Details

analyze4.0ms (0%)

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

Compiler

Compiled 10 to 8 computations (20% saved)

sample6.0s (53.1%)

Results

4.1s	4351×	body	2048	valid
1.3s	2033×	body	1024	valid
485.0ms	1035×	body	512	valid
96.0ms	837×	body	256	valid
2.0ms	15×	body	256	invalid

preprocess117.0ms (1%)

Algorithm

2×	egg-herbie

Rules

801×	`associate-/l*_binary64`
624×	`fma-def_binary64`
581×	`fma-neg_binary64`
548×	`unswap-sqr_binary64`
536×	`div-sub_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	273	13
6	709	13
7	1729	13
8	3145	13
9	7605	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))
(+.f64 -2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 10 to 8 computations (20% saved)

simplify83.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

801×	`associate-/l*_binary64`
624×	`fma-def_binary64`
581×	`fma-neg_binary64`
548×	`unswap-sqr_binary64`
536×	`div-sub_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	273	13
6	709	13
7	1729	13
8	3145	13
9	7605	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))
(+.f64 -2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

eval1.0ms (0%)

Compiler: Compiled 17 to 10 computations (41.2% saved)

prune1.0ms (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

28.7b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	28.8b	(+.f64 -2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	28.8b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
✓	3.3b	(+.f64 -2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 24 to 8 computations (66.7% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite126.0ms (1.1%)

Algorithm

2×	egg-rewrite-iter-limit
2×	egg-rewrite
1×	batch-egg-rewrite

Rules

96×	`add-sqr-sqrt_binary64`
96×	`add-sqr-sqrt_binary64`
92×	`add-log-exp_binary64`
92×	`add-log-exp_binary64`
90×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	182	18
2	3153	18
0	8	9
1	182	9
2	3153	9
0	8	9
0	6	6
1	129	6
2	2150	6
0	6	6

Stop Event

1×	iter limit
1×	unsound
1×	iter limit
1×	unsound
1×	unsound

Counts

2 → 23

Calls

Call 1

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

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

Outputs

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

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

simplify62.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

560×	`distribute-rgt-out_binary64`
421×	`associate-/l/_binary64`
415×	`unswap-sqr_binary64`
410×	`fma-def_binary64`
382×	`distribute-lft-out_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	34	295
1	85	283
2	186	279
3	525	279
4	2241	279
5	4801	279
6	5972	279

Stop Event

1×	node limit

Counts

47 → 43

Calls

Call 1

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

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

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (exp.f64 x) 2)
✓	4.3b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Compiler

Compiled 22 to 10 computations (54.5% saved)

series2.0ms (0%)

Counts

2 → 16

Calls

6 calls:

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

rewrite71.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

869×	`pow1_binary64`
818×	`add-log-exp_binary64`
815×	`log1p-expm1-u_binary64`
815×	`expm1-log1p-u_binary64`
804×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	181	17
2	2653	17

Stop Event

1×	node limit

Counts

2 → 74

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

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

simplify39.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

749×	`unswap-sqr_binary64`
682×	`distribute-rgt-out_binary64`
678×	`distribute-lft-out_binary64`
573×	`associate-l_binary64`
555×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	43	202
1	107	196
2	240	196
3	753	191
4	3557	191

Stop Event

1×	node limit

Counts

90 → 92

Calls

Call 1

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

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

eval58.0ms (0.5%)

Compiler: Compiled 1887 to 1095 computations (42% saved)

prune23.0ms (0.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	127	8	135
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	129	8	137

Error

0.0b

Counts

137 → 8

Alt Table

Click to see full alt table

Status	Error	Program
	0.6b	(fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))
▶	28.8b	(/.f64 (-.f64 4 (.f64 (.f64 2 (cosh.f64 x)) (.f64 2 (cosh.f64 x)))) (-.f64 -2 (.f64 2 (cosh.f64 x))))
▶	28.8b	(+.f64 -2 (*.f64 2 (cosh.f64 x)))
▶	0.9b	(*.f64 x x)
	29.8b	(+.f64 -1 (exp.f64 (neg.f64 x)))
▶	28.8b	(expm1.f64 (log1p.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))))
▶	0.5b	(fma.f64 x x (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4))))
	0.5b	(+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (.f64 1/12 (pow.f64 x 4))))

Compiler

Compiled 168 to 128 computations (23.8% saved)

localize56.0ms (0.5%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 40 to 30 computations (25% saved)

series4.0ms (0%)

Counts

2 → 12

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(*.f64 1/12 (pow.f64 x 4))
1.0ms	x	@	-inf	(fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4)))
1.0ms	x	@	inf	(fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4)))
1.0ms	x	@	inf	(*.f64 1/12 (pow.f64 x 4))
0.0ms	x	@	0	(fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4)))

rewrite98.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

825×	`pow1_binary64`
776×	`add-log-exp_binary64`
776×	`log1p-expm1-u_binary64`
776×	`expm1-log1p-u_binary64`
760×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	214	21
2	2255	21

Stop Event

1×	node limit

Counts

2 → 32

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 1/12 (pow.f64 x 4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/12 (pow.f64 x 4)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 1/12 (pow.f64 x 4)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 1/12 (pow.f64 x 4))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 x x) (sqrt.f64 1/12)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 8) 1/144))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/12) (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 1/12 (pow.f64 x 4)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 1/12 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 1/12 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 1/12 (pow.f64 x 4))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/360 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 1/360 (pow.f64 x 6)) 1) (*.f64 1/12 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4)))) (pow.f64 (cbrt.f64 (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4)))) 2) (cbrt.f64 (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4)))) (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 1/360 (pow.f64 x 6)) 3) (pow.f64 (*.f64 1/12 (pow.f64 x 4)) 3)) (+.f64 (*.f64 (*.f64 1/360 (pow.f64 x 6)) (*.f64 1/360 (pow.f64 x 6))) (-.f64 (*.f64 (pow.f64 x 8) 1/144) (*.f64 (*.f64 1/360 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 1/360 (pow.f64 x 6)) (*.f64 1/360 (pow.f64 x 6))) (*.f64 (pow.f64 x 8) 1/144)) (-.f64 (*.f64 1/360 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4)))))))))

simplify138.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

811×	`sqr-pow_binary64`
580×	`cube-prod_binary64`
503×	`associate-l_binary64`
467×	`unswap-sqr_binary64`
440×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	147
1	23	147
2	48	147
3	117	147
4	391	147
5	1750	147
6	3196	147
7	3534	147
8	3804	147
9	4068	147
10	4414	147
11	4871	147
12	5439	147
13	6084	147
14	6848	147
15	7295	147
16	7793	147

Stop Event

1×	node limit

Counts

44 → 35

Calls

Call 1

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

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

localize2.0ms (0%)

Compiler: Compiled 5 to 2 computations (60% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.3b	(+.f64 -2 (*.f64 2 (cosh.f64 x)))

Compiler

Compiled 16 to 10 computations (37.5% saved)

series3.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(+.f64 -2 (*.f64 2 (cosh.f64 x)))
1.0ms	x	@	inf	(+.f64 -2 (*.f64 2 (cosh.f64 x)))
1.0ms	x	@	0	(+.f64 -2 (*.f64 2 (cosh.f64 x)))

rewrite61.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

754×	`pow1_binary64`
704×	`add-log-exp_binary64`
702×	`log1p-expm1-u_binary64`
702×	`expm1-log1p-u_binary64`
692×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	154	7
2	1888	7

Stop Event

1×	node limit

Counts

1 → 32

Calls

Call 1

Inputs
(+.f64 -2 (*.f64 2 (cosh.f64 x)))

Outputs

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

simplify68.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

508×	`distribute-rgt-out_binary64`
413×	`unswap-sqr_binary64`
382×	`distribute-lft-out_binary64`
338×	`associate-l_binary64`
320×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	26	168
1	63	162
2	142	162
3	414	162
4	1949	162
5	4406	162
6	5019	162
7	6528	162

Stop Event

1×	node limit

Counts

44 → 42

Calls

Call 1

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

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

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (log1p.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))))
✓	0.0b	(log1p.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x))))
	3.3b	(+.f64 -2 (*.f64 2 (cosh.f64 x)))

Compiler

Compiled 31 to 21 computations (32.3% saved)

series69.0ms (0.6%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
37.0ms	x	@	inf	(log1p.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x))))
29.0ms	x	@	-inf	(log1p.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x))))
2.0ms	x	@	0	(log1p.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x))))
0.0ms	x	@	0	(expm1.f64 (log1p.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))))
0.0ms	x	@	-inf	(expm1.f64 (log1p.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))))

rewrite72.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

835×	`pow1_binary64`
778×	`add-log-exp_binary64`
777×	`expm1-log1p-u_binary64`
776×	`log1p-expm1-u_binary64`
764×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	175	16
2	2096	16

Stop Event

1×	node limit

Counts

2 → 51

Calls

Call 1

Inputs
(log1p.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x))))
(expm1.f64 (log1p.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))))

Outputs

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

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

simplify101.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

999×	`distribute-rgt-out_binary64`
760×	`distribute-lft-out_binary64`
565×	`fma-def_binary64`
527×	`associate-l_binary64`
419×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	40	346
1	102	316
2	238	316
3	686	316
4	3268	316
5	6730	316
6	7515	316

Stop Event

1×	node limit

Counts

75 → 69

Calls

Call 1

Inputs
(pow.f64 x 2)
(+.f64 (*.f64 -5/12 (pow.f64 x 4)) (pow.f64 x 2))
(+.f64 (.f64 -5/12 (pow.f64 x 4)) (+.f64 (.f64 91/360 (pow.f64 x 6)) (pow.f64 x 2)))
(+.f64 (.f64 -5/12 (pow.f64 x 4)) (+.f64 (.f64 91/360 (pow.f64 x 6)) (+.f64 (*.f64 -697/4032 (pow.f64 x 8)) (pow.f64 x 2))))
(log.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1))
(log.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1))
(log.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1))
(log.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1))
(log.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1))
(log.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1))
(log.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1))
(log.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1))
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) (*.f64 1/12 (pow.f64 x 4)))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (.f64 1/12 (pow.f64 x 4))))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/20160 (pow.f64 x 8)))))
(-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)
(-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)
(-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)
(-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)
(-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)
(-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)
(-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)
(-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)

Outputs
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 -5/12 (pow.f64 x 4)) (pow.f64 x 2))
(fma.f64 -5/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 -5/12 (pow.f64 x 4)))
(+.f64 (.f64 -5/12 (pow.f64 x 4)) (+.f64 (.f64 91/360 (pow.f64 x 6)) (pow.f64 x 2)))
(fma.f64 -5/12 (pow.f64 x 4) (fma.f64 91/360 (pow.f64 x 6) (*.f64 x x)))
(fma.f64 -5/12 (pow.f64 x 4) (fma.f64 x x (*.f64 91/360 (pow.f64 x 6))))
(fma.f64 x x (fma.f64 -5/12 (pow.f64 x 4) (*.f64 91/360 (pow.f64 x 6))))
(+.f64 (.f64 -5/12 (pow.f64 x 4)) (+.f64 (.f64 91/360 (pow.f64 x 6)) (+.f64 (*.f64 -697/4032 (pow.f64 x 8)) (pow.f64 x 2))))
(fma.f64 -5/12 (pow.f64 x 4) (fma.f64 91/360 (pow.f64 x 6) (fma.f64 -697/4032 (pow.f64 x 8) (*.f64 x x))))
(fma.f64 -5/12 (pow.f64 x 4) (fma.f64 91/360 (pow.f64 x 6) (fma.f64 x x (*.f64 -697/4032 (pow.f64 x 8)))))
(fma.f64 x x (fma.f64 -5/12 (pow.f64 x 4) (fma.f64 91/360 (pow.f64 x 6) (*.f64 -697/4032 (pow.f64 x 8)))))
(log.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1))
(log.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1)))
(log.f64 (+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x)))
(log.f64 (+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x))))
(log.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1))
(log.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1)))
(log.f64 (+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x)))
(log.f64 (+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x))))
(log.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1))
(log.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1)))
(log.f64 (+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x)))
(log.f64 (+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x))))
(log.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1))
(log.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1)))
(log.f64 (+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x)))
(log.f64 (+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x))))
(log.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1))
(log.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1)))
(log.f64 (+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x)))
(log.f64 (+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x))))
(log.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1))
(log.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1)))
(log.f64 (+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x)))
(log.f64 (+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x))))
(log.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1))
(log.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1)))
(log.f64 (+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x)))
(log.f64 (+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x))))
(log.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1))
(log.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1)))
(log.f64 (+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x)))
(log.f64 (+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x))))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) (*.f64 1/12 (pow.f64 x 4)))
(+.f64 (.f64 x x) (.f64 (pow.f64 x 4) 1/12))
(fma.f64 x x (*.f64 (pow.f64 x 4) 1/12))
(fma.f64 (pow.f64 x 4) 1/12 (*.f64 x x))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (.f64 1/12 (pow.f64 x 4))))
(fma.f64 1/360 (pow.f64 x 6) (+.f64 (.f64 x x) (.f64 (pow.f64 x 4) 1/12)))
(fma.f64 (pow.f64 x 6) 1/360 (fma.f64 x x (*.f64 (pow.f64 x 4) 1/12)))
(fma.f64 x x (fma.f64 (pow.f64 x 4) 1/12 (*.f64 (pow.f64 x 6) 1/360)))
(fma.f64 (pow.f64 x 4) 1/12 (fma.f64 (pow.f64 x 6) 1/360 (*.f64 x x)))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/20160 (pow.f64 x 8)))))
(fma.f64 1/360 (pow.f64 x 6) (+.f64 (.f64 x x) (fma.f64 1/12 (pow.f64 x 4) (.f64 (pow.f64 x 8) 1/20160))))
(fma.f64 (pow.f64 x 6) 1/360 (fma.f64 x x (fma.f64 (pow.f64 x 4) 1/12 (*.f64 (pow.f64 x 8) 1/20160))))
(fma.f64 (pow.f64 x 6) 1/360 (fma.f64 (pow.f64 x 4) 1/12 (fma.f64 (pow.f64 x 8) 1/20160 (*.f64 x x))))
(fma.f64 (pow.f64 x 4) (fma.f64 (pow.f64 x 4) 1/20160 1/12) (fma.f64 (pow.f64 x 6) 1/360 (*.f64 x x)))
(fma.f64 (pow.f64 x 4) 1/12 (fma.f64 (pow.f64 x 6) 1/360 (fma.f64 (pow.f64 x 8) 1/20160 (*.f64 x x))))
(-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)
(+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 2))
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
(-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)
(+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 2))
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
(-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)
(+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 2))
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
(-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)
(+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 2))
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
(-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)
(+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 2))
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
(-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)
(+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 2))
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
(-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)
(+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 2))
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
(-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)
(+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 2))
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))

localize39.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 -2 (*.f64 2 (cosh.f64 x)))
✓	0.0b	(.f64 (.f64 2 (cosh.f64 x)) (*.f64 2 (cosh.f64 x)))
✓	0.0b	(/.f64 (-.f64 4 (.f64 (.f64 2 (cosh.f64 x)) (.f64 2 (cosh.f64 x)))) (-.f64 -2 (.f64 2 (cosh.f64 x))))
✓	3.3b	(-.f64 4 (.f64 (.f64 2 (cosh.f64 x)) (*.f64 2 (cosh.f64 x))))

Compiler

Compiled 55 to 35 computations (36.4% saved)

series16.0ms (0.1%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
3.0ms	x	@	0	(-.f64 -2 (*.f64 2 (cosh.f64 x)))
2.0ms	x	@	-inf	(/.f64 (-.f64 4 (.f64 (.f64 2 (cosh.f64 x)) (.f64 2 (cosh.f64 x)))) (-.f64 -2 (.f64 2 (cosh.f64 x))))
2.0ms	x	@	inf	(/.f64 (-.f64 4 (.f64 (.f64 2 (cosh.f64 x)) (.f64 2 (cosh.f64 x)))) (-.f64 -2 (.f64 2 (cosh.f64 x))))
2.0ms	x	@	-inf	(-.f64 4 (.f64 (.f64 2 (cosh.f64 x)) (*.f64 2 (cosh.f64 x))))
2.0ms	x	@	inf	(-.f64 4 (.f64 (.f64 2 (cosh.f64 x)) (*.f64 2 (cosh.f64 x))))

rewrite235.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

639×	`log-prod_binary64`
553×	`prod-diff_binary64`
323×	`pow2_binary64`
253×	`fma-def_binary64`
223×	`pow1/3_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	53
1	262	39
2	3642	33

Stop Event

1×	node limit

Counts

4 → 317

Calls

Call 1

Inputs
(-.f64 4 (.f64 (.f64 2 (cosh.f64 x)) (*.f64 2 (cosh.f64 x))))
(/.f64 (-.f64 4 (.f64 (.f64 2 (cosh.f64 x)) (.f64 2 (cosh.f64 x)))) (-.f64 -2 (.f64 2 (cosh.f64 x))))
(.f64 (.f64 2 (cosh.f64 x)) (*.f64 2 (cosh.f64 x)))
(-.f64 -2 (*.f64 2 (cosh.f64 x)))

Outputs
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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 4 (pow.f64 (cosh.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 4) (pow.f64 (cosh.f64 x) 2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 4) (pow.f64 (cosh.f64 x) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 4) (pow.f64 (cosh.f64 x) 2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 4) (pow.f64 (cosh.f64 x) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 4 (pow.f64 (cosh.f64 x) 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (.f64 (cosh.f64 x) 4) (.f64 2 (cosh.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 2 (cosh.f64 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 4 (pow.f64 (cosh.f64 x) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (.f64 2 (cosh.f64 x))) 2) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 2 (cosh.f64 x)) 6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 2 (cosh.f64 x)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 4) (pow.f64 (cosh.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 4 (pow.f64 (cosh.f64 x) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 2 (cosh.f64 x)) 6))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 4 (pow.f64 (cosh.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 4 (pow.f64 (cosh.f64 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 2 (log.f64 (.f64 2 (cosh.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 2 (cosh.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 2 (log.f64 (*.f64 2 (cosh.f64 x)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 -2 (.f64 (cosh.f64 x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -2 (.f64 (.f64 (cosh.f64 x) -2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (cosh.f64 x) -2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (fma.f64 (cosh.f64 x) -2 -2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 (cosh.f64 x) -2 -2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 (cosh.f64 x) -2 -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 (cosh.f64 x) -2 -2)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 (cosh.f64 x) -2 -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 -4 (pow.f64 (cosh.f64 x) 2) 4) (/.f64 1 (fma.f64 2 (cosh.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 (cosh.f64 x) -2 -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 (cosh.f64 x) -2 -2))))) (#(struct:change #<rule egg-rr> (2) ((x 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(-.f64 -8 (.f64 (pow.f64 (cosh.f64 x) 3) 8))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 2 (cosh.f64 x) -2) (fma.f64 -4 (pow.f64 (cosh.f64 x) 2) 4)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 (cosh.f64 x) -2 -2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 (cosh.f64 x) -2 -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 (cosh.f64 x) -2 -2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 (cosh.f64 x) -2 -2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 (cosh.f64 x) -2 -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 (cosh.f64 x) -2 -2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 (cosh.f64 x) -2 -2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (fma.f64 (cosh.f64 x) -2 -2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 2 (neg.f64 (cosh.f64 x)) -2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cosh.f64 x) -2 -2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -2 (cosh.f64 x) -2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 (cosh.f64 x) -2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (.f64 2 (cosh.f64 x))) 2) (neg.f64 (cbrt.f64 (.f64 2 (cosh.f64 x)))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (.f64 2 (cosh.f64 x))) (neg.f64 (sqrt.f64 (.f64 2 (cosh.f64 x)))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (.f64 (cosh.f64 x) -2)) 2) (cbrt.f64 (.f64 (cosh.f64 x) -2)) -2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (.f64 (cosh.f64 x) -2)) (sqrt.f64 (.f64 (cosh.f64 x) -2)) -2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (.f64 2 (cosh.f64 x)) -2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (cosh.f64 x)) 2 -2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (pow.f64 (cbrt.f64 (.f64 2 (cosh.f64 x))) 2)) (cbrt.f64 (.f64 2 (cosh.f64 x))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (sqrt.f64 (.f64 2 (cosh.f64 x)))) (sqrt.f64 (.f64 2 (cosh.f64 x))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 -2 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2)) (cbrt.f64 (cosh.f64 x)) -2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -2 (sqrt.f64 (cosh.f64 x))) (sqrt.f64 (cosh.f64 x)) -2)))))

simplify102.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

640×	`distribute-lft-out_binary64`
458×	`fma-neg_binary64`
370×	`*-commutative_binary64`
321×	`cancel-sign-sub-inv_binary64`
295×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	68	850
1	181	839
2	456	817
3	1538	801
4	3263	801
5	7918	801

Stop Event

1×	node limit

Counts

365 → 355

Calls

Call 1

Inputs
(*.f64 -4 (pow.f64 x 2))
(+.f64 (.f64 -4 (pow.f64 x 2)) (.f64 -4/3 (pow.f64 x 4)))
(+.f64 (.f64 -4 (pow.f64 x 2)) (+.f64 (.f64 -4/3 (pow.f64 x 4)) (*.f64 -8/45 (pow.f64 x 6))))
(+.f64 (.f64 -4 (pow.f64 x 2)) (+.f64 (.f64 -4/3 (pow.f64 x 4)) (+.f64 (.f64 -8/45 (pow.f64 x 6)) (.f64 -4/315 (pow.f64 x 8)))))
(-.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(-.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(-.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(-.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(-.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(-.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(-.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(-.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) (*.f64 1/12 (pow.f64 x 4)))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (.f64 1/12 (pow.f64 x 4))))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/20160 (pow.f64 x 8)))))
(*.f64 -1 (/.f64 (-.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)) (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))))
(*.f64 -1 (/.f64 (-.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)) (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))))
(*.f64 -1 (/.f64 (-.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)) (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))))
(*.f64 -1 (/.f64 (-.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)) (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))))
(*.f64 -1 (/.f64 (-.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)) (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))))
(*.f64 -1 (/.f64 (-.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)) (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))))
(*.f64 -1 (/.f64 (-.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)) (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))))
(*.f64 -1 (/.f64 (-.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)) (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))))
4
(+.f64 (*.f64 4 (pow.f64 x 2)) 4)
(+.f64 (.f64 4 (pow.f64 x 2)) (+.f64 4 (.f64 4/3 (pow.f64 x 4))))
(+.f64 (.f64 4 (pow.f64 x 2)) (+.f64 4 (+.f64 (.f64 8/45 (pow.f64 x 6)) (*.f64 4/3 (pow.f64 x 4)))))
(pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)
(pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)
(pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)
(pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)
(pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)
(pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)
(pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)
(pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)
-4
(-.f64 (*.f64 -1 (pow.f64 x 2)) 4)
(-.f64 (+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 -1/12 (pow.f64 x 4))) 4)
(-.f64 (+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 -1/360 (pow.f64 x 6)) (*.f64 -1/12 (pow.f64 x 4)))) 4)
(*.f64 -1 (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(*.f64 -1 (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(*.f64 -1 (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(*.f64 -1 (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(*.f64 -1 (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(*.f64 -1 (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(*.f64 -1 (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(*.f64 -1 (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))

Outputs
(*.f64 -4 (pow.f64 x 2))
(.f64 -4 (.f64 x x))
(+.f64 (.f64 -4 (pow.f64 x 2)) (.f64 -4/3 (pow.f64 x 4)))
(fma.f64 -4 (.f64 x x) (.f64 -4/3 (pow.f64 x 4)))
(fma.f64 -4/3 (pow.f64 x 4) (.f64 -4 (.f64 x x)))
(+.f64 (.f64 -4 (pow.f64 x 2)) (+.f64 (.f64 -4/3 (pow.f64 x 4)) (*.f64 -8/45 (pow.f64 x 6))))
(fma.f64 -4 (.f64 x x) (fma.f64 -4/3 (pow.f64 x 4) (.f64 -8/45 (pow.f64 x 6))))
(fma.f64 -4 (.f64 x x) (fma.f64 -8/45 (pow.f64 x 6) (.f64 -4/3 (pow.f64 x 4))))
(fma.f64 -4/3 (pow.f64 x 4) (fma.f64 -8/45 (pow.f64 x 6) (.f64 -4 (.f64 x x))))
(+.f64 (.f64 -4 (pow.f64 x 2)) (+.f64 (.f64 -4/3 (pow.f64 x 4)) (+.f64 (.f64 -8/45 (pow.f64 x 6)) (.f64 -4/315 (pow.f64 x 8)))))
(fma.f64 -4 (.f64 x x) (fma.f64 -4/3 (pow.f64 x 4) (fma.f64 -8/45 (pow.f64 x 6) (.f64 -4/315 (pow.f64 x 8)))))
(fma.f64 -4/3 (pow.f64 x 4) (fma.f64 -4 (.f64 x x) (fma.f64 -8/45 (pow.f64 x 6) (.f64 -4/315 (pow.f64 x 8)))))
(-.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(-.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(-.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(-.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(-.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(-.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(-.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(-.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(-.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(-.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(-.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(-.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(-.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(-.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(-.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(-.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) (*.f64 1/12 (pow.f64 x 4)))
(+.f64 (.f64 x x) (.f64 (pow.f64 x 4) 1/12))
(fma.f64 x x (*.f64 (pow.f64 x 4) 1/12))
(fma.f64 (pow.f64 x 4) 1/12 (*.f64 x x))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (.f64 1/12 (pow.f64 x 4))))
(fma.f64 1/360 (pow.f64 x 6) (+.f64 (.f64 x x) (.f64 (pow.f64 x 4) 1/12)))
(fma.f64 (pow.f64 x 6) 1/360 (fma.f64 x x (*.f64 (pow.f64 x 4) 1/12)))
(fma.f64 x x (fma.f64 (pow.f64 x 4) 1/12 (*.f64 (pow.f64 x 6) 1/360)))
(fma.f64 (pow.f64 x 4) 1/12 (fma.f64 (pow.f64 x 6) 1/360 (*.f64 x x)))
(fma.f64 x x (fma.f64 (pow.f64 x 6) 1/360 (*.f64 (pow.f64 x 4) 1/12)))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/20160 (pow.f64 x 8)))))
(fma.f64 1/360 (pow.f64 x 6) (+.f64 (.f64 x x) (fma.f64 1/12 (pow.f64 x 4) (.f64 (pow.f64 x 8) 1/20160))))
(fma.f64 (pow.f64 x 6) 1/360 (fma.f64 x x (fma.f64 (pow.f64 x 8) 1/20160 (*.f64 (pow.f64 x 4) 1/12))))
(fma.f64 (pow.f64 x 6) 1/360 (fma.f64 (pow.f64 x 4) 1/12 (fma.f64 (pow.f64 x 8) 1/20160 (*.f64 x x))))
(fma.f64 x x (fma.f64 (pow.f64 x 6) 1/360 (fma.f64 (pow.f64 x 4) 1/12 (*.f64 (pow.f64 x 8) 1/20160))))
(fma.f64 x x (fma.f64 (pow.f64 x 6) 1/360 (fma.f64 (pow.f64 x 8) 1/20160 (*.f64 (pow.f64 x 4) 1/12))))
(*.f64 -1 (/.f64 (-.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)) (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))))
(neg.f64 (/.f64 (-.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
(neg.f64 (/.f64 (-.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 (+.f64 2 (exp.f64 x)) (exp.f64 (neg.f64 x)))))
(neg.f64 (/.f64 (-.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 (exp.f64 (neg.f64 x)) (+.f64 2 (exp.f64 x)))))
(/.f64 (+.f64 -4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 (exp.f64 (neg.f64 x)) (+.f64 2 (exp.f64 x))))
(/.f64 (+.f64 -4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 (exp.f64 x) (+.f64 2 (exp.f64 (neg.f64 x)))))
(*.f64 -1 (/.f64 (-.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)) (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))))
(neg.f64 (/.f64 (-.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
(neg.f64 (/.f64 (-.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 (+.f64 2 (exp.f64 x)) (exp.f64 (neg.f64 x)))))
(neg.f64 (/.f64 (-.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 (exp.f64 (neg.f64 x)) (+.f64 2 (exp.f64 x)))))
(/.f64 (+.f64 -4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 (exp.f64 (neg.f64 x)) (+.f64 2 (exp.f64 x))))
(/.f64 (+.f64 -4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 (exp.f64 x) (+.f64 2 (exp.f64 (neg.f64 x)))))
(*.f64 -1 (/.f64 (-.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)) (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))))
(neg.f64 (/.f64 (-.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
(neg.f64 (/.f64 (-.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 (+.f64 2 (exp.f64 x)) (exp.f64 (neg.f64 x)))))
(neg.f64 (/.f64 (-.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 (exp.f64 (neg.f64 x)) (+.f64 2 (exp.f64 x)))))
(/.f64 (+.f64 -4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 (exp.f64 (neg.f64 x)) (+.f64 2 (exp.f64 x))))
(/.f64 (+.f64 -4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 (exp.f64 x) (+.f64 2 (exp.f64 (neg.f64 x)))))
(*.f64 -1 (/.f64 (-.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)) (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))))
(neg.f64 (/.f64 (-.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
(neg.f64 (/.f64 (-.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 (+.f64 2 (exp.f64 x)) (exp.f64 (neg.f64 x)))))
(neg.f64 (/.f64 (-.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 (exp.f64 (neg.f64 x)) (+.f64 2 (exp.f64 x)))))
(/.f64 (+.f64 -4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 (exp.f64 (neg.f64 x)) (+.f64 2 (exp.f64 x))))
(/.f64 (+.f64 -4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 (exp.f64 x) (+.f64 2 (exp.f64 (neg.f64 x)))))
(*.f64 -1 (/.f64 (-.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)) (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))))
(neg.f64 (/.f64 (-.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
(neg.f64 (/.f64 (-.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 (+.f64 2 (exp.f64 x)) (exp.f64 (neg.f64 x)))))
(neg.f64 (/.f64 (-.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 (exp.f64 (neg.f64 x)) (+.f64 2 (exp.f64 x)))))
(/.f64 (+.f64 -4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 (exp.f64 (neg.f64 x)) (+.f64 2 (exp.f64 x))))
(/.f64 (+.f64 -4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 (exp.f64 x) (+.f64 2 (exp.f64 (neg.f64 x)))))
(*.f64 -1 (/.f64 (-.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)) (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))))
(neg.f64 (/.f64 (-.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
(neg.f64 (/.f64 (-.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 (+.f64 2 (exp.f64 x)) (exp.f64 (neg.f64 x)))))
(neg.f64 (/.f64 (-.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 (exp.f64 (neg.f64 x)) (+.f64 2 (exp.f64 x)))))
(/.f64 (+.f64 -4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 (exp.f64 (neg.f64 x)) (+.f64 2 (exp.f64 x))))
(/.f64 (+.f64 -4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 (exp.f64 x) (+.f64 2 (exp.f64 (neg.f64 x)))))
(*.f64 -1 (/.f64 (-.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)) (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))))
(neg.f64 (/.f64 (-.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
(neg.f64 (/.f64 (-.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 (+.f64 2 (exp.f64 x)) (exp.f64 (neg.f64 x)))))
(neg.f64 (/.f64 (-.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 (exp.f64 (neg.f64 x)) (+.f64 2 (exp.f64 x)))))
(/.f64 (+.f64 -4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 (exp.f64 (neg.f64 x)) (+.f64 2 (exp.f64 x))))
(/.f64 (+.f64 -4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 (exp.f64 x) (+.f64 2 (exp.f64 (neg.f64 x)))))
(*.f64 -1 (/.f64 (-.f64 4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)) (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))))
(neg.f64 (/.f64 (-.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
(neg.f64 (/.f64 (-.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 (+.f64 2 (exp.f64 x)) (exp.f64 (neg.f64 x)))))
(neg.f64 (/.f64 (-.f64 4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 (exp.f64 (neg.f64 x)) (+.f64 2 (exp.f64 x)))))
(/.f64 (+.f64 -4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 (exp.f64 (neg.f64 x)) (+.f64 2 (exp.f64 x))))
(/.f64 (+.f64 -4 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)) (+.f64 (exp.f64 x) (+.f64 2 (exp.f64 (neg.f64 x)))))
4
(+.f64 (*.f64 4 (pow.f64 x 2)) 4)
(fma.f64 4 (*.f64 x x) 4)
(fma.f64 (*.f64 x x) 4 4)
(*.f64 4 (fma.f64 x x 1))
(+.f64 (.f64 4 (pow.f64 x 2)) (+.f64 4 (.f64 4/3 (pow.f64 x 4))))
(+.f64 (fma.f64 4 (.f64 x x) 4) (.f64 (pow.f64 x 4) 4/3))
(fma.f64 (*.f64 x x) 4 (fma.f64 (pow.f64 x 4) 4/3 4))
(fma.f64 (pow.f64 x 4) 4/3 (fma.f64 (*.f64 x x) 4 4))
(fma.f64 x (*.f64 x 4) (fma.f64 (pow.f64 x 4) 4/3 4))
(+.f64 (.f64 4 (pow.f64 x 2)) (+.f64 4 (+.f64 (.f64 8/45 (pow.f64 x 6)) (*.f64 4/3 (pow.f64 x 4)))))
(+.f64 (fma.f64 4 (.f64 x x) 4) (fma.f64 8/45 (pow.f64 x 6) (.f64 (pow.f64 x 4) 4/3)))
(+.f64 (fma.f64 (.f64 x x) 4 4) (fma.f64 (pow.f64 x 6) 8/45 (.f64 (pow.f64 x 4) 4/3)))
(fma.f64 x (*.f64 x 4) (fma.f64 (pow.f64 x 4) 4/3 (fma.f64 (pow.f64 x 6) 8/45 4)))
(fma.f64 x (*.f64 x 4) (fma.f64 (pow.f64 x 6) 8/45 (fma.f64 (pow.f64 x 4) 4/3 4)))
(pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)
(pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
(pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)
(pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
(pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)
(pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
(pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)
(pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
(pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)
(pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
(pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)
(pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
(pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)
(pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
(pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2)
(pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
-4
(-.f64 (*.f64 -1 (pow.f64 x 2)) 4)
(fma.f64 -1 (*.f64 x x) -4)
(fma.f64 (*.f64 x x) -1 -4)
(-.f64 -4 (*.f64 x x))
(-.f64 (+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 -1/12 (pow.f64 x 4))) 4)
(+.f64 (fma.f64 -1 (.f64 x x) (.f64 (pow.f64 x 4) -1/12)) -4)
(fma.f64 (*.f64 x x) -1 (fma.f64 (pow.f64 x 4) -1/12 -4))
(fma.f64 (pow.f64 x 4) -1/12 (-.f64 -4 (*.f64 x x)))
(-.f64 -4 (fma.f64 x x (*.f64 (pow.f64 x 4) 1/12)))
(-.f64 (+.f64 (.f64 -1 (pow.f64 x 2)) (+.f64 (.f64 -1/360 (pow.f64 x 6)) (*.f64 -1/12 (pow.f64 x 4)))) 4)
(+.f64 (fma.f64 -1 (.f64 x x) (fma.f64 -1/360 (pow.f64 x 6) (.f64 (pow.f64 x 4) -1/12))) -4)
(+.f64 -4 (-.f64 (fma.f64 (pow.f64 x 4) -1/12 (.f64 (pow.f64 x 6) -1/360)) (.f64 x x)))
(-.f64 (fma.f64 (pow.f64 x 4) -1/12 (fma.f64 (pow.f64 x 6) -1/360 -4)) (*.f64 x x))
(-.f64 (fma.f64 (pow.f64 x 4) -1/12 (*.f64 (pow.f64 x 6) -1/360)) (fma.f64 x x 4))
(-.f64 -4 (fma.f64 x x (fma.f64 (pow.f64 x 6) 1/360 (*.f64 (pow.f64 x 4) 1/12))))
(*.f64 -1 (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(neg.f64 (+.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(neg.f64 (+.f64 (+.f64 2 (exp.f64 x)) (exp.f64 (neg.f64 x))))
(-.f64 -2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(-.f64 (-.f64 -2 (exp.f64 x)) (exp.f64 (neg.f64 x)))
(*.f64 -1 (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(neg.f64 (+.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(neg.f64 (+.f64 (+.f64 2 (exp.f64 x)) (exp.f64 (neg.f64 x))))
(-.f64 -2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(-.f64 (-.f64 -2 (exp.f64 x)) (exp.f64 (neg.f64 x)))
(*.f64 -1 (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(neg.f64 (+.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(neg.f64 (+.f64 (+.f64 2 (exp.f64 x)) (exp.f64 (neg.f64 x))))
(-.f64 -2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(-.f64 (-.f64 -2 (exp.f64 x)) (exp.f64 (neg.f64 x)))
(*.f64 -1 (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(neg.f64 (+.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(neg.f64 (+.f64 (+.f64 2 (exp.f64 x)) (exp.f64 (neg.f64 x))))
(-.f64 -2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(-.f64 (-.f64 -2 (exp.f64 x)) (exp.f64 (neg.f64 x)))
(*.f64 -1 (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(neg.f64 (+.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(neg.f64 (+.f64 (+.f64 2 (exp.f64 x)) (exp.f64 (neg.f64 x))))
(-.f64 -2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(-.f64 (-.f64 -2 (exp.f64 x)) (exp.f64 (neg.f64 x)))
(*.f64 -1 (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(neg.f64 (+.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(neg.f64 (+.f64 (+.f64 2 (exp.f64 x)) (exp.f64 (neg.f64 x))))
(-.f64 -2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(-.f64 (-.f64 -2 (exp.f64 x)) (exp.f64 (neg.f64 x)))
(*.f64 -1 (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(neg.f64 (+.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(neg.f64 (+.f64 (+.f64 2 (exp.f64 x)) (exp.f64 (neg.f64 x))))
(-.f64 -2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(-.f64 (-.f64 -2 (exp.f64 x)) (exp.f64 (neg.f64 x)))
(*.f64 -1 (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(neg.f64 (+.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(neg.f64 (+.f64 (+.f64 2 (exp.f64 x)) (exp.f64 (neg.f64 x))))
(-.f64 -2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(-.f64 (-.f64 -2 (exp.f64 x)) (exp.f64 (neg.f64 x)))

eval839.0ms (7.5%)

Compiler: Compiled 17475 to 12695 computations (27.4% saved)

prune72.0ms (0.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	538	5	543
Fresh	2	1	3
Picked	1	0	1
Done	1	3	4
Total	542	9	551

Error

0.0b

Counts

551 → 9

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.5b	(fma.f64 x x (.f64 (pow.f64 x 4) (fma.f64 1/360 (.f64 x x) 1/12)))
▶	28.8b	(/.f64 (-.f64 (.f64 (+.f64 -1 (.f64 2 (cosh.f64 x))) (+.f64 -1 (.f64 2 (cosh.f64 x)))) 1) (+.f64 (+.f64 -1 (.f64 2 (cosh.f64 x))) 1))
	29.1b	(/.f64 (log.f64 (exp.f64 (fma.f64 -4 (pow.f64 (cosh.f64 x) 2) 4))) (-.f64 -2 (*.f64 2 (cosh.f64 x))))
▶	0.6b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
✓	28.8b	(+.f64 -2 (*.f64 2 (cosh.f64 x)))
✓	0.9b	(*.f64 x x)
▶	29.8b	(+.f64 -1 (exp.f64 (neg.f64 x)))
✓	28.8b	(expm1.f64 (log1p.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))))
▶	28.8b	(/.f64 (-.f64 (.f64 (pow.f64 (cosh.f64 x) 2) 4) 4) (-.f64 (.f64 2 (cosh.f64 x)) -2))

Compiler

Compiled 194 to 150 computations (22.7% saved)

localize16.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 40 to 23 computations (42.5% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(.f64 (pow.f64 x 4) (fma.f64 1/360 (.f64 x x) 1/12))
1.0ms	x	@	inf	(.f64 (pow.f64 x 4) (fma.f64 1/360 (.f64 x x) 1/12))
0.0ms	x	@	inf	(fma.f64 1/360 (*.f64 x x) 1/12)
0.0ms	x	@	-inf	(.f64 (pow.f64 x 4) (fma.f64 1/360 (.f64 x x) 1/12))
0.0ms	x	@	-inf	(fma.f64 1/360 (*.f64 x x) 1/12)

rewrite56.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

740×	`pow1_binary64`
692×	`add-log-exp_binary64`
692×	`log1p-expm1-u_binary64`
692×	`expm1-log1p-u_binary64`
678×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	186	22
2	1954	22

Stop Event

1×	node limit

Counts

2 → 36

Calls

Call 1

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

Outputs

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

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1/12 (*.f64 1/360 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/360 (*.f64 x x)) 1/12)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 1/360 (*.f64 x x)) 1) 1/12)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 1/360 (*.f64 x x) 1/12)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 1/360 (*.f64 x x) 1/12) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 1/360 (*.f64 x x) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 1/360 (*.f64 x x) 1/12)) (pow.f64 (cbrt.f64 (fma.f64 1/360 (*.f64 x x) 1/12)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 1/360 (*.f64 x x) 1/12)) 2) (cbrt.f64 (fma.f64 1/360 (*.f64 x x) 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 1/360 (*.f64 x x) 1/12)) (sqrt.f64 (fma.f64 1/360 (*.f64 x x) 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 1/360 (*.f64 x x)) 3) 1/1728) (+.f64 (*.f64 (*.f64 1/360 (*.f64 x x)) (*.f64 1/360 (*.f64 x x))) (-.f64 1/144 (*.f64 (*.f64 1/360 (*.f64 x x)) 1/12))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 1/360 (*.f64 x x)) (*.f64 1/360 (*.f64 x x))) 1/144) (-.f64 (*.f64 1/360 (*.f64 x x)) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 1/360 (*.f64 x x) 1/12) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/360 (*.f64 x x) 1/12) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 1/360 (*.f64 x x) 1/12)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 1/360 (*.f64 x x) 1/12)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 1/360 (*.f64 x x) 1/12) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 1/360 (*.f64 x x) 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 1/360 (*.f64 x x) 1/12) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 1/360 (*.f64 x x) 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 1/360 (*.f64 x x) 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 1/360 (*.f64 x x) 1/12)))))))

simplify179.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1124×	`sqr-pow_binary64`
748×	`cube-prod_binary64`
653×	`pow-sqr_binary64`
429×	`unpow3_binary64`
423×	`cube-mult_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	252
1	32	234
2	66	234
3	175	234
4	730	234
5	1822	234
6	2172	234
7	2371	234
8	2565	234
9	2816	234
10	3131	234
11	3540	234
12	3976	234
13	4473	234
14	5076	234
15	5334	234
16	5584	234
17	5848	234
18	6118	234
19	6380	234
20	7785	234

Stop Event

1×	node limit

Counts

60 → 45

Calls

Call 1

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

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

localize6.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	6.1b	(+.f64 -1 (exp.f64 (neg.f64 x)))

Compiler

Compiled 13 to 6 computations (53.8% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(+.f64 -1 (exp.f64 (neg.f64 x)))
0.0ms	x	@	-inf	(+.f64 -1 (exp.f64 (neg.f64 x)))
0.0ms	x	@	inf	(+.f64 -1 (exp.f64 (neg.f64 x)))

rewrite42.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

543×	`pow1_binary64`
506×	`add-log-exp_binary64`
504×	`log1p-expm1-u_binary64`
504×	`expm1-log1p-u_binary64`
497×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	124	6
2	1587	6

Stop Event

1×	node limit

Counts

1 → 31

Calls

Call 1

Inputs
(+.f64 -1 (exp.f64 (neg.f64 x)))

Outputs

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

simplify53.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

633×	`cancel-sign-sub-inv_binary64`
499×	`fma-neg_binary64`
370×	`distribute-rgt-out--_binary64`
315×	`fma-def_binary64`
312×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	27	94
1	71	94
2	163	93
3	552	86
4	2019	86
5	5640	86

Stop Event

1×	node limit

Counts

43 → 42

Calls

Call 1

Inputs
(*.f64 -1 x)
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1 x))
(+.f64 (.f64 -1/6 (pow.f64 x 3)) (+.f64 (.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x)))
(+.f64 (.f64 -1/6 (pow.f64 x 3)) (+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 1/24 (pow.f64 x 4)) (.f64 -1 x))))
(-.f64 (exp.f64 (neg.f64 x)) 1)
(-.f64 (exp.f64 (neg.f64 x)) 1)
(-.f64 (exp.f64 (neg.f64 x)) 1)
(-.f64 (exp.f64 (neg.f64 x)) 1)
(-.f64 (exp.f64 (*.f64 -1 x)) 1)
(-.f64 (exp.f64 (*.f64 -1 x)) 1)
(-.f64 (exp.f64 (*.f64 -1 x)) 1)
(-.f64 (exp.f64 (*.f64 -1 x)) 1)

Outputs
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1 x))
(fma.f64 1/2 (*.f64 x x) (neg.f64 x))
(-.f64 (.f64 1/2 (.f64 x x)) x)
(-.f64 (.f64 x (.f64 x 1/2)) x)
(*.f64 x (fma.f64 x 1/2 -1))
(+.f64 (.f64 -1/6 (pow.f64 x 3)) (+.f64 (.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x)))
(fma.f64 -1/6 (pow.f64 x 3) (fma.f64 1/2 (*.f64 x x) (neg.f64 x)))
(-.f64 (fma.f64 -1/6 (pow.f64 x 3) (.f64 1/2 (.f64 x x))) x)
(-.f64 (.f64 (.f64 x x) (+.f64 1/2 (*.f64 x -1/6))) x)
(fma.f64 x (*.f64 x (fma.f64 x -1/6 1/2)) (neg.f64 x))
(+.f64 (.f64 -1/6 (pow.f64 x 3)) (+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 1/24 (pow.f64 x 4)) (.f64 -1 x))))
(fma.f64 -1/6 (pow.f64 x 3) (fma.f64 1/2 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 4) (neg.f64 x))))
(fma.f64 -1/6 (pow.f64 x 3) (fma.f64 1/2 (.f64 x x) (-.f64 (.f64 1/24 (pow.f64 x 4)) x)))
(-.f64 (fma.f64 -1/6 (pow.f64 x 3) (fma.f64 x (.f64 x 1/2) (.f64 1/24 (pow.f64 x 4)))) x)
(fma.f64 x (*.f64 x (fma.f64 x -1/6 1/2)) (fma.f64 1/24 (pow.f64 x 4) (neg.f64 x)))
(fma.f64 1/24 (pow.f64 x 4) (fma.f64 x (*.f64 x (fma.f64 x -1/6 1/2)) (neg.f64 x)))
(-.f64 (exp.f64 (neg.f64 x)) 1)
(expm1.f64 (neg.f64 x))
(-.f64 (exp.f64 (neg.f64 x)) 1)
(expm1.f64 (neg.f64 x))
(-.f64 (exp.f64 (neg.f64 x)) 1)
(expm1.f64 (neg.f64 x))
(-.f64 (exp.f64 (neg.f64 x)) 1)
(expm1.f64 (neg.f64 x))
(-.f64 (exp.f64 (*.f64 -1 x)) 1)
(expm1.f64 (neg.f64 x))
(-.f64 (exp.f64 (*.f64 -1 x)) 1)
(expm1.f64 (neg.f64 x))
(-.f64 (exp.f64 (*.f64 -1 x)) 1)
(expm1.f64 (neg.f64 x))
(-.f64 (exp.f64 (*.f64 -1 x)) 1)
(expm1.f64 (neg.f64 x))

localize9.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
	0.1b	(*.f64 1/12 (pow.f64 x 4))

Compiler

Compiled 20 to 14 computations (30% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 2 (cosh.f64 x)) -2)
✓	0.0b	(pow.f64 (cosh.f64 x) 2)
✓	0.0b	(/.f64 (-.f64 (.f64 (pow.f64 (cosh.f64 x) 2) 4) 4) (-.f64 (.f64 2 (cosh.f64 x)) -2))
✓	3.3b	(-.f64 (*.f64 (pow.f64 (cosh.f64 x) 2) 4) 4)

Compiler

Compiled 50 to 34 computations (32% saved)

series5.0ms (0%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(/.f64 (-.f64 (.f64 (pow.f64 (cosh.f64 x) 2) 4) 4) (-.f64 (.f64 2 (cosh.f64 x)) -2))
1.0ms	x	@	inf	(/.f64 (-.f64 (.f64 (pow.f64 (cosh.f64 x) 2) 4) 4) (-.f64 (.f64 2 (cosh.f64 x)) -2))
0.0ms	x	@	0	(-.f64 (*.f64 (pow.f64 (cosh.f64 x) 2) 4) 4)
0.0ms	x	@	0	(/.f64 (-.f64 (.f64 (pow.f64 (cosh.f64 x) 2) 4) 4) (-.f64 (.f64 2 (cosh.f64 x)) -2))
0.0ms	x	@	inf	(-.f64 (*.f64 (pow.f64 (cosh.f64 x) 2) 4) 4)

rewrite130.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

607×	`log-prod_binary64`
329×	`pow2_binary64`
321×	`fma-def_binary64`
292×	`prod-diff_binary64`
227×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	42
1	280	30
2	3703	30

Stop Event

1×	node limit

Counts

4 → 303

Calls

Call 1

Inputs
(-.f64 (*.f64 (pow.f64 (cosh.f64 x) 2) 4) 4)
(/.f64 (-.f64 (.f64 (pow.f64 (cosh.f64 x) 2) 4) 4) (-.f64 (.f64 2 (cosh.f64 x)) -2))
(pow.f64 (cosh.f64 x) 2)
(-.f64 (*.f64 2 (cosh.f64 x)) -2)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (pow.f64 (cosh.f64 x) 2) 4) -4)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -4 (.f64 (pow.f64 (cosh.f64 x) 2) 4))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (fma.f64 (pow.f64 (cosh.f64 x) 2) 4 -4))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 (pow.f64 (cosh.f64 x) 2) 4 -4))) 2)) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 (pow.f64 (cosh.f64 x) 2) 4 -4)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 (pow.f64 (cosh.f64 x) 2) 4 -4)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 (pow.f64 (cosh.f64 x) 2) 4 -4)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 (pow.f64 (cosh.f64 x) 2) 4 -4) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 (pow.f64 (cosh.f64 x) 2) 4 -4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 (pow.f64 (cosh.f64 x) 2) 4 -4)) (cbrt.f64 (pow.f64 (fma.f64 (pow.f64 (cosh.f64 x) 2) 4 -4) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (fma.f64 (pow.f64 (cosh.f64 x) 2) 4 -4) 2)) (cbrt.f64 (fma.f64 (pow.f64 (cosh.f64 x) 2) 4 -4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 (pow.f64 (cosh.f64 x) 2) 4 -4)) (sqrt.f64 (fma.f64 (pow.f64 (cosh.f64 x) 2) 4 -4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 (pow.f64 (pow.f64 (cosh.f64 x) 3) 2) 64 -64) (/.f64 1 (fma.f64 (pow.f64 (cosh.f64 x) 4) 16 (fma.f64 (pow.f64 (cosh.f64 x) 2) 16 16))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 (pow.f64 (cosh.f64 x) 4) 16 -16) (/.f64 1 (fma.f64 (pow.f64 (cosh.f64 x) 2) 4 4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (pow.f64 (cosh.f64 x) 4) 16 (fma.f64 (pow.f64 (cosh.f64 x) 2) 16 16)) (fma.f64 (pow.f64 (pow.f64 (cosh.f64 x) 3) 2) 64 -64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (pow.f64 (cosh.f64 x) 2) 4 4) (fma.f64 (pow.f64 (cosh.f64 x) 4) 16 -16)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 (pow.f64 (cosh.f64 x) 3) 2) 64 -64) (fma.f64 (pow.f64 (cosh.f64 x) 4) 16 (fma.f64 (pow.f64 (cosh.f64 x) 2) 16 16)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 (pow.f64 (cosh.f64 x) 3) 2) 64 -64) (fma.f64 (pow.f64 (cosh.f64 x) 4) 16 (-.f64 16 (.f64 (.f64 (pow.f64 (cosh.f64 x) 2) 4) -4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 (cosh.f64 x) 4) 16 -16) (fma.f64 (pow.f64 (cosh.f64 x) 2) 4 4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 (pow.f64 (pow.f64 (cosh.f64 x) 3) 2) 64 -64)) (neg.f64 (fma.f64 (pow.f64 (cosh.f64 x) 4) 16 (fma.f64 (pow.f64 (cosh.f64 x) 2) 16 16))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 (pow.f64 (cosh.f64 x) 4) 16 -16)) (neg.f64 (fma.f64 (pow.f64 (cosh.f64 x) 2) 4 4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 (pow.f64 (cosh.f64 x) 2) 4 -4) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 (pow.f64 (cosh.f64 x) 2) 4 -4) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 (pow.f64 (cosh.f64 x) 2) 4 -4) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 (pow.f64 (cosh.f64 x) 2) 4 -4)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 (pow.f64 (cosh.f64 x) 2) 4 -4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (pow.f64 (cosh.f64 x) 4) 16 (fma.f64 (pow.f64 (cosh.f64 x) 2) 16 16)) (fma.f64 (pow.f64 (pow.f64 (cosh.f64 x) 3) 2) 64 -64)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (pow.f64 (cosh.f64 x) 2) 4 4) (fma.f64 (pow.f64 (cosh.f64 x) 4) 16 -16)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 (pow.f64 (cosh.f64 x) 2) 4 -4) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 (pow.f64 (cosh.f64 x) 2) 4 -4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 (pow.f64 (cosh.f64 x) 2) 4 -4))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 (pow.f64 (cosh.f64 x) 2) 4 -4) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 (pow.f64 (cosh.f64 x) 2) 4 -4)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 (pow.f64 (cosh.f64 x) 2) 4 -4)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 (pow.f64 (cosh.f64 x) 2) 4 -4)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (fma.f64 (pow.f64 (cosh.f64 x) 2) 4 -4)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cosh.f64 x) (.f64 2 (.f64 (cosh.f64 x) 2)) -4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cosh.f64 x) (.f64 (cosh.f64 x) 4) -4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 2 (.f64 (cosh.f64 x) (.f64 (cosh.f64 x) 2)) -4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cosh.f64 x) 2) 4 -4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 4 (pow.f64 (cosh.f64 x) 2) -4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (pow.f64 (cosh.f64 x) 2) 4) 1 -4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (cosh.f64 x) 2) (.f64 (cosh.f64 x) 2) -4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 (pow.f64 (cosh.f64 x) 2) 4) -4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (cosh.f64 x) 4)) (.f64 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2) 4) -4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 (pow.f64 (cosh.f64 x) 2) 4)) (cbrt.f64 (.f64 (pow.f64 (cosh.f64 x) 4) 16)) -4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 (pow.f64 (cosh.f64 x) 2) 4)) (.f64 (cbrt.f64 (.f64 (cosh.f64 x) 2)) (.f64 (cosh.f64 x) 2)) -4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 (pow.f64 (cosh.f64 x) 4) 16)) (cbrt.f64 (.f64 (pow.f64 (cosh.f64 x) 2) 4)) -4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (.f64 (cosh.f64 x) 2)) (.f64 (sqrt.f64 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(#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (pow.f64 (cosh.f64 x) 2) 4 (fma.f64 (cosh.f64 x) -4 4)) (fma.f64 (pow.f64 (cosh.f64 x) 3) 8 8)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (cosh.f64 x) 2 -2) (fma.f64 (pow.f64 (cosh.f64 x) 2) 4 -4)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 (cosh.f64 x) 2 2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 (cosh.f64 x) 2 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 (cosh.f64 x) 2 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 (cosh.f64 x) 2 2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 (cosh.f64 x) 2 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 (cosh.f64 x) 2 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 (cosh.f64 x) 2 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (fma.f64 (cosh.f64 x) 2 2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cosh.f64 x) 2 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 2 (cosh.f64 x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (cosh.f64 x) 2) 1 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 (cosh.f64 x) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 (cosh.f64 x) 2)) (cbrt.f64 (.f64 (pow.f64 (cosh.f64 x) 2) 4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2) (.f64 (cbrt.f64 (cosh.f64 x)) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 (pow.f64 (cosh.f64 x) 2) 4)) (cbrt.f64 (.f64 (cosh.f64 x) 2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (.f64 (cosh.f64 x) 2)) (sqrt.f64 (.f64 (cosh.f64 x) 2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (cosh.f64 x)) (.f64 (sqrt.f64 (cosh.f64 x)) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (cbrt.f64 (.f64 (pow.f64 (cosh.f64 x) 4) 16))) (sqrt.f64 (cbrt.f64 (.f64 (pow.f64 (cosh.f64 x) 2) 4))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 2 (pow.f64 (cbrt.f64 (cosh.f64 x)) 2)) (cbrt.f64 (cosh.f64 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 2 (sqrt.f64 (cosh.f64 x))) (sqrt.f64 (cosh.f64 x)) 2)))))

simplify86.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

928×	`fma-def_binary64`
926×	`distribute-rgt-out_binary64`
729×	`associate-l_binary64`
549×	`associate-r_binary64`
437×	`unswap-sqr_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	55	836
1	136	818
2	347	810
3	1123	810
4	4968	810
5	7958	810

Stop Event

1×	node limit

Counts

351 → 341

Calls

Call 1

Inputs
(*.f64 4 (pow.f64 x 2))
(+.f64 (.f64 4 (pow.f64 x 2)) (.f64 4/3 (pow.f64 x 4)))
(+.f64 (.f64 4 (pow.f64 x 2)) (+.f64 (.f64 4/3 (pow.f64 x 4)) (*.f64 8/45 (pow.f64 x 6))))
(+.f64 (.f64 4 (pow.f64 x 2)) (+.f64 (.f64 4/3 (pow.f64 x 4)) (+.f64 (.f64 4/315 (pow.f64 x 8)) (.f64 8/45 (pow.f64 x 6)))))
(-.f64 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 4)
(-.f64 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 4)
(-.f64 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 4)
(-.f64 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 4)
(-.f64 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 4)
(-.f64 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 4)
(-.f64 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 4)
(-.f64 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 4)
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) (*.f64 1/12 (pow.f64 x 4)))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (.f64 1/12 (pow.f64 x 4))))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/20160 (pow.f64 x 8)))))
(/.f64 (-.f64 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 4) (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(/.f64 (-.f64 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 4) (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(/.f64 (-.f64 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 4) (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(/.f64 (-.f64 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 4) (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(/.f64 (-.f64 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 4) (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(/.f64 (-.f64 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 4) (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(/.f64 (-.f64 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 4) (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(/.f64 (-.f64 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 4) (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
1
(+.f64 1 (pow.f64 x 2))
(+.f64 1 (+.f64 (pow.f64 x 2) (*.f64 1/3 (pow.f64 x 4))))
(+.f64 (.f64 2/45 (pow.f64 x 6)) (+.f64 1 (+.f64 (pow.f64 x 2) (.f64 1/3 (pow.f64 x 4)))))
(*.f64 1/4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(*.f64 1/4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(*.f64 1/4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(*.f64 1/4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(*.f64 1/4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(*.f64 1/4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(*.f64 1/4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(*.f64 1/4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
4
(+.f64 4 (pow.f64 x 2))
(+.f64 4 (+.f64 (pow.f64 x 2) (*.f64 1/12 (pow.f64 x 4))))
(+.f64 4 (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (.f64 1/12 (pow.f64 x 4)))))
(+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))

Outputs
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
(+.f64 (.f64 4 (pow.f64 x 2)) (.f64 4/3 (pow.f64 x 4)))
(fma.f64 4 (.f64 x x) (.f64 4/3 (pow.f64 x 4)))
(fma.f64 4/3 (pow.f64 x 4) (.f64 4 (.f64 x x)))
(.f64 x (.f64 x (fma.f64 (*.f64 x x) 4/3 4)))
(.f64 x (.f64 x (fma.f64 x (*.f64 x 4/3) 4)))
(+.f64 (.f64 4 (pow.f64 x 2)) (+.f64 (.f64 4/3 (pow.f64 x 4)) (*.f64 8/45 (pow.f64 x 6))))
(fma.f64 4 (.f64 x x) (fma.f64 4/3 (pow.f64 x 4) (.f64 8/45 (pow.f64 x 6))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x 4/3) 4) (*.f64 8/45 (pow.f64 x 6)))
(+.f64 (.f64 4 (pow.f64 x 2)) (+.f64 (.f64 4/3 (pow.f64 x 4)) (+.f64 (.f64 4/315 (pow.f64 x 8)) (.f64 8/45 (pow.f64 x 6)))))
(fma.f64 4 (.f64 x x) (fma.f64 4/3 (pow.f64 x 4) (fma.f64 4/315 (pow.f64 x 8) (.f64 8/45 (pow.f64 x 6)))))
(fma.f64 4 (.f64 x x) (fma.f64 4/3 (pow.f64 x 4) (fma.f64 8/45 (pow.f64 x 6) (.f64 4/315 (pow.f64 x 8)))))
(fma.f64 4 (.f64 x x) (fma.f64 8/45 (pow.f64 x 6) (fma.f64 4/3 (pow.f64 x 4) (.f64 4/315 (pow.f64 x 8)))))
(-.f64 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 4)
(+.f64 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2) -4)
(-.f64 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 4)
(+.f64 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2) -4)
(-.f64 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 4)
(+.f64 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2) -4)
(-.f64 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 4)
(+.f64 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2) -4)
(-.f64 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 4)
(+.f64 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2) -4)
(-.f64 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 4)
(+.f64 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2) -4)
(-.f64 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 4)
(+.f64 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2) -4)
(-.f64 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 4)
(+.f64 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2) -4)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) (*.f64 1/12 (pow.f64 x 4)))
(+.f64 (.f64 x x) (.f64 (pow.f64 x 4) 1/12))
(fma.f64 x x (*.f64 (pow.f64 x 4) 1/12))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (.f64 1/12 (pow.f64 x 4))))
(fma.f64 1/360 (pow.f64 x 6) (+.f64 (.f64 x x) (.f64 (pow.f64 x 4) 1/12)))
(fma.f64 (pow.f64 x 6) 1/360 (fma.f64 x x (*.f64 (pow.f64 x 4) 1/12)))
(fma.f64 x x (fma.f64 (pow.f64 x 4) 1/12 (*.f64 (pow.f64 x 6) 1/360)))
(fma.f64 (pow.f64 x 4) 1/12 (fma.f64 (pow.f64 x 6) 1/360 (*.f64 x x)))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/20160 (pow.f64 x 8)))))
(fma.f64 1/360 (pow.f64 x 6) (+.f64 (.f64 x x) (fma.f64 1/12 (pow.f64 x 4) (.f64 (pow.f64 x 8) 1/20160))))
(fma.f64 (pow.f64 x 6) 1/360 (fma.f64 x x (fma.f64 (pow.f64 x 8) 1/20160 (*.f64 (pow.f64 x 4) 1/12))))
(fma.f64 x x (fma.f64 (pow.f64 x 6) 1/360 (fma.f64 (pow.f64 x 4) 1/12 (*.f64 (pow.f64 x 8) 1/20160))))
(fma.f64 x x (fma.f64 (pow.f64 x 4) 1/12 (fma.f64 (pow.f64 x 6) 1/360 (*.f64 (pow.f64 x 8) 1/20160))))
(fma.f64 (pow.f64 x 4) 1/12 (fma.f64 (pow.f64 x 6) 1/360 (fma.f64 (pow.f64 x 8) 1/20160 (*.f64 x x))))
(/.f64 (-.f64 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 4) (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(/.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2) -4) (+.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(/.f64 (-.f64 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 4) (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(/.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2) -4) (+.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(/.f64 (-.f64 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 4) (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(/.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2) -4) (+.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(/.f64 (-.f64 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 4) (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(/.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2) -4) (+.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(/.f64 (-.f64 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 4) (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(/.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2) -4) (+.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(/.f64 (-.f64 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 4) (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(/.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2) -4) (+.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(/.f64 (-.f64 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 4) (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(/.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2) -4) (+.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(/.f64 (-.f64 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 4) (+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x))))
(/.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2) -4) (+.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
1
(+.f64 1 (pow.f64 x 2))
(+.f64 (*.f64 x x) 1)
(fma.f64 x x 1)
(+.f64 1 (+.f64 (pow.f64 x 2) (*.f64 1/3 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 x x) (.f64 (pow.f64 x 4) 1/3)))
(+.f64 1 (fma.f64 (pow.f64 x 4) 1/3 (*.f64 x x)))
(fma.f64 x x (fma.f64 (pow.f64 x 4) 1/3 1))
(fma.f64 (pow.f64 x 4) 1/3 (fma.f64 x x 1))
(+.f64 (.f64 2/45 (pow.f64 x 6)) (+.f64 1 (+.f64 (pow.f64 x 2) (.f64 1/3 (pow.f64 x 4)))))
(fma.f64 2/45 (pow.f64 x 6) (+.f64 1 (+.f64 (.f64 x x) (.f64 (pow.f64 x 4) 1/3))))
(+.f64 (fma.f64 (pow.f64 x 4) 1/3 (*.f64 x x)) (fma.f64 (pow.f64 x 6) 2/45 1))
(fma.f64 (pow.f64 x 6) 2/45 (fma.f64 x x (fma.f64 (pow.f64 x 4) 1/3 1)))
(fma.f64 x x (fma.f64 (pow.f64 x 4) 1/3 (fma.f64 (pow.f64 x 6) 2/45 1)))
(*.f64 1/4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(*.f64 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2) 1/4)
(*.f64 1/4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(*.f64 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2) 1/4)
(*.f64 1/4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(*.f64 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2) 1/4)
(*.f64 1/4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(*.f64 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2) 1/4)
(*.f64 1/4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(*.f64 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2) 1/4)
(*.f64 1/4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(*.f64 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2) 1/4)
(*.f64 1/4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(*.f64 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2) 1/4)
(*.f64 1/4 (pow.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2))
(*.f64 (pow.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2) 1/4)
4
(+.f64 4 (pow.f64 x 2))
(+.f64 4 (*.f64 x x))
(fma.f64 x x 4)
(+.f64 4 (+.f64 (pow.f64 x 2) (*.f64 1/12 (pow.f64 x 4))))
(+.f64 4 (+.f64 (.f64 x x) (.f64 (pow.f64 x 4) 1/12)))
(+.f64 (*.f64 (pow.f64 x 4) 1/12) (fma.f64 x x 4))
(fma.f64 x x (fma.f64 (pow.f64 x 4) 1/12 4))
(fma.f64 (pow.f64 x 4) 1/12 (fma.f64 x x 4))
(+.f64 4 (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (.f64 1/12 (pow.f64 x 4)))))
(+.f64 4 (fma.f64 1/360 (pow.f64 x 6) (+.f64 (.f64 x x) (.f64 (pow.f64 x 4) 1/12))))
(+.f64 4 (fma.f64 (pow.f64 x 6) 1/360 (fma.f64 x x (*.f64 (pow.f64 x 4) 1/12))))
(fma.f64 (pow.f64 x 6) 1/360 (fma.f64 x x (fma.f64 (pow.f64 x 4) 1/12 4)))
(fma.f64 (pow.f64 x 4) 1/12 (fma.f64 (pow.f64 x 6) 1/360 (fma.f64 x x 4)))
(fma.f64 x x (fma.f64 (pow.f64 x 4) 1/12 (fma.f64 (pow.f64 x 6) 1/360 4)))
(+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(+.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(+.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(+.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(+.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(+.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(+.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(+.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(+.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 -1 (*.f64 2 (cosh.f64 x)))
✓	0.0b	(.f64 (+.f64 -1 (.f64 2 (cosh.f64 x))) (+.f64 -1 (*.f64 2 (cosh.f64 x))))
✓	0.0b	(/.f64 (-.f64 (.f64 (+.f64 -1 (.f64 2 (cosh.f64 x))) (+.f64 -1 (.f64 2 (cosh.f64 x)))) 1) (+.f64 (+.f64 -1 (.f64 2 (cosh.f64 x))) 1))
✓	3.3b	(-.f64 (.f64 (+.f64 -1 (.f64 2 (cosh.f64 x))) (+.f64 -1 (*.f64 2 (cosh.f64 x)))) 1)

Compiler

Compiled 77 to 55 computations (28.6% saved)

series7.0ms (0.1%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(/.f64 (-.f64 (.f64 (+.f64 -1 (.f64 2 (cosh.f64 x))) (+.f64 -1 (.f64 2 (cosh.f64 x)))) 1) (+.f64 (+.f64 -1 (.f64 2 (cosh.f64 x))) 1))
1.0ms	x	@	-inf	(/.f64 (-.f64 (.f64 (+.f64 -1 (.f64 2 (cosh.f64 x))) (+.f64 -1 (.f64 2 (cosh.f64 x)))) 1) (+.f64 (+.f64 -1 (.f64 2 (cosh.f64 x))) 1))
1.0ms	x	@	-inf	(-.f64 (.f64 (+.f64 -1 (.f64 2 (cosh.f64 x))) (+.f64 -1 (*.f64 2 (cosh.f64 x)))) 1)
1.0ms	x	@	inf	(-.f64 (.f64 (+.f64 -1 (.f64 2 (cosh.f64 x))) (+.f64 -1 (*.f64 2 (cosh.f64 x)))) 1)
1.0ms	x	@	0	(-.f64 (.f64 (+.f64 -1 (.f64 2 (cosh.f64 x))) (+.f64 -1 (*.f64 2 (cosh.f64 x)))) 1)

rewrite138.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

726×	`prod-diff_binary64`
624×	`log-prod_binary64`
521×	`fma-def_binary64`
285×	`fma-neg_binary64`
225×	`expm1-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	65
1	278	39
2	4040	37

Stop Event

1×	node limit

Counts

4 → 322

Calls

Call 1

Inputs
(-.f64 (.f64 (+.f64 -1 (.f64 2 (cosh.f64 x))) (+.f64 -1 (*.f64 2 (cosh.f64 x)))) 1)
(/.f64 (-.f64 (.f64 (+.f64 -1 (.f64 2 (cosh.f64 x))) (+.f64 -1 (.f64 2 (cosh.f64 x)))) 1) (+.f64 (+.f64 -1 (.f64 2 (cosh.f64 x))) 1))
(.f64 (+.f64 -1 (.f64 2 (cosh.f64 x))) (+.f64 -1 (*.f64 2 (cosh.f64 x))))
(+.f64 -1 (*.f64 2 (cosh.f64 x)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (pow.f64 (fma.f64 2 (cosh.f64 x) -1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (fma.f64 2 (cosh.f64 x) -1) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (+.f64 -1 (pow.f64 (fma.f64 2 (cosh.f64 x) -1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 -2 (cosh.f64 x) 1) (fma.f64 (.f64 2 (cosh.f64 x)) (fma.f64 2 (cosh.f64 x) -1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (cosh.f64 x) -1) 2)))) (cbrt.f64 (exp.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (cosh.f64 x) -1) 2)))))) (log.f64 (cbrt.f64 (exp.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (cosh.f64 x) -1) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (cosh.f64 x) -1) 2))))) (log.f64 (sqrt.f64 (exp.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (cosh.f64 x) -1) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 2 (cosh.f64 x)) (fma.f64 2 (cosh.f64 x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (+.f64 -1 (pow.f64 (fma.f64 2 (cosh.f64 x) -1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 -1 (pow.f64 (fma.f64 2 (cosh.f64 x) -1) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 (pow.f64 (cosh.f64 x) 2) 4)) (.f64 (cbrt.f64 (.f64 2 (cosh.f64 x))) (fma.f64 2 (cosh.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (cosh.f64 x) -1) 2))) (cbrt.f64 (pow.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (cosh.f64 x) -1) 2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (cosh.f64 x) -1) 2)) 2)) (cbrt.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (cosh.f64 x) -1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 2 (cosh.f64 x))) (.f64 (sqrt.f64 (.f64 2 (cosh.f64 x))) (fma.f64 2 (cosh.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (+.f64 -1 (pow.f64 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(cosh.f64 x) -2)) (fma.f64 2 (cosh.f64 x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 1 (pow.f64 (fma.f64 2 (cosh.f64 x) -1) 3)) (fma.f64 2 (cosh.f64 x) -2)) (+.f64 (pow.f64 (fma.f64 2 (cosh.f64 x) -1) 2) (+.f64 1 (fma.f64 -2 (cosh.f64 x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (cosh.f64 x) -1) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (cosh.f64 x) -1) 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (cosh.f64 x) -1) 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (cosh.f64 x) -1) 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (cosh.f64 x) -1) 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (cosh.f64 x) -1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (cosh.f64 x) -1) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (cosh.f64 x) -1) 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (.f64 2 (log.f64 (fma.f64 2 (cosh.f64 x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (.f64 (log.f64 (fma.f64 2 (cosh.f64 x) -1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (.f64 (.f64 2 (log.f64 (fma.f64 2 (cosh.f64 x) -1))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (cosh.f64 x) -1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (cosh.f64 x) -1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (cosh.f64 x) -1) 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (fma.f64 2 (cosh.f64 x) -1) (fma.f64 (.f64 2 (cosh.f64 x)) (fma.f64 2 (cosh.f64 x) 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(.f64 2 (cosh.f64 x))) (sqrt.f64 (fma.f64 2 (cosh.f64 x) -1))) (sqrt.f64 (fma.f64 -2 (cosh.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log.f64 (.f64 2 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (.f64 (log.f64 (.f64 2 (cosh.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 2 (cosh.f64 x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 2 (cosh.f64 x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (fma.f64 2 (cosh.f64 x) -1)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 2 (cosh.f64 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cosh.f64 x) 2 -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 2 (cosh.f64 x)) 1 -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 2 (cosh.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 -1 (pow.f64 (fma.f64 2 (cosh.f64 x) -1) 2)) (/.f64 1 (fma.f64 2 (cosh.f64 x) 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fma.f64 (*.f64 2 (sqrt.f64 (cosh.f64 x))) (sqrt.f64 (cosh.f64 x)) -1)))))

simplify62.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

917×	`fma-def_binary64`
801×	`distribute-rgt-out_binary64`
599×	`associate-l_binary64`
461×	`distribute-rgt-in_binary64`
460×	`associate-r_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	51	861
1	136	751
2	333	747
3	1144	747
4	5213	603

Stop Event

1×	node limit

Counts

370 → 359

Calls

Call 1

Inputs
(*.f64 2 (pow.f64 x 2))
(+.f64 (.f64 7/6 (pow.f64 x 4)) (.f64 2 (pow.f64 x 2)))
(+.f64 (.f64 7/6 (pow.f64 x 4)) (+.f64 (.f64 2 (pow.f64 x 2)) (*.f64 31/180 (pow.f64 x 6))))
(+.f64 (.f64 7/6 (pow.f64 x 4)) (+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 (.f64 31/180 (pow.f64 x 6)) (.f64 127/10080 (pow.f64 x 8)))))
(-.f64 (pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2) 1)
(-.f64 (pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2) 1)
(-.f64 (pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2) 1)
(-.f64 (pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2) 1)
(-.f64 (pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2) 1)
(-.f64 (pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2) 1)
(-.f64 (pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2) 1)
(-.f64 (pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2) 1)
(pow.f64 x 2)
(+.f64 (pow.f64 x 2) (*.f64 1/12 (pow.f64 x 4)))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (.f64 1/12 (pow.f64 x 4))))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/20160 (pow.f64 x 8)))))
(/.f64 (-.f64 (pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2) 1) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2) 1) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2) 1) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2) 1) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2) 1) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2) 1) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2) 1) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (-.f64 (pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2) 1) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
1
(+.f64 (*.f64 2 (pow.f64 x 2)) 1)
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 (.f64 7/6 (pow.f64 x 4)) 1))
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 (.f64 7/6 (pow.f64 x 4)) (+.f64 1 (*.f64 31/180 (pow.f64 x 6)))))
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2)
1
(+.f64 1 (pow.f64 x 2))
(+.f64 1 (+.f64 (pow.f64 x 2) (*.f64 1/12 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (.f64 1/12 (pow.f64 x 4)))))
(-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1)
(-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1)
(-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1)
(-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1)
(-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1)
(-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1)
(-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1)
(-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1)

Outputs
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(+.f64 (.f64 7/6 (pow.f64 x 4)) (.f64 2 (pow.f64 x 2)))
(fma.f64 7/6 (pow.f64 x 4) (.f64 2 (.f64 x x)))
(fma.f64 2 (.f64 x x) (.f64 7/6 (pow.f64 x 4)))
(.f64 (.f64 x x) (fma.f64 x (*.f64 x 7/6) 2))
(.f64 x (.f64 x (fma.f64 x (*.f64 x 7/6) 2)))
(+.f64 (.f64 7/6 (pow.f64 x 4)) (+.f64 (.f64 2 (pow.f64 x 2)) (*.f64 31/180 (pow.f64 x 6))))
(fma.f64 7/6 (pow.f64 x 4) (fma.f64 2 (.f64 x x) (.f64 31/180 (pow.f64 x 6))))
(fma.f64 2 (.f64 x x) (fma.f64 31/180 (pow.f64 x 6) (.f64 7/6 (pow.f64 x 4))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x 7/6) 2) (*.f64 31/180 (pow.f64 x 6)))
(+.f64 (.f64 7/6 (pow.f64 x 4)) (+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 (.f64 31/180 (pow.f64 x 6)) (.f64 127/10080 (pow.f64 x 8)))))
(fma.f64 7/6 (pow.f64 x 4) (fma.f64 2 (.f64 x x) (fma.f64 31/180 (pow.f64 x 6) (.f64 127/10080 (pow.f64 x 8)))))
(fma.f64 7/6 (pow.f64 x 4) (fma.f64 2 (.f64 x x) (fma.f64 127/10080 (pow.f64 x 8) (.f64 31/180 (pow.f64 x 6)))))
(fma.f64 2 (.f64 x x) (fma.f64 7/6 (pow.f64 x 4) (fma.f64 31/180 (pow.f64 x 6) (.f64 127/10080 (pow.f64 x 8)))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x 7/6) 2) (fma.f64 31/180 (pow.f64 x 6) (*.f64 127/10080 (pow.f64 x 8))))
(-.f64 (pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2) 1)
(+.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1)) 2) -1)
(+.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x)) 2) -1)
(+.f64 (pow.f64 (+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x))) 2) -1)
(-.f64 (pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2) 1)
(+.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1)) 2) -1)
(+.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x)) 2) -1)
(+.f64 (pow.f64 (+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x))) 2) -1)
(-.f64 (pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2) 1)
(+.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1)) 2) -1)
(+.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x)) 2) -1)
(+.f64 (pow.f64 (+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x))) 2) -1)
(-.f64 (pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2) 1)
(+.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1)) 2) -1)
(+.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x)) 2) -1)
(+.f64 (pow.f64 (+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x))) 2) -1)
(-.f64 (pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2) 1)
(+.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1)) 2) -1)
(+.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x)) 2) -1)
(+.f64 (pow.f64 (+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x))) 2) -1)
(-.f64 (pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2) 1)
(+.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1)) 2) -1)
(+.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x)) 2) -1)
(+.f64 (pow.f64 (+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x))) 2) -1)
(-.f64 (pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2) 1)
(+.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1)) 2) -1)
(+.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x)) 2) -1)
(+.f64 (pow.f64 (+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x))) 2) -1)
(-.f64 (pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2) 1)
(+.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1)) 2) -1)
(+.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x)) 2) -1)
(+.f64 (pow.f64 (+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x))) 2) -1)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) (*.f64 1/12 (pow.f64 x 4)))
(+.f64 (.f64 x x) (.f64 (pow.f64 x 4) 1/12))
(fma.f64 (pow.f64 x 4) 1/12 (*.f64 x x))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (.f64 1/12 (pow.f64 x 4))))
(fma.f64 1/360 (pow.f64 x 6) (+.f64 (.f64 x x) (.f64 (pow.f64 x 4) 1/12)))
(fma.f64 (pow.f64 x 6) 1/360 (fma.f64 (pow.f64 x 4) 1/12 (*.f64 x x)))
(fma.f64 x x (fma.f64 (pow.f64 x 4) 1/12 (*.f64 (pow.f64 x 6) 1/360)))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/20160 (pow.f64 x 8)))))
(fma.f64 1/360 (pow.f64 x 6) (+.f64 (.f64 x x) (fma.f64 1/12 (pow.f64 x 4) (.f64 (pow.f64 x 8) 1/20160))))
(fma.f64 (pow.f64 x 6) 1/360 (fma.f64 x x (fma.f64 (pow.f64 x 4) 1/12 (*.f64 (pow.f64 x 8) 1/20160))))
(fma.f64 (pow.f64 x 6) 1/360 (fma.f64 (pow.f64 x 8) 1/20160 (fma.f64 (pow.f64 x 4) 1/12 (*.f64 x x))))
(fma.f64 (pow.f64 x 4) (fma.f64 (pow.f64 x 4) 1/20160 1/12) (fma.f64 x x (*.f64 (pow.f64 x 6) 1/360)))
(fma.f64 (pow.f64 x 4) 1/12 (fma.f64 (pow.f64 x 6) 1/360 (fma.f64 (pow.f64 x 8) 1/20160 (*.f64 x x))))
(/.f64 (-.f64 (pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2) 1) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1)) 2) -1) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x)) 2) -1) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x))) 2) -1) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 (expm1.f64 x) (expm1.f64 (neg.f64 x)))
(/.f64 (-.f64 (pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2) 1) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1)) 2) -1) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x)) 2) -1) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x))) 2) -1) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 (expm1.f64 x) (expm1.f64 (neg.f64 x)))
(/.f64 (-.f64 (pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2) 1) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1)) 2) -1) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x)) 2) -1) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x))) 2) -1) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 (expm1.f64 x) (expm1.f64 (neg.f64 x)))
(/.f64 (-.f64 (pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2) 1) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1)) 2) -1) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x)) 2) -1) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x))) 2) -1) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 (expm1.f64 x) (expm1.f64 (neg.f64 x)))
(/.f64 (-.f64 (pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2) 1) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1)) 2) -1) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x)) 2) -1) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x))) 2) -1) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 (expm1.f64 x) (expm1.f64 (neg.f64 x)))
(/.f64 (-.f64 (pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2) 1) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1)) 2) -1) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x)) 2) -1) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x))) 2) -1) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 (expm1.f64 x) (expm1.f64 (neg.f64 x)))
(/.f64 (-.f64 (pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2) 1) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1)) 2) -1) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x)) 2) -1) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x))) 2) -1) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 (expm1.f64 x) (expm1.f64 (neg.f64 x)))
(/.f64 (-.f64 (pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2) 1) (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(/.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1)) 2) -1) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x)) 2) -1) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x))) 2) -1) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 (expm1.f64 x) (expm1.f64 (neg.f64 x)))
1
(+.f64 (*.f64 2 (pow.f64 x 2)) 1)
(fma.f64 2 (*.f64 x x) 1)
(fma.f64 x (*.f64 2 x) 1)
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 (.f64 7/6 (pow.f64 x 4)) 1))
(fma.f64 2 (*.f64 x x) (fma.f64 7/6 (pow.f64 x 4) 1))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x 7/6) 2) 1)
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 (.f64 7/6 (pow.f64 x 4)) (+.f64 1 (*.f64 31/180 (pow.f64 x 6)))))
(fma.f64 2 (.f64 x x) (fma.f64 7/6 (pow.f64 x 4) (+.f64 (.f64 31/180 (pow.f64 x 6)) 1)))
(fma.f64 2 (*.f64 x x) (fma.f64 7/6 (pow.f64 x 4) (fma.f64 31/180 (pow.f64 x 6) 1)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x 7/6) 2) (fma.f64 31/180 (pow.f64 x 6) 1))
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1)) 2)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x)) 2)
(pow.f64 (+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x))) 2)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1)) 2)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x)) 2)
(pow.f64 (+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x))) 2)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1)) 2)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x)) 2)
(pow.f64 (+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x))) 2)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1)) 2)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x)) 2)
(pow.f64 (+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x))) 2)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1)) 2)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x)) 2)
(pow.f64 (+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x))) 2)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1)) 2)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x)) 2)
(pow.f64 (+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x))) 2)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1)) 2)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x)) 2)
(pow.f64 (+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x))) 2)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1) 2)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1)) 2)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x)) 2)
(pow.f64 (+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x))) 2)
1
(+.f64 1 (pow.f64 x 2))
(+.f64 (*.f64 x x) 1)
(fma.f64 x x 1)
(+.f64 1 (+.f64 (pow.f64 x 2) (*.f64 1/12 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 x x) (.f64 (pow.f64 x 4) 1/12)))
(+.f64 1 (fma.f64 (pow.f64 x 4) 1/12 (*.f64 x x)))
(fma.f64 (pow.f64 x 4) 1/12 (fma.f64 x x 1))
(+.f64 1 (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (.f64 1/12 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 1/360 (pow.f64 x 6) (+.f64 (.f64 x x) (.f64 (pow.f64 x 4) 1/12))))
(+.f64 1 (fma.f64 (pow.f64 x 6) 1/360 (fma.f64 (pow.f64 x 4) 1/12 (*.f64 x x))))
(fma.f64 (pow.f64 x 6) 1/360 (fma.f64 (pow.f64 x 4) 1/12 (fma.f64 x x 1)))
(fma.f64 x x (fma.f64 (pow.f64 x 4) 1/12 (fma.f64 (pow.f64 x 6) 1/360 1)))
(-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1)
(+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1))
(+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x))
(+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x)))
(-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1)
(+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1))
(+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x))
(+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x)))
(-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1)
(+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1))
(+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x))
(+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x)))
(-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1)
(+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1))
(+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x))
(+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x)))
(-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1)
(+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1))
(+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x))
(+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x)))
(-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1)
(+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1))
(+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x))
(+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x)))
(-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1)
(+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1))
(+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x))
(+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x)))
(-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 1)
(+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 1))
(+.f64 (exp.f64 (neg.f64 x)) (expm1.f64 x))
(+.f64 (exp.f64 x) (expm1.f64 (neg.f64 x)))

eval583.0ms (5.2%)

Compiler: Compiled 29151 to 21583 computations (26% saved)

prune119.0ms (1.1%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	924	4	928
Fresh	1	0	1
Picked	1	0	1
Done	3	4	7
Total	929	8	937

Error

0.0b

Counts

937 → 8

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.6b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
▶	60.3b	(neg.f64 x)
▶	27.8b	(+.f64 (expm1.f64 x) (expm1.f64 (neg.f64 x)))
✓	28.8b	(+.f64 -2 (*.f64 2 (cosh.f64 x)))
✓	0.9b	(*.f64 x x)
▶	60.1b	(expm1.f64 (neg.f64 x))
✓	28.8b	(expm1.f64 (log1p.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))))
▶	0.5b	(fma.f64 x x (.f64 (pow.f64 x 4) (+.f64 (.f64 1/360 (*.f64 x x)) 1/12)))

Compiler

Compiled 58 to 42 computations (27.6% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (neg.f64 x))

Compiler

Compiled 7 to 3 computations (57.1% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(expm1.f64 (neg.f64 x))
0.0ms	x	@	inf	(expm1.f64 (neg.f64 x))
0.0ms	x	@	-inf	(expm1.f64 (neg.f64 x))

rewrite51.0ms (0.5%)

Algorithm

1×	egg-rewrite-iter-limit
1×	batch-egg-rewrite

Rules

286×	`associate-r_binary64`
282×	`pow1_binary64`
274×	`add-sqr-sqrt_binary64`
268×	`*-un-lft-identity_binary64`
261×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	5
1	80	5
2	958	5
0	4	5

Stop Event

1×	iter limit
1×	node limit

Counts

1 → 9

Calls

Call 1

Inputs
(expm1.f64 (neg.f64 x))

Outputs

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

simplify52.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

633×	`cancel-sign-sub-inv_binary64`
499×	`fma-neg_binary64`
370×	`distribute-rgt-out--_binary64`
315×	`fma-def_binary64`
312×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	27	94
1	71	94
2	163	93
3	552	86
4	2019	86
5	5640	86

Stop Event

1×	node limit

Counts

21 → 19

Calls

Call 1

Inputs
(*.f64 -1 x)
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1 x))
(+.f64 (.f64 -1/6 (pow.f64 x 3)) (+.f64 (.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x)))
(+.f64 (.f64 -1/6 (pow.f64 x 3)) (+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 1/24 (pow.f64 x 4)) (.f64 -1 x))))
(-.f64 (exp.f64 (neg.f64 x)) 1)
(-.f64 (exp.f64 (neg.f64 x)) 1)
(-.f64 (exp.f64 (neg.f64 x)) 1)
(-.f64 (exp.f64 (neg.f64 x)) 1)
(-.f64 (exp.f64 (*.f64 -1 x)) 1)
(-.f64 (exp.f64 (*.f64 -1 x)) 1)
(-.f64 (exp.f64 (*.f64 -1 x)) 1)
(-.f64 (exp.f64 (*.f64 -1 x)) 1)

Outputs
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1 x))
(fma.f64 1/2 (*.f64 x x) (neg.f64 x))
(-.f64 (.f64 1/2 (.f64 x x)) x)
(-.f64 (.f64 x (.f64 x 1/2)) x)
(*.f64 x (fma.f64 x 1/2 -1))
(+.f64 (.f64 -1/6 (pow.f64 x 3)) (+.f64 (.f64 1/2 (pow.f64 x 2)) (*.f64 -1 x)))
(fma.f64 -1/6 (pow.f64 x 3) (fma.f64 1/2 (*.f64 x x) (neg.f64 x)))
(-.f64 (fma.f64 -1/6 (pow.f64 x 3) (.f64 1/2 (.f64 x x))) x)
(-.f64 (.f64 (.f64 x x) (+.f64 1/2 (*.f64 x -1/6))) x)
(fma.f64 x (*.f64 x (fma.f64 x -1/6 1/2)) (neg.f64 x))
(+.f64 (.f64 -1/6 (pow.f64 x 3)) (+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 1/24 (pow.f64 x 4)) (.f64 -1 x))))
(fma.f64 -1/6 (pow.f64 x 3) (fma.f64 1/2 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 4) (neg.f64 x))))
(fma.f64 -1/6 (pow.f64 x 3) (fma.f64 1/2 (.f64 x x) (-.f64 (.f64 1/24 (pow.f64 x 4)) x)))
(-.f64 (fma.f64 -1/6 (pow.f64 x 3) (fma.f64 x (.f64 x 1/2) (.f64 1/24 (pow.f64 x 4)))) x)
(fma.f64 x (*.f64 x (fma.f64 x -1/6 1/2)) (fma.f64 1/24 (pow.f64 x 4) (neg.f64 x)))
(fma.f64 1/24 (pow.f64 x 4) (fma.f64 x (*.f64 x (fma.f64 x -1/6 1/2)) (neg.f64 x)))
(-.f64 (exp.f64 (neg.f64 x)) 1)
(expm1.f64 (neg.f64 x))
(-.f64 (exp.f64 (neg.f64 x)) 1)
(expm1.f64 (neg.f64 x))
(-.f64 (exp.f64 (neg.f64 x)) 1)
(expm1.f64 (neg.f64 x))
(-.f64 (exp.f64 (neg.f64 x)) 1)
(expm1.f64 (neg.f64 x))
(-.f64 (exp.f64 (*.f64 -1 x)) 1)
(expm1.f64 (neg.f64 x))
(-.f64 (exp.f64 (*.f64 -1 x)) 1)
(expm1.f64 (neg.f64 x))
(-.f64 (exp.f64 (*.f64 -1 x)) 1)
(expm1.f64 (neg.f64 x))
(-.f64 (exp.f64 (*.f64 -1 x)) 1)
(expm1.f64 (neg.f64 x))

localize2.0ms (0%)

Compiler: Compiled 4 to 2 computations (50% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(expm1.f64 (neg.f64 x))
✓	6.1b	(+.f64 (expm1.f64 x) (expm1.f64 (neg.f64 x)))

Compiler

Compiled 15 to 5 computations (66.7% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(+.f64 (expm1.f64 x) (expm1.f64 (neg.f64 x)))
0.0ms	x	@	-inf	(+.f64 (expm1.f64 x) (expm1.f64 (neg.f64 x)))
0.0ms	x	@	inf	(+.f64 (expm1.f64 x) (expm1.f64 (neg.f64 x)))

rewrite41.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

492×	`pow1_binary64`
479×	`add-sqr-sqrt_binary64`
459×	`add-log-exp_binary64`
459×	`log1p-expm1-u_binary64`
459×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	129	8
2	1874	8

Stop Event

1×	node limit

Counts

1 → 30

Calls

Call 1

Inputs
(+.f64 (expm1.f64 x) (expm1.f64 (neg.f64 x)))

Outputs

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

simplify57.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

558×	`distribute-rgt-out_binary64`
423×	`associate-/l/_binary64`
415×	`unswap-sqr_binary64`
382×	`distribute-lft-out_binary64`
342×	`associate-/r/_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	31	168
1	76	162
2	157	162
3	449	162
4	2059	162
5	4616	162
6	5791	162

Stop Event

1×	node limit

Counts

42 → 41

Calls

Call 1

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

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

localize19.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 1/360 (.f64 x x)) 1/12)
✓	0.1b	(.f64 (pow.f64 x 4) (+.f64 (.f64 1/360 (*.f64 x x)) 1/12))
✓	0.1b	(.f64 1/360 (.f64 x x))

Compiler

Compiled 48 to 28 computations (41.7% saved)

series3.0ms (0%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(.f64 1/360 (.f64 x x))
0.0ms	x	@	0	(.f64 1/360 (.f64 x x))
0.0ms	x	@	inf	(.f64 (pow.f64 x 4) (+.f64 (.f64 1/360 (*.f64 x x)) 1/12))
0.0ms	x	@	0	(.f64 (pow.f64 x 4) (+.f64 (.f64 1/360 (*.f64 x x)) 1/12))
0.0ms	x	@	-inf	(.f64 (pow.f64 x 4) (+.f64 (.f64 1/360 (*.f64 x x)) 1/12))

rewrite69.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

466×	`log-prod_binary64`
401×	`prod-diff_binary64`
350×	`exp-prod_binary64`
310×	`pow-prod-down_binary64`
259×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	29
1	225	29
2	2717	29

Stop Event

1×	node limit

Counts

3 → 140

Calls

Call 1

Inputs
(.f64 1/360 (.f64 x x))
(.f64 (pow.f64 x 4) (+.f64 (.f64 1/360 (*.f64 x x)) 1/12))
(+.f64 (.f64 1/360 (.f64 x x)) 1/12)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 1/360 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (*.f64 1/360 x)) x)) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (*.f64 1/360 x)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (*.f64 1/360 x)) x))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (*.f64 1/360 x)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 1/360 (*.f64 x x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/360 (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 4) 1/129600) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 1/360 (*.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 1/360)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/46656000 (pow.f64 x 6)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (fma.f64 2 (log.f64 x) (log1p.f64 -359/360)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (fma.f64 2 (log.f64 x) (log1p.f64 -359/360))) 2)) (cbrt.f64 (fma.f64 2 (log.f64 x) (log1p.f64 -359/360))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (fma.f64 2 (log.f64 x) (log1p.f64 -359/360)))) (sqrt.f64 (fma.f64 2 (log.f64 x) (log1p.f64 -359/360))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 4) 1/129600))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (*.f64 1/360 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 1/360 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 1/46656000 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 1/360 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 1/360 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (fma.f64 2 (log.f64 x) (log1p.f64 -359/360)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (fma.f64 2 (log.f64 x) (log1p.f64 -359/360)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 1/360 (*.f64 x x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 x (sqrt.f64 1/360))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 1/46656000 (pow.f64 x 6))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (fma.f64 2 (log.f64 x) (log1p.f64 -359/360)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (fma.f64 2 (log.f64 x) (log1p.f64 -359/360)) 3) 1/3))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/360 (pow.f64 x 6)) (*.f64 (pow.f64 x 4) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 x 4) 1/12) (*.f64 1/360 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (pow.f64 x 4) (fma.f64 1/360 (*.f64 x x) 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 1/360 (pow.f64 x 6)) 1) (*.f64 (*.f64 (pow.f64 x 4) 1/12) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 1/360 (*.f64 x x) 1/12)) (pow.f64 x 4))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 1/360 (*.f64 x x) 1/12)) (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (fma.f64 1/360 (*.f64 x x) 1/12)) (pow.f64 x 4)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (fma.f64 1/360 (*.f64 x x) 1/12)) (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 x 4) (fma.f64 1/360 (*.f64 x x) 1/12)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 1/360 (pow.f64 x 6)) 3) (pow.f64 (*.f64 (pow.f64 x 4) 1/12) 3)) (+.f64 (pow.f64 (*.f64 1/360 (pow.f64 x 6)) 2) (-.f64 (pow.f64 (*.f64 (pow.f64 x 4) 1/12) 2) (*.f64 (*.f64 1/360 (pow.f64 x 6)) (*.f64 (pow.f64 x 4) 1/12)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 1/360 (pow.f64 x 6)) 2) (pow.f64 (*.f64 (pow.f64 x 4) 1/12) 2)) (-.f64 (*.f64 1/360 (pow.f64 x 6)) (*.f64 (pow.f64 x 4) 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (fma.f64 1/46656000 (pow.f64 x 6) 1/1728) (pow.f64 x 4)) (-.f64 (fma.f64 (pow.f64 x 4) 1/129600 1/144) (*.f64 (*.f64 x x) 1/4320)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (fma.f64 (pow.f64 x 4) 1/129600 -1/144) (pow.f64 x 4)) (fma.f64 1/360 (*.f64 x x) -1/12))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 x 4) (fma.f64 1/46656000 (pow.f64 x 6) 1/1728)) (-.f64 (fma.f64 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(cbrt.f64 (log.f64 (*.f64 (pow.f64 x 4) (fma.f64 1/360 (*.f64 x x) 1/12)))) 2)) (cbrt.f64 (log.f64 (*.f64 (pow.f64 x 4) (fma.f64 1/360 (*.f64 x x) 1/12)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (pow.f64 x 4) (fma.f64 1/360 (*.f64 x x) 1/12))))) (sqrt.f64 (log.f64 (*.f64 (pow.f64 x 4) (fma.f64 1/360 (*.f64 x x) 1/12)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (fma.f64 1/360 (*.f64 x x) 1/12) 2) (pow.f64 x 8)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (fma.f64 1/360 (*.f64 x x) 1/12)) (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 x 4) (fma.f64 1/360 (*.f64 x x) 1/12)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (fma.f64 1/360 (*.f64 x x) 1/12) 3) (pow.f64 x 12)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 x 4) (fma.f64 1/360 (*.f64 x x) 1/12))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 x 4) (fma.f64 1/360 (*.f64 x x) 1/12))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 x 4) (fma.f64 1/360 (*.f64 x x) 1/12))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 x 4) (fma.f64 1/360 (*.f64 x x) 1/12))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 (fma.f64 1/360 (*.f64 x x) 1/12) 3) (pow.f64 x 12))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) (fma.f64 1/360 (*.f64 x x) 1/12)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (*.f64 x x) (sqrt.f64 (fma.f64 1/360 (*.f64 x x) 1/12)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (pow.f64 x 4) (fma.f64 1/360 (*.f64 x x) 1/12))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/360 (pow.f64 x 6) (*.f64 (pow.f64 x 4) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) (pow.f64 (*.f64 x (*.f64 x (sqrt.f64 1/360))) 2) (*.f64 (pow.f64 x 4) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) (*.f64 (*.f64 x x) 1/12) (*.f64 1/360 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) (*.f64 1/360 (pow.f64 x 4)) (*.f64 (pow.f64 x 4) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/360 (*.f64 x x)) (pow.f64 x 4) (*.f64 (pow.f64 x 4) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 4) (*.f64 1/360 (*.f64 x x)) (*.f64 (pow.f64 x 4) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 4) 1/12 (*.f64 1/360 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/12 (pow.f64 x 4) (*.f64 1/360 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 1/360 (pow.f64 x 6)) (*.f64 (pow.f64 x 4) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 (pow.f64 x 4) 1/12) (*.f64 1/360 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 6) 1/360 (*.f64 (pow.f64 x 4) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 1/129600)) (*.f64 (cbrt.f64 (*.f64 1/360 (*.f64 x x))) (pow.f64 x 4)) (*.f64 (pow.f64 x 4) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 8) (*.f64 (*.f64 (cbrt.f64 x) x) 1/12) (*.f64 1/360 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 8) (*.f64 (*.f64 (cbrt.f64 x) x) (*.f64 1/360 (*.f64 x x))) (*.f64 (pow.f64 x 4) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (sqrt.f64 1/360)) (*.f64 (*.f64 x (sqrt.f64 1/360)) (pow.f64 x 4)) (*.f64 (pow.f64 x 4) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/360 (pow.f64 x 6)) 1 (*.f64 (*.f64 (pow.f64 x 4) 1/12) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/360 x) (pow.f64 x 5) (*.f64 (pow.f64 x 4) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 1/360 (pow.f64 x 6))) 2) (cbrt.f64 (*.f64 1/360 (pow.f64 x 6))) (*.f64 (pow.f64 x 4) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 1/12)) 2) (cbrt.f64 (*.f64 (pow.f64 x 4) 1/12)) (*.f64 1/360 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 1/360 (pow.f64 x 6))) (sqrt.f64 (*.f64 1/360 (pow.f64 x 6))) (*.f64 (pow.f64 x 4) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 (pow.f64 x 4) 1/12)) (sqrt.f64 (*.f64 (pow.f64 x 4) 1/12)) (*.f64 1/360 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (*.f64 (*.f64 x (sqrt.f64 1/360)) x) 2) (*.f64 x x) (*.f64 (pow.f64 x 4) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/12 (*.f64 x x)) (*.f64 x x) (*.f64 1/360 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/12 (pow.f64 (cbrt.f64 x) 8)) (*.f64 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((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 1/360 (*.f64 x x) 1/12))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (pow.f64 x 4) 1/129600) (fma.f64 1/360 (*.f64 x x) -1/12)) (/.f64 1/144 (fma.f64 1/360 (*.f64 x x) -1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 1/360 (*.f64 x x) 1/12) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 1/360 (*.f64 x x) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 1/360 (*.f64 x x) 1/12)) (pow.f64 (cbrt.f64 (fma.f64 1/360 (*.f64 x x) 1/12)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 1/360 (*.f64 x x) 1/12)) 2) (cbrt.f64 (fma.f64 1/360 (*.f64 x x) 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 1/360 (*.f64 x x) 1/12)) (sqrt.f64 (fma.f64 1/360 (*.f64 x x) 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 1/46656000 (pow.f64 x 6) 1/1728) (/.f64 1 (-.f64 (fma.f64 (pow.f64 x 4) 1/129600 1/144) (*.f64 (*.f64 x x) 1/4320))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (pow.f64 x 4) 1/129600 -1/144) (/.f64 1 (fma.f64 1/360 (*.f64 x x) -1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (fma.f64 (pow.f64 x 4) 1/129600 1/144) (*.f64 (*.f64 x x) 1/4320)) (fma.f64 1/46656000 (pow.f64 x 6) 1/1728)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 1/360 (*.f64 x x) -1/12) (fma.f64 (pow.f64 x 4) 1/129600 -1/144)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 1/46656000 (pow.f64 x 6) 1/1728) (-.f64 (fma.f64 (pow.f64 x 4) 1/129600 1/144) (*.f64 (*.f64 x x) 1/4320)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 1/46656000 (pow.f64 x 6) 1/1728) (+.f64 1/144 (-.f64 (*.f64 (pow.f64 x 4) 1/129600) (*.f64 (*.f64 x x) 1/4320))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 x 4) 1/129600 -1/144) (fma.f64 1/360 (*.f64 x x) -1/12))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 1/46656000 (pow.f64 x 6) 1/1728)) (neg.f64 (-.f64 (fma.f64 (pow.f64 x 4) 1/129600 1/144) (*.f64 (*.f64 x x) 1/4320))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 (pow.f64 x 4) 1/129600 -1/144)) (neg.f64 (fma.f64 1/360 (*.f64 x x) -1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/144 (*.f64 (pow.f64 x 4) 1/129600)) (-.f64 1/12 (*.f64 1/360 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 1/360 (*.f64 x x) 1/12) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/360 (*.f64 x x) 1/12) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/360 (*.f64 x x) 1/12) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 1/360 (*.f64 x x) 1/12)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 1/360 (*.f64 x x) 1/12)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (fma.f64 1/360 (*.f64 x x) 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (fma.f64 (pow.f64 x 4) 1/129600 1/144) (*.f64 (*.f64 x x) 1/4320)) (fma.f64 1/46656000 (pow.f64 x 6) 1/1728)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 1/360 (*.f64 x x) -1/12) (fma.f64 (pow.f64 x 4) 1/129600 -1/144)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (fma.f64 1/360 (*.f64 x x) 1/12))) 2)) (cbrt.f64 (log.f64 (fma.f64 1/360 (*.f64 x x) 1/12))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (fma.f64 1/360 (*.f64 x x) 1/12)))) (sqrt.f64 (log.f64 (fma.f64 1/360 (*.f64 x x) 1/12))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 1/360 (*.f64 x x) 1/12) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 1/360 (*.f64 x x) 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 1/360 (*.f64 x x) 1/12))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 1/360 (*.f64 x x) 1/12) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 1/360 (*.f64 x x) 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 1/360 (*.f64 x x) 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 1/360 (*.f64 x x) 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 1/360 (*.f64 x x) 1/12)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 1/360 (*.f64 x x) 1/12) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (fma.f64 1/360 (*.f64 x x) 1/12))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (fma.f64 1/360 (*.f64 x x) 1/12))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (fma.f64 1/360 (*.f64 x x) 1/12)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/360 (*.f64 x x) 1/12)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (*.f64 1/360 x) 1/12)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) 1/360 1/12)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/360 (*.f64 x x)) 1 1/12)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 1/360 (*.f64 x x)) 1/12)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 1/360 (*.f64 x x))) (cbrt.f64 (*.f64 (pow.f64 x 4) 1/129600)) 1/12)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 1/129600)) (cbrt.f64 (*.f64 1/360 (*.f64 x x))) 1/12)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 x) x) (*.f64 (pow.f64 (cbrt.f64 x) 2) 1/360) 1/12)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (sqrt.f64 1/360)) (*.f64 x (sqrt.f64 1/360)) 1/12)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/360 x) x 1/12)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/360 (*.f64 (cbrt.f64 x) x)) (pow.f64 (cbrt.f64 x) 2) 1/12)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 1/360 x) 1) x 1/12)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 1/360 x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) 1/12)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 1/360 x) (sqrt.f64 x)) (sqrt.f64 x) 1/12)))))

simplify183.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1124×	`sqr-pow_binary64`
748×	`cube-prod_binary64`
653×	`pow-sqr_binary64`
429×	`unpow3_binary64`
423×	`cube-mult_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	336
1	32	318
2	66	318
3	175	318
4	728	318
5	1824	318
6	2174	318
7	2369	318
8	2563	318
9	2814	318
10	3129	318
11	3537	318
12	3973	318
13	4463	318
14	5070	318
15	5322	318
16	5570	318
17	5834	318
18	6104	318
19	6366	318
20	7771	318

Stop Event

1×	node limit

Counts

176 → 148

Calls

Call 1

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

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

eval74.0ms (0.7%)

Compiler: Compiled 3624 to 2195 computations (39.4% saved)

prune30.0ms (0.3%)

Pruning

8 alts after pruning (0 fresh and 8 done)

	Pruned	Kept	Total
New	227	0	227
Fresh	0	0	0
Picked	0	1	1
Done	0	7	7
Total	227	8	235

Error

0.0b

Counts

235 → 8

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.6b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
✓	60.3b	(neg.f64 x)
✓	27.8b	(+.f64 (expm1.f64 x) (expm1.f64 (neg.f64 x)))
✓	28.8b	(+.f64 -2 (*.f64 2 (cosh.f64 x)))
✓	0.9b	(*.f64 x x)
✓	60.1b	(expm1.f64 (neg.f64 x))
✓	28.8b	(expm1.f64 (log1p.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))))
✓	0.5b	(fma.f64 x x (.f64 (pow.f64 x 4) (+.f64 (.f64 1/360 (*.f64 x x)) 1/12)))

Compiler

Compiled 58 to 42 computations (27.6% saved)

regimes19.0ms (0.2%)

Counts

19 → 1

Calls

Call 1

Inputs
(neg.f64 x)
(*.f64 x x)
(expm1.f64 (neg.f64 x))
(+.f64 -1 (exp.f64 (neg.f64 x)))
(+.f64 -2 (*.f64 2 (cosh.f64 x)))
(+.f64 (expm1.f64 x) (expm1.f64 (neg.f64 x)))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))
(+.f64 -2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
(fma.f64 x x (.f64 (pow.f64 x 4) (+.f64 (.f64 1/360 (*.f64 x x)) 1/12)))
(expm1.f64 (log1p.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))))
(fma.f64 x x (.f64 (pow.f64 x 4) (fma.f64 1/360 (.f64 x x) 1/12)))
(/.f64 (-.f64 (.f64 (pow.f64 (cosh.f64 x) 2) 4) 4) (-.f64 (.f64 2 (cosh.f64 x)) -2))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (.f64 1/12 (pow.f64 x 4))))
(/.f64 (-.f64 4 (.f64 (.f64 2 (cosh.f64 x)) (.f64 2 (cosh.f64 x)))) (-.f64 -2 (.f64 2 (cosh.f64 x))))
(/.f64 (-.f64 (.f64 (+.f64 -1 (.f64 2 (cosh.f64 x))) (+.f64 -1 (.f64 2 (cosh.f64 x)))) 1) (+.f64 (+.f64 -1 (.f64 2 (cosh.f64 x))) 1))
(fma.f64 x x (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4))))
(/.f64 (log.f64 (exp.f64 (fma.f64 -4 (pow.f64 (cosh.f64 x) 2) 4))) (-.f64 -2 (*.f64 2 (cosh.f64 x))))

Outputs
(fma.f64 x x (.f64 (pow.f64 x 4) (+.f64 (.f64 1/360 (*.f64 x x)) 1/12)))

Calls

2 calls:

10.0ms	x
4.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Results

Error	Segments	Branch
0.5b	1	`x`
0.5b	1	`(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))`

Compiler

Compiled 205 to 133 computations (35.1% saved)

regimes12.0ms (0.1%)

Counts

10 → 1

Calls

Call 1

Inputs
(neg.f64 x)
(*.f64 x x)
(expm1.f64 (neg.f64 x))
(+.f64 -1 (exp.f64 (neg.f64 x)))
(+.f64 -2 (*.f64 2 (cosh.f64 x)))
(+.f64 (expm1.f64 x) (expm1.f64 (neg.f64 x)))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))
(+.f64 -2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Outputs
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))

Calls

2 calls:

7.0ms	x
2.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Results

Error	Segments	Branch
0.6b	1	`x`
0.6b	1	`(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))`

Compiler

Compiled 69 to 38 computations (44.9% saved)

regimes6.0ms (0.1%)

Accuracy

Total -59.6b remaining (-6690.4%)

Threshold costs -59.6b (-6690.4%)

Counts

6 → 1

Calls

Call 1

Inputs
(neg.f64 x)
(*.f64 x x)
(expm1.f64 (neg.f64 x))
(+.f64 -1 (exp.f64 (neg.f64 x)))
(+.f64 -2 (*.f64 2 (cosh.f64 x)))
(+.f64 (expm1.f64 x) (expm1.f64 (neg.f64 x)))

Outputs
(*.f64 x x)

Calls

1 calls:

5.0ms

Results

Error	Segments	Branch
0.9b	1	`x`

Compiler

Compiled 28 to 15 computations (46.4% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
2×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	38
1	22	38
2	24	38
3	25	38

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(fma.f64 x x (.f64 (pow.f64 x 4) (+.f64 (.f64 1/360 (*.f64 x x)) 1/12)))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(*.f64 x x)
(neg.f64 x)

Outputs
(fma.f64 x x (.f64 (pow.f64 x 4) (+.f64 (.f64 1/360 (*.f64 x x)) 1/12)))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(fma.f64 x x (*.f64 (pow.f64 x 4) 1/12))
(*.f64 x x)
(neg.f64 x)

Compiler

Compiled 31 to 20 computations (35.5% saved)

soundness460.0ms (4.1%)

Algorithm

3×	egg-herbie

Rules

811×	`sqr-pow_binary64`
801×	`associate-/l*_binary64`
624×	`fma-def_binary64`
581×	`fma-neg_binary64`
580×	`cube-prod_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	273	13
6	709	13
7	1729	13
8	3145	13
9	7605	13
0	34	295
1	85	283
2	186	279
3	525	279
4	2241	279
5	4801	279
6	5972	279
0	11	147
1	23	147
2	48	147
3	117	147
4	391	147
5	1750	147
6	3196	147
7	3534	147
8	3804	147
9	4068	147
10	4414	147
11	4871	147
12	5439	147
13	6084	147
14	6848	147
15	7295	147
16	7793	147

Stop Event

1×	node limit
1×	node limit
1×	node limit

Compiler

Compiled 385 to 309 computations (19.7% saved)

end28.0ms (0.2%)

Compiler: Compiled 28 to 16 computations (42.9% saved)

Details

analyze4.0ms (0%)

sample6.0s (53.1%)

preprocess117.0ms (1%)

simplify83.0ms (0.7%)

eval1.0ms (0%)

prune1.0ms (0%)

localize9.0ms (0.1%)

series2.0ms (0%)

rewrite126.0ms (1.1%)

simplify62.0ms (0.6%)

localize9.0ms (0.1%)

series2.0ms (0%)

rewrite71.0ms (0.6%)

simplify39.0ms (0.3%)

eval58.0ms (0.5%)

prune23.0ms (0.2%)

localize56.0ms (0.5%)

series4.0ms (0%)

rewrite98.0ms (0.9%)

simplify138.0ms (1.2%)

localize2.0ms (0%)

localize6.0ms (0.1%)

series3.0ms (0%)

rewrite61.0ms (0.5%)

simplify68.0ms (0.6%)

localize14.0ms (0.1%)

series69.0ms (0.6%)

rewrite72.0ms (0.6%)

simplify101.0ms (0.9%)

localize39.0ms (0.3%)

series16.0ms (0.1%)

rewrite235.0ms (2.1%)

simplify102.0ms (0.9%)

eval839.0ms (7.5%)

prune72.0ms (0.6%)

localize16.0ms (0.1%)

series2.0ms (0%)

rewrite56.0ms (0.5%)

simplify179.0ms (1.6%)

localize6.0ms (0%)

series1.0ms (0%)

rewrite42.0ms (0.4%)

simplify53.0ms (0.5%)

localize9.0ms (0.1%)

localize21.0ms (0.2%)

series5.0ms (0%)

rewrite130.0ms (1.2%)

simplify86.0ms (0.8%)

localize28.0ms (0.2%)

series7.0ms (0.1%)

rewrite138.0ms (1.2%)

simplify62.0ms (0.6%)

eval583.0ms (5.2%)

prune119.0ms (1.1%)

localize4.0ms (0%)

series1.0ms (0%)

rewrite51.0ms (0.5%)

simplify52.0ms (0.5%)

localize2.0ms (0%)

localize7.0ms (0.1%)

series1.0ms (0%)

rewrite41.0ms (0.4%)

simplify57.0ms (0.5%)

localize19.0ms (0.2%)

series3.0ms (0%)

rewrite69.0ms (0.6%)

simplify183.0ms (1.6%)

eval74.0ms (0.7%)

prune30.0ms (0.3%)

regimes19.0ms (0.2%)

regimes12.0ms (0.1%)

regimes6.0ms (0.1%)

simplify4.0ms (0%)

soundness460.0ms (4.1%)

end28.0ms (0.2%)

Profiling