 (exp.f64 x) 6)))
(+.f64 4 (+.f64 (pow.f64 (exp.f64 x) 4) (-.f64 (pow.f64 (exp.f64 x) 2) (*.f64 (exp.f64 x) 6))))
(+.f64 (+.f64 4 (pow.f64 (exp.f64 x) 4)) (*.f64 (exp.f64 x) (-.f64 (exp.f64 x) 6)))
(+.f64 (pow.f64 (exp.f64 x) 4) (+.f64 4 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) -6))))
(-.f64 (+.f64 4 (+.f64 (pow.f64 (exp.f64 x) 4) (pow.f64 (exp.f64 x) 2))) (*.f64 6 (exp.f64 x)))
(+.f64 4 (-.f64 (+.f64 (pow.f64 (exp.f64 x) 4) (pow.f64 (exp.f64 x) 2)) (*.f64 (exp.f64 x) 6)))
(+.f64 4 (+.f64 (pow.f64 (exp.f64 x) 4) (-.f64 (pow.f64 (exp.f64 x) 2) (*.f64 (exp.f64 x) 6))))
(+.f64 (+.f64 4 (pow.f64 (exp.f64 x) 4)) (*.f64 (exp.f64 x) (-.f64 (exp.f64 x) 6)))
(+.f64 (pow.f64 (exp.f64 x) 4) (+.f64 4 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) -6))))
(-.f64 (+.f64 4 (+.f64 (pow.f64 (exp.f64 x) 4) (pow.f64 (exp.f64 x) 2))) (*.f64 6 (exp.f64 x)))
(+.f64 4 (-.f64 (+.f64 (pow.f64 (exp.f64 x) 4) (pow.f64 (exp.f64 x) 2)) (*.f64 (exp.f64 x) 6)))
(+.f64 4 (+.f64 (pow.f64 (exp.f64 x) 4) (-.f64 (pow.f64 (exp.f64 x) 2) (*.f64 (exp.f64 x) 6))))
(+.f64 (+.f64 4 (pow.f64 (exp.f64 x) 4)) (*.f64 (exp.f64 x) (-.f64 (exp.f64 x) 6)))
(+.f64 (pow.f64 (exp.f64 x) 4) (+.f64 4 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) -6))))
(-.f64 (+.f64 4 (+.f64 (pow.f64 (exp.f64 x) 4) (pow.f64 (exp.f64 x) 2))) (*.f64 6 (exp.f64 x)))
(+.f64 4 (-.f64 (+.f64 (pow.f64 (exp.f64 x) 4) (pow.f64 (exp.f64 x) 2)) (*.f64 (exp.f64 x) 6)))
(+.f64 4 (+.f64 (pow.f64 (exp.f64 x) 4) (-.f64 (pow.f64 (exp.f64 x) 2) (*.f64 (exp.f64 x) 6))))
(+.f64 (+.f64 4 (pow.f64 (exp.f64 x) 4)) (*.f64 (exp.f64 x) (-.f64 (exp.f64 x) 6)))
(+.f64 (pow.f64 (exp.f64 x) 4) (+.f64 4 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) -6))))
(-.f64 (+.f64 4 (+.f64 (pow.f64 (exp.f64 x) 4) (pow.f64 (exp.f64 x) 2))) (*.f64 6 (exp.f64 x)))
(+.f64 4 (-.f64 (+.f64 (pow.f64 (exp.f64 x) 4) (pow.f64 (exp.f64 x) 2)) (*.f64 (exp.f64 x) 6)))
(+.f64 4 (+.f64 (pow.f64 (exp.f64 x) 4) (-.f64 (pow.f64 (exp.f64 x) 2) (*.f64 (exp.f64 x) 6))))
(+.f64 (+.f64 4 (pow.f64 (exp.f64 x) 4)) (*.f64 (exp.f64 x) (-.f64 (exp.f64 x) 6)))
(+.f64 (pow.f64 (exp.f64 x) 4) (+.f64 4 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) -6))))
(-.f64 (+.f64 4 (+.f64 (pow.f64 (exp.f64 x) 4) (pow.f64 (exp.f64 x) 2))) (*.f64 6 (exp.f64 x)))
(+.f64 4 (-.f64 (+.f64 (pow.f64 (exp.f64 x) 4) (pow.f64 (exp.f64 x) 2)) (*.f64 (exp.f64 x) 6)))
(+.f64 4 (+.f64 (pow.f64 (exp.f64 x) 4) (-.f64 (pow.f64 (exp.f64 x) 2) (*.f64 (exp.f64 x) 6))))
(+.f64 (+.f64 4 (pow.f64 (exp.f64 x) 4)) (*.f64 (exp.f64 x) (-.f64 (exp.f64 x) 6)))
(+.f64 (pow.f64 (exp.f64 x) 4) (+.f64 4 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) -6))))
1
(+.f64 1 (*.f64 3 x))
(+.f64 1 (*.f64 x 3))
(fma.f64 x 3 1)
(+.f64 1 (+.f64 (.f64 9/2 (pow.f64 x 2)) (.f64 3 x)))
(+.f64 1 (fma.f64 9/2 (.f64 x x) (.f64 x 3)))
(+.f64 (.f64 x (.f64 x 9/2)) (fma.f64 x 3 1))
(fma.f64 x 3 (fma.f64 x (*.f64 x 9/2) 1))
(+.f64 1 (+.f64 (.f64 9/2 (pow.f64 x 2)) (+.f64 (.f64 3 x) (*.f64 9/2 (pow.f64 x 3)))))
(+.f64 1 (fma.f64 9/2 (.f64 x x) (fma.f64 3 x (.f64 (pow.f64 x 3) 9/2))))
(+.f64 1 (fma.f64 (.f64 x x) 9/2 (fma.f64 (pow.f64 x 3) 9/2 (.f64 x 3))))
(+.f64 1 (fma.f64 x 3 (.f64 (.f64 x 9/2) (fma.f64 x x x))))
(+.f64 1 (.f64 x (+.f64 3 (.f64 9/2 (fma.f64 x x x)))))
1
(+.f64 1 (*.f64 2 x))
(+.f64 1 (*.f64 x 2))
(fma.f64 x 2 1)
(+.f64 1 (+.f64 (.f64 2 (pow.f64 x 2)) (.f64 2 x)))
(+.f64 1 (.f64 2 (+.f64 (.f64 x x) x)))
(fma.f64 2 (fma.f64 x x x) 1)
(+.f64 1 (+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 (.f64 2 x) (*.f64 4/3 (pow.f64 x 3)))))
(+.f64 1 (fma.f64 2 (.f64 x x) (fma.f64 2 x (.f64 (pow.f64 x 3) 4/3))))
(+.f64 1 (fma.f64 2 (fma.f64 x x x) (*.f64 (pow.f64 x 3) 4/3)))
(fma.f64 2 (fma.f64 x x x) (fma.f64 (pow.f64 x 3) 4/3 1))
7
(+.f64 7 (*.f64 11 x))
(+.f64 7 (*.f64 x 11))
(fma.f64 x 11 7)
(+.f64 7 (+.f64 (.f64 21/2 (pow.f64 x 2)) (.f64 11 x)))
(+.f64 7 (fma.f64 21/2 (.f64 x x) (.f64 x 11)))
(+.f64 7 (fma.f64 (.f64 x x) 21/2 (.f64 x 11)))
(fma.f64 x 11 (fma.f64 x (*.f64 x 21/2) 7))
(+.f64 7 (+.f64 (.f64 21/2 (pow.f64 x 2)) (+.f64 (.f64 11 x) (*.f64 47/6 (pow.f64 x 3)))))
(+.f64 7 (fma.f64 21/2 (.f64 x x) (fma.f64 11 x (.f64 (pow.f64 x 3) 47/6))))
(+.f64 7 (fma.f64 (.f64 x x) 21/2 (fma.f64 x 11 (.f64 (pow.f64 x 3) 47/6))))
(+.f64 (.f64 x (+.f64 11 (.f64 x 21/2))) (fma.f64 (pow.f64 x 3) 47/6 7))
(+.f64 7 (.f64 x (+.f64 11 (.f64 x (+.f64 21/2 (*.f64 x 47/6))))))
(.f64 (exp.f64 x) (+.f64 4 (+.f64 (.f64 2 (exp.f64 x)) (pow.f64 (exp.f64 x) 2))))
(*.f64 (exp.f64 x) (+.f64 4 (fma.f64 2 (exp.f64 x) (pow.f64 (exp.f64 x) 2))))
(.f64 (exp.f64 x) (+.f64 4 (.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)))))
(*.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)) 4))
(.f64 (exp.f64 x) (+.f64 4 (+.f64 (.f64 2 (exp.f64 x)) (pow.f64 (exp.f64 x) 2))))
(*.f64 (exp.f64 x) (+.f64 4 (fma.f64 2 (exp.f64 x) (pow.f64 (exp.f64 x) 2))))
(.f64 (exp.f64 x) (+.f64 4 (.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)))))
(*.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)) 4))
(.f64 (exp.f64 x) (+.f64 4 (+.f64 (.f64 2 (exp.f64 x)) (pow.f64 (exp.f64 x) 2))))
(*.f64 (exp.f64 x) (+.f64 4 (fma.f64 2 (exp.f64 x) (pow.f64 (exp.f64 x) 2))))
(.f64 (exp.f64 x) (+.f64 4 (.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)))))
(*.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)) 4))
(.f64 (exp.f64 x) (+.f64 4 (+.f64 (.f64 2 (exp.f64 x)) (pow.f64 (exp.f64 x) 2))))
(*.f64 (exp.f64 x) (+.f64 4 (fma.f64 2 (exp.f64 x) (pow.f64 (exp.f64 x) 2))))
(.f64 (exp.f64 x) (+.f64 4 (.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)))))
(*.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)) 4))
(.f64 (exp.f64 x) (+.f64 4 (+.f64 (.f64 2 (exp.f64 x)) (pow.f64 (exp.f64 x) 2))))
(*.f64 (exp.f64 x) (+.f64 4 (fma.f64 2 (exp.f64 x) (pow.f64 (exp.f64 x) 2))))
(.f64 (exp.f64 x) (+.f64 4 (.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)))))
(*.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)) 4))
(.f64 (exp.f64 x) (+.f64 4 (+.f64 (.f64 2 (exp.f64 x)) (pow.f64 (exp.f64 x) 2))))
(*.f64 (exp.f64 x) (+.f64 4 (fma.f64 2 (exp.f64 x) (pow.f64 (exp.f64 x) 2))))
(.f64 (exp.f64 x) (+.f64 4 (.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)))))
(*.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)) 4))
(.f64 (exp.f64 x) (+.f64 4 (+.f64 (.f64 2 (exp.f64 x)) (pow.f64 (exp.f64 x) 2))))
(*.f64 (exp.f64 x) (+.f64 4 (fma.f64 2 (exp.f64 x) (pow.f64 (exp.f64 x) 2))))
(.f64 (exp.f64 x) (+.f64 4 (.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)))))
(*.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)) 4))
(.f64 (exp.f64 x) (+.f64 4 (+.f64 (.f64 2 (exp.f64 x)) (pow.f64 (exp.f64 x) 2))))
(*.f64 (exp.f64 x) (+.f64 4 (fma.f64 2 (exp.f64 x) (pow.f64 (exp.f64 x) 2))))
(.f64 (exp.f64 x) (+.f64 4 (.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)))))
(*.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)) 4))

prune222.0ms (3.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	175	1	176
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	176	3	179

Error

0.0b

Counts

179 → 3

Alt Table

Status

Error

Program

✓

0.8b

(fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))))

✓

26.2b

(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

▶

26.1b

(/.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (*.f64 (exp.f64 x) 2))) (*.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 3) -8))) (+.f64 (*.f64 (+.f64 (pow.f64 (exp.f64 x) 2) 4) (exp.f64 x)) (*.f64 (*.f64 (exp.f64 x) 2) (exp.f64 x))))

Compiler

Compiled 7512 to 4676 computations (37.8% saved)

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 (exp.f64 x) 2) (exp.f64 x))
	0.0b	(pow.f64 (exp.f64 x) 2)
	0.1b	(pow.f64 (exp.f64 x) 3)
	5.7b	(+.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2))) (.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 3) -8)))

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(.f64 (.f64 (exp.f64 x) 2) (exp.f64 x))
0.0ms	x	@	0	(.f64 (.f64 (exp.f64 x) 2) (exp.f64 x))
0.0ms	x	@	-inf	(.f64 (.f64 (exp.f64 x) 2) (exp.f64 x))

rewrite31.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

513×	`pow1_binary64`
471×	`add-log-exp_binary64`
471×	`log1p-expm1-u_binary64`
471×	`expm1-log1p-u_binary64`
461×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	117	9
2	1309	9

Stop Event

1×	node limit

Counts

1 → 13

Calls

Call 1

Inputs
(.f64 (.f64 (exp.f64 x) 2) (exp.f64 x))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 2 (pow.f64 (exp.f64 x) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (pow.f64 (exp.f64 x) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (pow.f64 (exp.f64 x) 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 2 (pow.f64 (exp.f64 x) 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 2 (pow.f64 (exp.f64 x) 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 2 (pow.f64 (exp.f64 x) 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 2 (pow.f64 (exp.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 2 (pow.f64 (exp.f64 x) 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (*.f64 (exp.f64 x) 2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 2 (pow.f64 (exp.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 x (+.f64 x (log.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 2 (pow.f64 (exp.f64 x) 2))))))))

simplify40.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

654×	`unswap-sqr_binary64`
629×	`associate-l_binary64`
523×	`fma-def_binary64`
368×	`associate-r_binary64`
234×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	20	114
1	54	105
2	129	103
3	352	103
4	909	100
5	2836	100
6	4712	100

Stop Event

1×	node limit

Counts

25 → 21

Calls

Call 1

Inputs
2
(+.f64 2 (*.f64 4 x))
(+.f64 2 (+.f64 (.f64 4 (pow.f64 x 2)) (.f64 4 x)))
(+.f64 2 (+.f64 (.f64 4 (pow.f64 x 2)) (+.f64 (.f64 4 x) (*.f64 8/3 (pow.f64 x 3)))))
(*.f64 2 (pow.f64 (exp.f64 x) 2))
(*.f64 2 (pow.f64 (exp.f64 x) 2))
(*.f64 2 (pow.f64 (exp.f64 x) 2))
(*.f64 2 (pow.f64 (exp.f64 x) 2))
(*.f64 2 (pow.f64 (exp.f64 x) 2))
(*.f64 2 (pow.f64 (exp.f64 x) 2))
(*.f64 2 (pow.f64 (exp.f64 x) 2))
(*.f64 2 (pow.f64 (exp.f64 x) 2))

Outputs
2
(+.f64 2 (*.f64 4 x))
(fma.f64 4 x 2)
(+.f64 2 (+.f64 (.f64 4 (pow.f64 x 2)) (.f64 4 x)))
(+.f64 2 (.f64 4 (+.f64 (.f64 x x) x)))
(fma.f64 4 (fma.f64 x x x) 2)
(fma.f64 x (fma.f64 4 x 4) 2)
(+.f64 2 (+.f64 (.f64 4 (pow.f64 x 2)) (+.f64 (.f64 4 x) (*.f64 8/3 (pow.f64 x 3)))))
(+.f64 2 (fma.f64 4 (.f64 x x) (fma.f64 4 x (.f64 8/3 (pow.f64 x 3)))))
(+.f64 (fma.f64 4 (fma.f64 x x x) 2) (*.f64 8/3 (pow.f64 x 3)))
(fma.f64 4 (fma.f64 x x x) (fma.f64 8/3 (pow.f64 x 3) 2))
(fma.f64 x (fma.f64 x (fma.f64 x 8/3 4) 4) 2)
(*.f64 2 (pow.f64 (exp.f64 x) 2))
(*.f64 2 (pow.f64 (exp.f64 x) 2))
(*.f64 2 (pow.f64 (exp.f64 x) 2))
(*.f64 2 (pow.f64 (exp.f64 x) 2))
(*.f64 2 (pow.f64 (exp.f64 x) 2))
(*.f64 2 (pow.f64 (exp.f64 x) 2))
(*.f64 2 (pow.f64 (exp.f64 x) 2))
(*.f64 2 (pow.f64 (exp.f64 x) 2))

prune169.0ms (3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	149	3	152

Error

0.0b

Counts

152 → 3

Alt Table

Status

Error

Program

✓

0.8b

(fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))))

✓

26.2b

(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

✓

26.1b

(/.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (*.f64 (exp.f64 x) 2))) (*.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 3) -8))) (+.f64 (*.f64 (+.f64 (pow.f64 (exp.f64 x) 2) 4) (exp.f64 x)) (*.f64 (*.f64 (exp.f64 x) 2) (exp.f64 x))))

Compiler

Compiled 6783 to 4144 computations (38.9% saved)

regimes44.0ms (0.8%)

Accuracy

Total 0.5b remaining (98.4%)

Threshold costs 0.5b (98.4%)

Counts

39 → 1

Compiler

Compiled 832 to 513 computations (38.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	16	25

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))))

Outputs
(fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))))

end156.0ms (2.7%)

Stop Event

1×

done

Compiler

Compiled 106 to 74 computations (30.2% saved)

Details

analyze4.0ms (0.1%)

sample4.4s (77.8%)

preprocess32.0ms (0.6%)

simplify28.0ms (0.5%)

prune3.0ms (0%)

localize5.0ms (0.1%)

series3.0ms (0%)

rewrite44.0ms (0.8%)

simplify30.0ms (0.5%)

prune73.0ms (1.3%)

localize10.0ms (0.2%)

series6.0ms (0.1%)

rewrite57.0ms (1%)

simplify58.0ms (1%)

prune113.0ms (2%)

localize12.0ms (0.2%)

series10.0ms (0.2%)

rewrite48.0ms (0.8%)

simplify36.0ms (0.6%)

prune222.0ms (3.9%)

localize24.0ms (0.4%)

series2.0ms (0%)

rewrite31.0ms (0.6%)

simplify40.0ms (0.7%)

prune169.0ms (3%)

regimes44.0ms (0.8%)

simplify2.0ms (0%)

end156.0ms (2.7%)

Profiling