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)

sample6.8s (56.5%)

Results

5.0s	4279×	body	2048	valid
1.4s	2034×	body	1024	valid
312.0ms	1012×	body	512	valid
125.0ms	931×	body	256	valid
1.0ms	8×	body	256	invalid

preprocess85.0ms (0.7%)

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)

simplify63.0ms (0.5%)

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

31.1b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	31.1b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
▶	31.2b	(+.f64 -2 (+.f64 (exp.f64 x) (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)

series4.0ms (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)))

rewrite100.0ms (0.8%)

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))))))))

simplify66.0ms (0.5%)

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))

localize38.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

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)

rewrite64.0ms (0.5%)

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)))))

simplify48.0ms (0.4%)

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))

eval38.0ms (0.3%)

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

prune45.0ms (0.4%)

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
▶	0.8b	(fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))
	31.2b	(exp.f64 (log.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))))
▶	0.6b	(fma.f64 x x (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4))))
	0.6b	(+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (.f64 1/12 (pow.f64 x 4))))
	31.2b	(+.f64 -2 (*.f64 2 (cosh.f64 x)))
▶	1.3b	(*.f64 x x)
▶	63.5b	(+.f64 (pow.f64 (sqrt.f64 (+.f64 (exp.f64 x) -2)) 2) (exp.f64 (neg.f64 x)))
▶	31.7b	(log.f64 (exp.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))))

Compiler

Compiled 160 to 126 computations (21.3% saved)

localize63.0ms (0.5%)

Local error

Found 3 expressions with local error:

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

series5.0ms (0%)

Counts

3 → 24

Calls

9 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)))

rewrite73.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

927×	`pow1_binary64`
869×	`add-log-exp_binary64`
869×	`log1p-expm1-u_binary64`
869×	`expm1-log1p-u_binary64`
851×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	234	39
2	2497	39

Stop Event

1×	node limit

Counts

3 → 54

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

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

simplify189.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1287×	`fma-def_binary64`
726×	`sqr-pow_binary64`
544×	`cube-prod_binary64`
353×	`*-commutative_binary64`
336×	`unpow3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	326
1	35	312
2	75	312
3	191	312
4	839	312
5	2320	312
6	3430	312
7	3668	312
8	3868	312
9	4119	312
10	4434	312
11	4879	312
12	5638	312
13	6137	312
14	6800	312
15	7088	312
16	7340	312
17	7600	312
18	7870	312

Stop Event

1×	node limit

Counts

78 → 63

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)))
(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 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 (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 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 (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))))

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 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 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 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 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 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 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 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 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 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 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 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 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 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 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 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 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 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 1/12))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) (*.f64 1/12 (pow.f64 x 4)))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 x x))
(fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) 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 1/12 (pow.f64 x 4)) (.f64 x x)))
(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 x x (*.f64 1/360 (pow.f64 x 6))))
(fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (*.f64 1/360 (pow.f64 x 6))))
(fma.f64 1/12 (pow.f64 x 4) (*.f64 x (fma.f64 1/360 (pow.f64 x 5) x)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) (fma.f64 1/360 (pow.f64 x 5) 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 1/12 (pow.f64 x 4)) (.f64 x x)))
(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 x x (*.f64 1/360 (pow.f64 x 6))))
(fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (*.f64 1/360 (pow.f64 x 6))))
(fma.f64 1/12 (pow.f64 x 4) (*.f64 x (fma.f64 1/360 (pow.f64 x 5) x)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) (fma.f64 1/360 (pow.f64 x 5) x)))
(*.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 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 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 1/12 (pow.f64 x 4)) (.f64 x x)))
(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 x x (*.f64 1/360 (pow.f64 x 6))))
(fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (*.f64 1/360 (pow.f64 x 6))))
(fma.f64 1/12 (pow.f64 x 4) (*.f64 x (fma.f64 1/360 (pow.f64 x 5) x)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) (fma.f64 1/360 (pow.f64 x 5) 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 1/12 (pow.f64 x 4)) (.f64 x x)))
(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 x x (*.f64 1/360 (pow.f64 x 6))))
(fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (*.f64 1/360 (pow.f64 x 6))))
(fma.f64 1/12 (pow.f64 x 4) (*.f64 x (fma.f64 1/360 (pow.f64 x 5) x)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) (fma.f64 1/360 (pow.f64 x 5) x)))
(*.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 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 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 1/12 (pow.f64 x 4)) (.f64 x x)))
(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 x x (*.f64 1/360 (pow.f64 x 6))))
(fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (*.f64 1/360 (pow.f64 x 6))))
(fma.f64 1/12 (pow.f64 x 4) (*.f64 x (fma.f64 1/360 (pow.f64 x 5) x)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) (fma.f64 1/360 (pow.f64 x 5) 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 1/12 (pow.f64 x 4)) (.f64 x x)))
(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 x x (*.f64 1/360 (pow.f64 x 6))))
(fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (*.f64 1/360 (pow.f64 x 6))))
(fma.f64 1/12 (pow.f64 x 4) (*.f64 x (fma.f64 1/360 (pow.f64 x 5) x)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) (fma.f64 1/360 (pow.f64 x 5) x)))

localize6.0ms (0%)

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

localize19.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 18 to 10 computations (44.4% saved)

series3.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite88.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

562×	`pow1_binary64`
525×	`add-log-exp_binary64`
525×	`log1p-expm1-u_binary64`
525×	`expm1-log1p-u_binary64`
513×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	145	11
2	1510	11

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

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

Outputs

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

simplify210.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1057×	`sqr-pow_binary64`
963×	`fma-def_binary64`
506×	`pow-sqr_binary64`
451×	`cube-prod_binary64`
363×	`fabs-mul_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	135
1	18	117
2	38	117
3	86	117
4	293	117
5	1235	117
6	2593	117
7	3274	117
8	3485	117
9	3726	117
10	4023	117
11	4409	117
12	4874	117
13	5415	117
14	6041	117
15	6792	117
16	7102	117
17	7324	117
18	7520	117
19	7578	117
20	7602	117

Stop Event

1×	node limit

Counts

33 → 26

Calls

Call 1

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

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 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) 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 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) 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 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))
(*.f64 1/12 (pow.f64 x 4))
(+.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 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) 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 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) 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 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))
(*.f64 1/12 (pow.f64 x 4))
(+.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 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) 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 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) 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 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(cosh.f64 x)
✓	3.3b	(+.f64 -2 (*.f64 2 (cosh.f64 x)))
✓	3.5b	(log.f64 (exp.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))))

Compiler

Compiled 31 to 21 computations (32.3% saved)

series6.0ms (0%)

Counts

3 → 36

Calls

9 calls:

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

rewrite221.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

826×	`pow1_binary64`
769×	`add-log-exp_binary64`
767×	`log1p-expm1-u_binary64`
767×	`expm1-log1p-u_binary64`
755×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	178	17
2	2083	17

Stop Event

1×	node limit

Counts

3 → 88

Calls

Call 1

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

Outputs

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

((#(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 (pow.f64 (*.f64 2 (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 (pow.f64 (cosh.f64 x) 3) 8)) (/.f64 1 (+.f64 4 (-.f64 (pow.f64 (*.f64 2 (cosh.f64 x)) 2) (*.f64 -4 (cosh.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 4 (pow.f64 (*.f64 2 (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 (pow.f64 (*.f64 2 (cosh.f64 x)) 2) (*.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 (pow.f64 (*.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 4 (-.f64 (pow.f64 (*.f64 2 (cosh.f64 x)) 2) (*.f64 -4 (cosh.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 -8 (*.f64 (pow.f64 (cosh.f64 x) 3) 8)) (+.f64 (pow.f64 (*.f64 2 (cosh.f64 x)) 2) (-.f64 4 (*.f64 -4 (cosh.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 4 (pow.f64 (*.f64 2 (cosh.f64 x)) 2)) (+.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 (pow.f64 (*.f64 2 (cosh.f64 x)) 2) (*.f64 -4 (cosh.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 4 (pow.f64 (*.f64 2 (cosh.f64 x)) 2))) (neg.f64 (+.f64 -2 (*.f64 -2 (cosh.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 2 (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)))))

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

simplify74.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

664×	`distribute-rgt-out_binary64`
518×	`distribute-lft-out_binary64`
514×	`fma-def_binary64`
460×	`*-commutative_binary64`
457×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	39	492
1	98	478
2	228	468
3	671	466
4	2814	466
5	5767	466
6	6426	466

Stop Event

1×	node limit

Counts

124 → 76

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)
(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)
1
(+.f64 1 (*.f64 1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 1/24 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6)))))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 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)))
(+.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 1/20160 (pow.f64 x 8) (fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))))
(fma.f64 x x (fma.f64 1/360 (pow.f64 x 6) (*.f64 (pow.f64 x 4) (fma.f64 (pow.f64 x 4) 1/20160 1/12))))
(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 (/.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 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 (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 (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 (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 (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 (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 (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 (exp.f64 x) (+.f64 (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 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)))
(+.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 1/20160 (pow.f64 x 8) (fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))))
(fma.f64 x x (fma.f64 1/360 (pow.f64 x 6) (*.f64 (pow.f64 x 4) (fma.f64 (pow.f64 x 4) 1/20160 1/12))))
(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 (/.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 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 (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 (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 (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 (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 (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 (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 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
1
(+.f64 1 (*.f64 1/2 (pow.f64 x 2)))
(+.f64 1 (.f64 (.f64 x x) 1/2))
(fma.f64 (*.f64 x x) 1/2 1)
(+.f64 1 (+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 1/24 (pow.f64 x 4))))
(+.f64 1 (fma.f64 1/2 (.f64 x x) (.f64 (pow.f64 x 4) 1/24)))
(+.f64 1 (fma.f64 (.f64 x x) 1/2 (.f64 (pow.f64 x 4) 1/24)))
(fma.f64 (pow.f64 x 4) 1/24 (fma.f64 (*.f64 x x) 1/2 1))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) 1/24 1/2) 1)
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x 1/24) 1/2) 1)
(+.f64 1 (+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (.f64 1/24 (pow.f64 x 4)) (*.f64 1/720 (pow.f64 x 6)))))
(+.f64 1 (fma.f64 1/2 (.f64 x x) (fma.f64 1/24 (pow.f64 x 4) (.f64 (pow.f64 x 6) 1/720))))
(+.f64 1 (fma.f64 (.f64 x x) 1/2 (fma.f64 (pow.f64 x 4) 1/24 (.f64 (pow.f64 x 6) 1/720))))
(+.f64 (fma.f64 (.f64 x x) 1/2 1) (fma.f64 (pow.f64 x 4) 1/24 (.f64 (pow.f64 x 6) 1/720)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) 1/24 1/2) (fma.f64 (pow.f64 x 6) 1/720 1))
(fma.f64 x (*.f64 x 1/2) (fma.f64 (pow.f64 x 4) 1/24 (fma.f64 (pow.f64 x 6) 1/720 1)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(fma.f64 (exp.f64 x) 1/2 (/.f64 1/2 (exp.f64 x)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(fma.f64 (exp.f64 x) 1/2 (/.f64 1/2 (exp.f64 x)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(fma.f64 (exp.f64 x) 1/2 (/.f64 1/2 (exp.f64 x)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(fma.f64 (exp.f64 x) 1/2 (/.f64 1/2 (exp.f64 x)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(fma.f64 (exp.f64 x) 1/2 (/.f64 1/2 (exp.f64 x)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(fma.f64 (exp.f64 x) 1/2 (/.f64 1/2 (exp.f64 x)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(fma.f64 (exp.f64 x) 1/2 (/.f64 1/2 (exp.f64 x)))
(*.f64 1/2 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)))
(*.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 1/2)
(fma.f64 (exp.f64 x) 1/2 (/.f64 1/2 (exp.f64 x)))

localize15.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 38 to 22 computations (42.1% saved)

series8.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
5.0ms	x	@	0	(+.f64 (pow.f64 (sqrt.f64 (+.f64 (exp.f64 x) -2)) 2) (exp.f64 (neg.f64 x)))
1.0ms	x	@	inf	(+.f64 (pow.f64 (sqrt.f64 (+.f64 (exp.f64 x) -2)) 2) (exp.f64 (neg.f64 x)))
1.0ms	x	@	-inf	(+.f64 (pow.f64 (sqrt.f64 (+.f64 (exp.f64 x) -2)) 2) (exp.f64 (neg.f64 x)))
0.0ms	x	@	0	(pow.f64 (sqrt.f64 (+.f64 (exp.f64 x) -2)) 2)
0.0ms	x	@	0	(+.f64 (exp.f64 x) -2)

rewrite121.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

972×	`pow1_binary64`
914×	`add-log-exp_binary64`
910×	`log1p-expm1-u_binary64`
910×	`expm1-log1p-u_binary64`
112×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	25
1	242	23
2	3005	23

Stop Event

1×	node limit

Counts

3 → 107

Calls

Call 1

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

Outputs

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

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

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

simplify58.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

539×	`distribute-rgt-in_binary64`
529×	`distribute-lft-in_binary64`
296×	`*-commutative_binary64`
254×	`+-commutative_binary64`
244×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	78	597
1	228	439
2	772	306
3	3116	300

Stop Event

1×	node limit

Counts

143 → 99

Calls

Call 1

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

Outputs
-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 x (fma.f64 x (*.f64 x 1/2) -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 (fma.f64 1/2 (*.f64 x x) x) (fma.f64 1/6 (pow.f64 x 3) -1))
(+.f64 (fma.f64 x (*.f64 x 1/2) x) (fma.f64 1/6 (pow.f64 x 3) -1))
(+.f64 x (fma.f64 (.f64 x x) (+.f64 1/2 (.f64 x 1/6)) -1))
(-.f64 (exp.f64 x) 2)
(+.f64 (exp.f64 x) -2)
(-.f64 (exp.f64 x) 2)
(+.f64 (exp.f64 x) -2)
(-.f64 (exp.f64 x) 2)
(+.f64 (exp.f64 x) -2)
(-.f64 (exp.f64 x) 2)
(+.f64 (exp.f64 x) -2)
(-.f64 (exp.f64 x) 2)
(+.f64 (exp.f64 x) -2)
(-.f64 (exp.f64 x) 2)
(+.f64 (exp.f64 x) -2)
(-.f64 (exp.f64 x) 2)
(+.f64 (exp.f64 x) -2)
(-.f64 (exp.f64 x) 2)
(+.f64 (exp.f64 x) -2)
(+.f64 1 (pow.f64 (sqrt.f64 -1) 2))
0
(+.f64 (.f64 (-.f64 (+.f64 1 (.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2)))) (pow.f64 (/.f64 1/2 (sqrt.f64 -1)) 2)) (pow.f64 x 2)) (+.f64 1 (pow.f64 (sqrt.f64 -1) 2)))
(fma.f64 (+.f64 1 (-.f64 (/.f64 1/4 (pow.f64 (sqrt.f64 -1) 2)) (pow.f64 (/.f64 1/2 (sqrt.f64 -1)) 2))) (*.f64 x x) (+.f64 1 (pow.f64 (sqrt.f64 -1) 2)))
(fma.f64 (*.f64 x x) (-.f64 3/4 (pow.f64 (/.f64 1/2 (sqrt.f64 -1)) 2)) 0)
(*.f64 x x)
(+.f64 (.f64 (-.f64 (+.f64 1 (.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2)))) (pow.f64 (/.f64 1/2 (sqrt.f64 -1)) 2)) (pow.f64 x 2)) (+.f64 1 (+.f64 (.f64 (-.f64 (+.f64 1/12 (.f64 1/4 (/.f64 (pow.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 -1)) 2)) 2) (pow.f64 (sqrt.f64 -1) 2)))) (pow.f64 (*.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 -1)) 2)) (sqrt.f64 -1))) 2)) (pow.f64 x 4)) (pow.f64 (sqrt.f64 -1) 2))))
(fma.f64 (+.f64 1 (-.f64 (/.f64 1/4 (pow.f64 (sqrt.f64 -1) 2)) (pow.f64 (/.f64 1/2 (sqrt.f64 -1)) 2))) (.f64 x x) (+.f64 1 (fma.f64 (+.f64 1/12 (-.f64 (.f64 1/4 (/.f64 (pow.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 -1)) 2)) 2) (pow.f64 (sqrt.f64 -1) 2))) (pow.f64 (*.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 -1)) 2)) (sqrt.f64 -1))) 2))) (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 2))))
(+.f64 (fma.f64 (.f64 x x) (-.f64 3/4 (pow.f64 (/.f64 1/2 (sqrt.f64 -1)) 2)) 0) (.f64 (-.f64 (fma.f64 1/4 (/.f64 (pow.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 -1)) 2)) 2) -1) 1/12) (*.f64 1/4 (/.f64 (pow.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 -1)) 2)) 2) -1))) (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)))
(+.f64 (.f64 (-.f64 (+.f64 (.f64 1/4 (/.f64 (pow.f64 (-.f64 1/6 (.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 -1)) 2)) (pow.f64 (sqrt.f64 -1) 2)))) 2) (pow.f64 (sqrt.f64 -1) 2))) 1/360) (pow.f64 (.f64 1/2 (/.f64 (-.f64 1/6 (.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 -1)) 2)) (pow.f64 (sqrt.f64 -1) 2)))) (sqrt.f64 -1))) 2)) (pow.f64 x 6)) (+.f64 (.f64 (-.f64 (+.f64 1 (.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2)))) (pow.f64 (/.f64 1/2 (sqrt.f64 -1)) 2)) (pow.f64 x 2)) (+.f64 1 (+.f64 (.f64 (-.f64 (+.f64 1/12 (.f64 1/4 (/.f64 (pow.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 -1)) 2)) 2) (pow.f64 (sqrt.f64 -1) 2)))) (pow.f64 (.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 -1)) 2)) (sqrt.f64 -1))) 2)) (pow.f64 x 4)) (pow.f64 (sqrt.f64 -1) 2)))))
(fma.f64 (-.f64 (fma.f64 1/4 (/.f64 (pow.f64 (+.f64 1/6 (.f64 -1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 -1)) 2)) (pow.f64 (sqrt.f64 -1) 2)))) 2) (pow.f64 (sqrt.f64 -1) 2)) 1/360) (pow.f64 (.f64 1/2 (/.f64 (+.f64 1/6 (.f64 -1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 -1)) 2)) (pow.f64 (sqrt.f64 -1) 2)))) (sqrt.f64 -1))) 2)) (pow.f64 x 6) (fma.f64 (+.f64 1 (-.f64 (/.f64 1/4 (pow.f64 (sqrt.f64 -1) 2)) (pow.f64 (/.f64 1/2 (sqrt.f64 -1)) 2))) (.f64 x x) (+.f64 1 (fma.f64 (+.f64 1/12 (-.f64 (.f64 1/4 (/.f64 (pow.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 -1)) 2)) 2) (pow.f64 (sqrt.f64 -1) 2))) (pow.f64 (.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 -1)) 2)) (sqrt.f64 -1))) 2))) (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 2)))))
(fma.f64 1/360 (pow.f64 x 6) (+.f64 (fma.f64 (.f64 x x) (-.f64 3/4 (pow.f64 (/.f64 1/2 (sqrt.f64 -1)) 2)) 0) (.f64 (-.f64 (fma.f64 1/4 (/.f64 (pow.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 -1)) 2)) 2) -1) 1/12) (*.f64 1/4 (/.f64 (pow.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 -1)) 2)) 2) -1))) (pow.f64 x 4))))
(+.f64 (.f64 x x) (fma.f64 1/360 (pow.f64 x 6) (.f64 1/12 (pow.f64 x 4))))
(fma.f64 x x (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4))))
(-.f64 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)) 2)
(+.f64 (exp.f64 x) (-.f64 (exp.f64 (neg.f64 x)) 2))
(+.f64 (+.f64 (exp.f64 x) -2) (exp.f64 (neg.f64 x)))
(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))
(-.f64 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)) 2)
(+.f64 (exp.f64 x) (-.f64 (exp.f64 (neg.f64 x)) 2))
(+.f64 (+.f64 (exp.f64 x) -2) (exp.f64 (neg.f64 x)))
(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))
(-.f64 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)) 2)
(+.f64 (exp.f64 x) (-.f64 (exp.f64 (neg.f64 x)) 2))
(+.f64 (+.f64 (exp.f64 x) -2) (exp.f64 (neg.f64 x)))
(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))
(-.f64 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)) 2)
(+.f64 (exp.f64 x) (-.f64 (exp.f64 (neg.f64 x)) 2))
(+.f64 (+.f64 (exp.f64 x) -2) (exp.f64 (neg.f64 x)))
(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))
(-.f64 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))) 2)
(+.f64 (exp.f64 x) (-.f64 (exp.f64 (neg.f64 x)) 2))
(+.f64 (+.f64 (exp.f64 x) -2) (exp.f64 (neg.f64 x)))
(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))
(-.f64 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))) 2)
(+.f64 (exp.f64 x) (-.f64 (exp.f64 (neg.f64 x)) 2))
(+.f64 (+.f64 (exp.f64 x) -2) (exp.f64 (neg.f64 x)))
(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))
(-.f64 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))) 2)
(+.f64 (exp.f64 x) (-.f64 (exp.f64 (neg.f64 x)) 2))
(+.f64 (+.f64 (exp.f64 x) -2) (exp.f64 (neg.f64 x)))
(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))
(-.f64 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))) 2)
(+.f64 (exp.f64 x) (-.f64 (exp.f64 (neg.f64 x)) 2))
(+.f64 (+.f64 (exp.f64 x) -2) (exp.f64 (neg.f64 x)))
(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))
(pow.f64 (sqrt.f64 -1) 2)
-1
(+.f64 (pow.f64 (sqrt.f64 -1) 2) x)
(+.f64 x -1)
(+.f64 (.f64 (-.f64 (+.f64 1/2 (.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2)))) (pow.f64 (/.f64 1/2 (sqrt.f64 -1)) 2)) (pow.f64 x 2)) (+.f64 (pow.f64 (sqrt.f64 -1) 2) x))
(+.f64 (fma.f64 1/2 (*.f64 x x) x) -1)
(+.f64 x (fma.f64 x (*.f64 x 1/2) -1))
(+.f64 (.f64 (-.f64 (+.f64 1/2 (.f64 1/4 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2)))) (pow.f64 (/.f64 1/2 (sqrt.f64 -1)) 2)) (pow.f64 x 2)) (+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 (pow.f64 (sqrt.f64 -1) 2) x)))
(+.f64 (fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/2 (*.f64 x x) x)) -1)
(+.f64 (fma.f64 1/2 (*.f64 x x) x) (fma.f64 1/6 (pow.f64 x 3) -1))
(+.f64 (fma.f64 x (*.f64 x 1/2) x) (fma.f64 1/6 (pow.f64 x 3) -1))
(+.f64 x (fma.f64 (.f64 x x) (+.f64 1/2 (.f64 x 1/6)) -1))
(-.f64 (exp.f64 x) 2)
(+.f64 (exp.f64 x) -2)
(-.f64 (exp.f64 x) 2)
(+.f64 (exp.f64 x) -2)
(-.f64 (exp.f64 x) 2)
(+.f64 (exp.f64 x) -2)
(-.f64 (exp.f64 x) 2)
(+.f64 (exp.f64 x) -2)
(-.f64 (exp.f64 x) 2)
(+.f64 (exp.f64 x) -2)
(-.f64 (exp.f64 x) 2)
(+.f64 (exp.f64 x) -2)
(-.f64 (exp.f64 x) 2)
(+.f64 (exp.f64 x) -2)
(-.f64 (exp.f64 x) 2)
(+.f64 (exp.f64 x) -2)

eval209.0ms (1.7%)

Compiler: Compiled 4169 to 2888 computations (30.7% saved)

prune87.0ms (0.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	255	9	264
Fresh	3	0	3
Picked	1	0	1
Done	2	2	4
Total	261	11	272

Error

0.0b

Counts

272 → 11

Alt Table

Click to see full alt table

Status	Error	Program
▶	31.2b	(cbrt.f64 (pow.f64 (fma.f64 2 (cosh.f64 x) -2) 3))
	31.2b	(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))
▶	32.3b	(*.f64 1/12 (pow.f64 x 4))
✓	1.3b	(*.f64 x x)
✓	31.7b	(log.f64 (exp.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))))
	0.6b	(+.f64 (+.f64 (.f64 x x) (.f64 1/360 (pow.f64 x 6))) (*.f64 1/12 (pow.f64 x 4)))
▶	0.8b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
▶	0.8b	(+.f64 (.f64 x x) (.f64 1/12 (pow.f64 x 4)))
	32.9b	0
▶	0.6b	(fma.f64 x x (.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 1/12)))
	31.2b	(+.f64 (*.f64 2 (cosh.f64 x)) -2)

Compiler

Compiled 175 to 132 computations (24.6% saved)

localize45.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 1/12)))
✓	0.0b	(fma.f64 x (*.f64 x 1/360) 1/12)
✓	0.1b	(.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 1/12))
✓	0.3b	(*.f64 x 1/360)

Compiler

Compiled 40 to 27 computations (32.5% saved)

series5.0ms (0%)

Counts

4 → 48

Calls

12 calls:

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

rewrite73.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

896×	`pow1_binary64`
833×	`add-log-exp_binary64`
833×	`log1p-expm1-u_binary64`
833×	`expm1-log1p-u_binary64`
816×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	44
1	208	44
2	2277	44

Stop Event

1×	node limit

Counts

4 → 68

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (.f64 x 1/360)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 x 1/360) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 x 1/360) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 x 1/360)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 x 1/360)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (.f64 x x) 1/129600))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (.f64 x 1/360)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 x 1/360) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 x 1/360)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 x 1/360)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 x 1/360)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 x (.f64 x 1/360)) (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 x (.f64 x 1/360))) (.f64 (pow.f64 x 4) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 1/12))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 1/12)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 1/12)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 1/12))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (.f64 x x) (sqrt.f64 (fma.f64 x (.f64 x 1/360) 1/12))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (pow.f64 (fma.f64 x (.f64 x 1/360) 1/12) 2) (pow.f64 x 8)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 x 4)) (fma.f64 x (.f64 x 1/360) 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 1/12)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (pow.f64 x 4) 3) (pow.f64 (fma.f64 x (.f64 x 1/360) 1/12) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (fma.f64 x (.f64 x 1/360) 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 x (.f64 x 1/360) 1/12))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 1/12))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 1/12))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1/12 (.f64 x (.f64 x 1/360)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (.f64 x 1/360)) 1/12)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 x (.f64 x 1/360)) 1) 1/12)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 x (.f64 x 1/360) 1/12)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 x (.f64 x 1/360) 1/12) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 x (.f64 x 1/360) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 x (.f64 x 1/360) 1/12)) (cbrt.f64 (pow.f64 (fma.f64 x (.f64 x 1/360) 1/12) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (fma.f64 x (.f64 x 1/360) 1/12) 2)) (cbrt.f64 (fma.f64 x (.f64 x 1/360) 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 x (.f64 x 1/360) 1/12)) (sqrt.f64 (fma.f64 x (.f64 x 1/360) 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 x (.f64 x 1/360)) 3) 1/1728) (+.f64 (.f64 (.f64 x (.f64 x 1/360)) (.f64 x (.f64 x 1/360))) (-.f64 1/144 (.f64 (.f64 x (.f64 x 1/360)) 1/12))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (.f64 x (.f64 x 1/360)) (.f64 x (.f64 x 1/360))) 1/144) (-.f64 (.f64 x (.f64 x 1/360)) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x (.f64 x 1/360) 1/12) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x (.f64 x 1/360) 1/12) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x (.f64 x 1/360) 1/12)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x (.f64 x 1/360) 1/12)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x (.f64 x 1/360) 1/12) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x (.f64 x 1/360) 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x (.f64 x 1/360) 1/12) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x (.f64 x 1/360) 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x (.f64 x 1/360) 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x (.f64 x 1/360) 1/12)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 1/12)) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x x) (.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 x x) 1) (.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 x x (.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 1/12)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 x x (.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 1/12))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 x x (.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 1/12))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 x x (.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 1/12)))) (pow.f64 (cbrt.f64 (fma.f64 x x (.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 1/12)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 x x (.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 1/12)))) 2) (cbrt.f64 (fma.f64 x x (.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 1/12)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 x (.f64 (.f64 x x) (sqrt.f64 (fma.f64 x (.f64 x 1/360) 1/12)))) (hypot.f64 x (.f64 (.f64 x x) (sqrt.f64 (fma.f64 x (.f64 x 1/360) 1/12)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 x x) 3) (pow.f64 (.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 1/12)) 3)) (+.f64 (pow.f64 x 4) (-.f64 (.f64 (pow.f64 (fma.f64 x (.f64 x 1/360) 1/12) 2) (pow.f64 x 8)) (.f64 (.f64 x x) (.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 1/12))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (.f64 (pow.f64 (fma.f64 x (.f64 x 1/360) 1/12) 2) (pow.f64 x 8))) (-.f64 (.f64 x x) (.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 1/12))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x x (.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 1/12))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x (.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 1/12))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x x (.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 1/12)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x (.f64 (.f64 x x) (sqrt.f64 (fma.f64 x (.f64 x 1/360) 1/12)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x x (.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 1/12))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x x (.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 1/12)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x x (.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 1/12))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x x (.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 1/12)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x x (.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 1/12)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x x (.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 1/12)))))))))

simplify286.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

1292×	`fma-def_binary64`
726×	`sqr-pow_binary64`
544×	`cube-prod_binary64`
354×	`*-commutative_binary64`
336×	`unpow3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	479
1	41	447
2	85	447
3	209	447
4	864	447
5	2361	447
6	3453	447
7	3686	447
8	3886	447
9	4137	447
10	4452	447
11	4898	447
12	5664	447
13	6164	447
14	6827	447
15	7111	447
16	7361	447
17	7625	447
18	7895	447

Stop Event

1×	node limit

Counts

116 → 84

Calls

Call 1

Inputs
(*.f64 1/360 x)
(*.f64 1/360 x)
(*.f64 1/360 x)
(*.f64 1/360 x)
(*.f64 1/360 x)
(*.f64 1/360 x)
(*.f64 1/360 x)
(*.f64 1/360 x)
(*.f64 1/360 x)
(*.f64 1/360 x)
(*.f64 1/360 x)
(*.f64 1/360 x)
(*.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)))
(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 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 (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 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 (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))))

Outputs
(*.f64 1/360 x)
(*.f64 1/360 x)
(*.f64 1/360 x)
(*.f64 1/360 x)
(*.f64 1/360 x)
(*.f64 1/360 x)
(*.f64 1/360 x)
(*.f64 1/360 x)
(*.f64 1/360 x)
(*.f64 1/360 x)
(*.f64 1/360 x)
(*.f64 1/360 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 1/12 (.f64 1/360 (.f64 x x)))
(fma.f64 1/360 (*.f64 x x) 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)
(+.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)
(*.f64 1/360 (pow.f64 x 2))
(.f64 1/360 (.f64 x x))
(+.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)
(+.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)
(+.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)
(*.f64 1/360 (pow.f64 x 2))
(.f64 1/360 (.f64 x x))
(+.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)
(+.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)
(+.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)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) (*.f64 1/12 (pow.f64 x 4)))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) 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 1/12 (pow.f64 x 4)) (.f64 x x)))
(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) (*.f64 x x)))
(.f64 x (fma.f64 (pow.f64 x 3) (fma.f64 1/360 (.f64 x x) 1/12) x))
(.f64 x (fma.f64 (fma.f64 1/360 (.f64 x x) 1/12) (pow.f64 x 3) x))
(fma.f64 1/360 (pow.f64 x 6) (*.f64 x (fma.f64 1/12 (pow.f64 x 3) 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 1/12 (pow.f64 x 4)) (.f64 x x)))
(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) (*.f64 x x)))
(.f64 x (fma.f64 (pow.f64 x 3) (fma.f64 1/360 (.f64 x x) 1/12) x))
(.f64 x (fma.f64 (fma.f64 1/360 (.f64 x x) 1/12) (pow.f64 x 3) x))
(fma.f64 1/360 (pow.f64 x 6) (*.f64 x (fma.f64 1/12 (pow.f64 x 3) x)))
(*.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 (pow.f64 x 2) (.f64 1/12 (pow.f64 x 4))))
(fma.f64 1/360 (pow.f64 x 6) (+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 x x)))
(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) (*.f64 x x)))
(.f64 x (fma.f64 (pow.f64 x 3) (fma.f64 1/360 (.f64 x x) 1/12) x))
(.f64 x (fma.f64 (fma.f64 1/360 (.f64 x x) 1/12) (pow.f64 x 3) x))
(fma.f64 1/360 (pow.f64 x 6) (*.f64 x (fma.f64 1/12 (pow.f64 x 3) 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 1/12 (pow.f64 x 4)) (.f64 x x)))
(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) (*.f64 x x)))
(.f64 x (fma.f64 (pow.f64 x 3) (fma.f64 1/360 (.f64 x x) 1/12) x))
(.f64 x (fma.f64 (fma.f64 1/360 (.f64 x x) 1/12) (pow.f64 x 3) x))
(fma.f64 1/360 (pow.f64 x 6) (*.f64 x (fma.f64 1/12 (pow.f64 x 3) x)))
(*.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 (pow.f64 x 2) (.f64 1/12 (pow.f64 x 4))))
(fma.f64 1/360 (pow.f64 x 6) (+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 x x)))
(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) (*.f64 x x)))
(.f64 x (fma.f64 (pow.f64 x 3) (fma.f64 1/360 (.f64 x x) 1/12) x))
(.f64 x (fma.f64 (fma.f64 1/360 (.f64 x x) 1/12) (pow.f64 x 3) x))
(fma.f64 1/360 (pow.f64 x 6) (*.f64 x (fma.f64 1/12 (pow.f64 x 3) 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 1/12 (pow.f64 x 4)) (.f64 x x)))
(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) (*.f64 x x)))
(.f64 x (fma.f64 (pow.f64 x 3) (fma.f64 1/360 (.f64 x x) 1/12) x))
(.f64 x (fma.f64 (fma.f64 1/360 (.f64 x x) 1/12) (pow.f64 x 3) x))
(fma.f64 1/360 (pow.f64 x 6) (*.f64 x (fma.f64 1/12 (pow.f64 x 3) x)))

localize12.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 12 to 9 computations (25% saved)

localize22.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 24 to 15 computations (37.5% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite100.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

799×	`pow1_binary64`
752×	`add-log-exp_binary64`
752×	`log1p-expm1-u_binary64`
752×	`expm1-log1p-u_binary64`
735×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	178	11
2	2166	11

Stop Event

1×	node limit

Counts

1 → 35

Calls

Call 1

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

Outputs

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

simplify179.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

1057×	`sqr-pow_binary64`
963×	`fma-def_binary64`
506×	`pow-sqr_binary64`
451×	`cube-prod_binary64`
363×	`fabs-mul_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	135
1	18	117
2	38	117
3	86	117
4	293	117
5	1235	117
6	2593	117
7	3274	117
8	3485	117
9	3726	117
10	4023	117
11	4409	117
12	4874	117
13	5415	117
14	6041	117
15	6792	117
16	7102	117
17	7324	117
18	7520	117
19	7578	117
20	7602	117

Stop Event

1×	node limit

Counts

47 → 40

Calls

Call 1

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

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 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) 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 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) 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 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))
(*.f64 1/12 (pow.f64 x 4))
(+.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 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) 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 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) 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 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))
(*.f64 1/12 (pow.f64 x 4))
(+.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 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) 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 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) 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 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 20 to 14 computations (30% saved)

series42.0ms (0.3%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
41.0ms	x	@	-inf	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
0.0ms	x	@	0	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
0.0ms	x	@	inf	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))

rewrite48.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

600×	`pow1_binary64`
558×	`add-log-exp_binary64`
558×	`log1p-expm1-u_binary64`
558×	`expm1-log1p-u_binary64`
546×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	146	11
2	1558	11

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

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

Outputs

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

simplify184.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

1057×	`sqr-pow_binary64`
963×	`fma-def_binary64`
506×	`pow-sqr_binary64`
451×	`cube-prod_binary64`
363×	`fabs-mul_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	135
1	18	117
2	38	117
3	86	117
4	293	117
5	1235	117
6	2593	117
7	3274	117
8	3485	117
9	3726	117
10	4023	117
11	4409	117
12	4874	117
13	5415	117
14	6041	117
15	6792	117
16	7102	117
17	7324	117
18	7520	117
19	7578	117
20	7602	117

Stop Event

1×	node limit

Counts

33 → 26

Calls

Call 1

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

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 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) 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 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) 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 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))
(*.f64 1/12 (pow.f64 x 4))
(+.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 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) 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 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) 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 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))
(*.f64 1/12 (pow.f64 x 4))
(+.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 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) 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 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) 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 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(cosh.f64 x)
✓	0.0b	(pow.f64 (fma.f64 2 (cosh.f64 x) -2) 3)
✓	0.0b	(cbrt.f64 (pow.f64 (fma.f64 2 (cosh.f64 x) -2) 3))
✓	3.3b	(fma.f64 2 (cosh.f64 x) -2)

Compiler

Compiled 27 to 19 computations (29.6% saved)

series5.0ms (0%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(pow.f64 (fma.f64 2 (cosh.f64 x) -2) 3)
1.0ms	x	@	inf	(pow.f64 (fma.f64 2 (cosh.f64 x) -2) 3)
1.0ms	x	@	0	(pow.f64 (fma.f64 2 (cosh.f64 x) -2) 3)
0.0ms	x	@	0	(fma.f64 2 (cosh.f64 x) -2)
0.0ms	x	@	0	(cbrt.f64 (pow.f64 (fma.f64 2 (cosh.f64 x) -2) 3))

rewrite199.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

697×	`pow1_binary64`
656×	`add-log-exp_binary64`
654×	`log1p-expm1-u_binary64`
654×	`expm1-log1p-u_binary64`
642×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	24
1	191	24
2	1855	24

Stop Event

1×	node limit

Counts

3 → 71

Calls

Call 1

Inputs
(fma.f64 2 (cosh.f64 x) -2)
(cbrt.f64 (pow.f64 (fma.f64 2 (cosh.f64 x) -2) 3))
(pow.f64 (fma.f64 2 (cosh.f64 x) -2) 3)

Outputs

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

simplify69.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

704×	`fma-def_binary64`
653×	`associate-l_binary64`
506×	`associate-r_binary64`
483×	`times-frac_binary64`
424×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	43	522
1	111	510
2	276	510
3	1013	510
4	5782	510
5	6527	510

Stop Event

1×	node limit

Counts

107 → 66

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)
(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)
(pow.f64 x 6)
(+.f64 (*.f64 1/4 (pow.f64 x 8)) (pow.f64 x 6))
(+.f64 (.f64 1/4 (pow.f64 x 8)) (+.f64 (.f64 7/240 (pow.f64 x 10)) (pow.f64 x 6)))
(+.f64 (.f64 1/4 (pow.f64 x 8)) (+.f64 (.f64 2/945 (pow.f64 x 12)) (+.f64 (*.f64 7/240 (pow.f64 x 10)) (pow.f64 x 6))))
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 3)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 3)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 3)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 3)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 3)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 3)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 3)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 3)

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 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.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))))
(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 1/12 (pow.f64 x 4) (*.f64 x x)))
(fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (*.f64 1/360 (pow.f64 x 6))))
(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 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 (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 (/.f64 1 (exp.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 (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 (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 (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 (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 (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 (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 (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 (neg.f64 x)) (+.f64 (exp.f64 x) -2))
(+.f64 (exp.f64 x) (+.f64 (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 1/12 (pow.f64 x 4)))
(fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(+.f64 (.f64 1/360 (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 1/12 (pow.f64 x 4) (*.f64 x x)))
(fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (*.f64 1/360 (pow.f64 x 6))))
(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 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 (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 (/.f64 1 (exp.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 (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 (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 (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 (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 (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 (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 (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 (neg.f64 x)) (+.f64 (exp.f64 x) -2))
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
(pow.f64 x 6)
(+.f64 (*.f64 1/4 (pow.f64 x 8)) (pow.f64 x 6))
(fma.f64 1/4 (pow.f64 x 8) (pow.f64 x 6))
(fma.f64 (pow.f64 x 8) 1/4 (pow.f64 x 6))
(+.f64 (.f64 1/4 (pow.f64 x 8)) (+.f64 (.f64 7/240 (pow.f64 x 10)) (pow.f64 x 6)))
(fma.f64 1/4 (pow.f64 x 8) (fma.f64 7/240 (pow.f64 x 10) (pow.f64 x 6)))
(fma.f64 (pow.f64 x 8) 1/4 (fma.f64 7/240 (pow.f64 x 10) (pow.f64 x 6)))
(+.f64 (.f64 1/4 (pow.f64 x 8)) (+.f64 (.f64 2/945 (pow.f64 x 12)) (+.f64 (*.f64 7/240 (pow.f64 x 10)) (pow.f64 x 6))))
(fma.f64 1/4 (pow.f64 x 8) (fma.f64 2/945 (pow.f64 x 12) (fma.f64 7/240 (pow.f64 x 10) (pow.f64 x 6))))
(fma.f64 (pow.f64 x 8) 1/4 (fma.f64 2/945 (pow.f64 x 12) (fma.f64 7/240 (pow.f64 x 10) (pow.f64 x 6))))
(fma.f64 (pow.f64 x 8) 1/4 (fma.f64 7/240 (pow.f64 x 10) (fma.f64 2/945 (pow.f64 x 12) (pow.f64 x 6))))
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 3)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 2)) 3)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (+.f64 (exp.f64 x) -2)) 3)
(pow.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2)) 3)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 3)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 2)) 3)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (+.f64 (exp.f64 x) -2)) 3)
(pow.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2)) 3)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 3)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 2)) 3)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (+.f64 (exp.f64 x) -2)) 3)
(pow.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2)) 3)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 3)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 2)) 3)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (+.f64 (exp.f64 x) -2)) 3)
(pow.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2)) 3)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 3)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 2)) 3)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (+.f64 (exp.f64 x) -2)) 3)
(pow.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2)) 3)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 3)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 2)) 3)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (+.f64 (exp.f64 x) -2)) 3)
(pow.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2)) 3)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 3)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 2)) 3)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (+.f64 (exp.f64 x) -2)) 3)
(pow.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2)) 3)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 3)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 2)) 3)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (+.f64 (exp.f64 x) -2)) 3)
(pow.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2)) 3)

eval166.0ms (1.4%)

Compiler: Compiled 3902 to 2775 computations (28.9% saved)

prune43.0ms (0.4%)

Pruning

10 alts after pruning (5 fresh and 5 done)

	Pruned	Kept	Total
New	276	2	278
Fresh	1	3	4
Picked	1	0	1
Done	1	5	6
Total	279	10	289

Error

0.0b

Counts

289 → 10

Alt Table

Click to see full alt table

Status	Error	Program
▶	31.2b	(cbrt.f64 (pow.f64 (+.f64 (*.f64 2 (cosh.f64 x)) -2) 3))
▶	31.2b	(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))
✓	32.3b	(*.f64 1/12 (pow.f64 x 4))
✓	1.3b	(*.f64 x x)
✓	31.7b	(log.f64 (exp.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))))
✓	0.8b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
▶	0.6b	(fma.f64 x x (.f64 (pow.f64 x 4) (+.f64 (.f64 x (*.f64 x 1/360)) 1/12)))
✓	0.8b	(+.f64 (.f64 x x) (.f64 1/12 (pow.f64 x 4)))
	32.9b	0
▶	31.2b	(+.f64 (*.f64 2 (cosh.f64 x)) -2)

Compiler

Compiled 81 to 62 computations (23.5% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(cosh.f64 x)
✓	0.0b	(pow.f64 (+.f64 (*.f64 2 (cosh.f64 x)) -2) 3)
✓	0.0b	(cbrt.f64 (pow.f64 (+.f64 (*.f64 2 (cosh.f64 x)) -2) 3))
✓	3.3b	(+.f64 (*.f64 2 (cosh.f64 x)) -2)

Compiler

Compiled 34 to 24 computations (29.4% saved)

series6.0ms (0%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(cbrt.f64 (pow.f64 (+.f64 (*.f64 2 (cosh.f64 x)) -2) 3))
1.0ms	x	@	inf	(pow.f64 (+.f64 (*.f64 2 (cosh.f64 x)) -2) 3)
1.0ms	x	@	-inf	(pow.f64 (+.f64 (*.f64 2 (cosh.f64 x)) -2) 3)
0.0ms	x	@	0	(+.f64 (*.f64 2 (cosh.f64 x)) -2)
0.0ms	x	@	inf	(+.f64 (*.f64 2 (cosh.f64 x)) -2)

rewrite74.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

898×	`pow1_binary64`
844×	`add-log-exp_binary64`
842×	`log1p-expm1-u_binary64`
842×	`expm1-log1p-u_binary64`
827×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	221	24
2	2348	24

Stop Event

1×	node limit

Counts

3 → 102

Calls

Call 1

Inputs
(+.f64 (*.f64 2 (cosh.f64 x)) -2)
(cbrt.f64 (pow.f64 (+.f64 (*.f64 2 (cosh.f64 x)) -2) 3))
(pow.f64 (+.f64 (*.f64 2 (cosh.f64 x)) -2) 3)

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

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

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

simplify70.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

704×	`fma-def_binary64`
653×	`associate-l_binary64`
506×	`associate-r_binary64`
483×	`times-frac_binary64`
424×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	43	522
1	111	510
2	276	510
3	1013	510
4	5782	510
5	6527	510

Stop Event

1×	node limit

Counts

138 → 86

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)
(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)
(pow.f64 x 6)
(+.f64 (*.f64 1/4 (pow.f64 x 8)) (pow.f64 x 6))
(+.f64 (.f64 1/4 (pow.f64 x 8)) (+.f64 (.f64 7/240 (pow.f64 x 10)) (pow.f64 x 6)))
(+.f64 (.f64 1/4 (pow.f64 x 8)) (+.f64 (.f64 2/945 (pow.f64 x 12)) (+.f64 (*.f64 7/240 (pow.f64 x 10)) (pow.f64 x 6))))
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 3)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 3)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 3)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 3)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 3)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 3)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 3)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 3)

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 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.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))))
(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 1/12 (pow.f64 x 4) (*.f64 x x)))
(fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (*.f64 1/360 (pow.f64 x 6))))
(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 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 (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 (/.f64 1 (exp.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 (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 (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 (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 (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 (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 (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 (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 (neg.f64 x)) (+.f64 (exp.f64 x) -2))
(+.f64 (exp.f64 x) (+.f64 (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 1/12 (pow.f64 x 4)))
(fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(+.f64 (.f64 1/360 (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 1/12 (pow.f64 x 4) (*.f64 x x)))
(fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (*.f64 1/360 (pow.f64 x 6))))
(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 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 (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 (/.f64 1 (exp.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 (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 (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 (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 (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 (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 (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 (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 (neg.f64 x)) (+.f64 (exp.f64 x) -2))
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
(pow.f64 x 6)
(+.f64 (*.f64 1/4 (pow.f64 x 8)) (pow.f64 x 6))
(fma.f64 1/4 (pow.f64 x 8) (pow.f64 x 6))
(fma.f64 (pow.f64 x 8) 1/4 (pow.f64 x 6))
(+.f64 (.f64 1/4 (pow.f64 x 8)) (+.f64 (.f64 7/240 (pow.f64 x 10)) (pow.f64 x 6)))
(fma.f64 1/4 (pow.f64 x 8) (fma.f64 7/240 (pow.f64 x 10) (pow.f64 x 6)))
(fma.f64 (pow.f64 x 8) 1/4 (fma.f64 7/240 (pow.f64 x 10) (pow.f64 x 6)))
(+.f64 (.f64 1/4 (pow.f64 x 8)) (+.f64 (.f64 2/945 (pow.f64 x 12)) (+.f64 (*.f64 7/240 (pow.f64 x 10)) (pow.f64 x 6))))
(fma.f64 1/4 (pow.f64 x 8) (fma.f64 2/945 (pow.f64 x 12) (fma.f64 7/240 (pow.f64 x 10) (pow.f64 x 6))))
(fma.f64 (pow.f64 x 8) 1/4 (fma.f64 2/945 (pow.f64 x 12) (fma.f64 7/240 (pow.f64 x 10) (pow.f64 x 6))))
(fma.f64 (pow.f64 x 8) 1/4 (fma.f64 7/240 (pow.f64 x 10) (fma.f64 2/945 (pow.f64 x 12) (pow.f64 x 6))))
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 3)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 2)) 3)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (+.f64 (exp.f64 x) -2)) 3)
(pow.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2)) 3)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 3)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 2)) 3)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (+.f64 (exp.f64 x) -2)) 3)
(pow.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2)) 3)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 3)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 2)) 3)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (+.f64 (exp.f64 x) -2)) 3)
(pow.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2)) 3)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 3)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 2)) 3)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (+.f64 (exp.f64 x) -2)) 3)
(pow.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2)) 3)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 3)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 2)) 3)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (+.f64 (exp.f64 x) -2)) 3)
(pow.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2)) 3)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 3)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 2)) 3)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (+.f64 (exp.f64 x) -2)) 3)
(pow.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2)) 3)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 3)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 2)) 3)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (+.f64 (exp.f64 x) -2)) 3)
(pow.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2)) 3)
(pow.f64 (-.f64 (+.f64 (/.f64 1 (exp.f64 x)) (exp.f64 x)) 2) 3)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (-.f64 (exp.f64 x) 2)) 3)
(pow.f64 (+.f64 (exp.f64 (neg.f64 x)) (+.f64 (exp.f64 x) -2)) 3)
(pow.f64 (+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2)) 3)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 16 to 10 computations (37.5% saved)

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 2 (exp.f64 (neg.f64 x)))
✓	4.5b	(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))

Compiler

Compiled 23 to 10 computations (56.5% saved)

series2.0ms (0%)

Counts

2 → 20

Calls

6 calls:

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

rewrite69.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

883×	`pow1_binary64`
829×	`add-log-exp_binary64`
826×	`log1p-expm1-u_binary64`
826×	`expm1-log1p-u_binary64`
815×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	181	17
2	2646	17

Stop Event

1×	node limit

Counts

2 → 68

Calls

Call 1

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

Outputs

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

simplify61.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

811×	`distribute-rgt-out_binary64`
749×	`unswap-sqr_binary64`
677×	`distribute-lft-out_binary64`
563×	`associate-l_binary64`
549×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	43	234
1	107	228
2	241	228
3	725	224
4	3415	224
5	7346	224

Stop Event

1×	node limit

Counts

88 → 88

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

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 x (.f64 x 1/360)) 1/12)
✓	0.1b	(.f64 (pow.f64 x 4) (+.f64 (.f64 x (*.f64 x 1/360)) 1/12))
✓	0.1b	(.f64 x (.f64 x 1/360))
	0.3b	(*.f64 x 1/360)

Compiler

Compiled 48 to 33 computations (31.3% saved)

series3.0ms (0%)

Counts

3 → 36

Calls

9 calls:

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

rewrite117.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

495×	`log-prod_binary64`
388×	`prod-diff_binary64`
365×	`exp-prod_binary64`
329×	`pow-prod-down_binary64`
268×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	29
1	226	29
2	2772	29

Stop Event

1×	node limit

Counts

3 → 143

Calls

Call 1

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

Outputs

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

simplify250.0ms (2.1%)

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

179 → 151

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)

eval268.0ms (2.2%)

Compiler: Compiled 6928 to 4850 computations (30% saved)

prune64.0ms (0.5%)

Pruning

10 alts after pruning (2 fresh and 8 done)

	Pruned	Kept	Total
New	440	1	441
Fresh	0	1	1
Picked	0	1	1
Done	1	7	8
Total	441	10	451

Error

0.0b

Counts

451 → 10

Alt Table

Click to see full alt table

Status	Error	Program
	32.5b	(-.f64 (exp.f64 x) 1)
✓	31.2b	(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))
✓	31.2b	(cbrt.f64 (pow.f64 (+.f64 (*.f64 2 (cosh.f64 x)) -2) 3))
✓	31.7b	(log.f64 (exp.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))))
✓	0.8b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
✓	0.6b	(fma.f64 x x (.f64 (pow.f64 x 4) (+.f64 (.f64 x (*.f64 x 1/360)) 1/12)))
✓	0.8b	(+.f64 (.f64 x x) (.f64 1/12 (pow.f64 x 4)))
✓	1.3b	(*.f64 x x)
	32.9b	0
✓	31.2b	(+.f64 (*.f64 2 (cosh.f64 x)) -2)

Compiler

Compiled 80 to 61 computations (23.8% saved)

regimes73.0ms (0.6%)

Counts

22 → 1

Calls

Call 1

Inputs
0
(*.f64 x x)
(-.f64 (exp.f64 x) 1)
(*.f64 1/12 (pow.f64 x 4))
(+.f64 (*.f64 2 (cosh.f64 x)) -2)
(+.f64 -2 (*.f64 2 (cosh.f64 x)))
(+.f64 (.f64 x x) (.f64 1/12 (pow.f64 x 4)))
(-.f64 (exp.f64 x) (-.f64 2 (exp.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 x (*.f64 x 1/360)) 1/12)))
(+.f64 (+.f64 (.f64 x x) (.f64 1/360 (pow.f64 x 6))) (*.f64 1/12 (pow.f64 x 4)))
(exp.f64 (log.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))))
(log.f64 (exp.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))))
(cbrt.f64 (pow.f64 (+.f64 (*.f64 2 (cosh.f64 x)) -2) 3))
(fma.f64 x x (.f64 (pow.f64 x 4) (fma.f64 x (.f64 x 1/360) 1/12)))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (.f64 1/12 (pow.f64 x 4))))
(cbrt.f64 (pow.f64 (fma.f64 2 (cosh.f64 x) -2) 3))
(+.f64 (pow.f64 (sqrt.f64 (+.f64 (exp.f64 x) -2)) 2) (exp.f64 (neg.f64 x)))
(fma.f64 x x (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4))))

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

Calls

3 calls:

60.0ms	x
3.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
3.0ms	(+.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)))`
0.6b	1	`(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))`

Compiler

Compiled 209 to 138 computations (34% saved)

regimes16.0ms (0.1%)

Counts

12 → 1

Calls

Call 1

Inputs
0
(*.f64 x x)
(-.f64 (exp.f64 x) 1)
(*.f64 1/12 (pow.f64 x 4))
(+.f64 (*.f64 2 (cosh.f64 x)) -2)
(+.f64 -2 (*.f64 2 (cosh.f64 x)))
(+.f64 (.f64 x x) (.f64 1/12 (pow.f64 x 4)))
(-.f64 (exp.f64 x) (-.f64 2 (exp.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

3 calls:

7.0ms	x
3.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
3.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Results

Error	Segments	Branch
0.8b	1	`x`
0.8b	1	`(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))`
0.8b	1	`(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))`

Compiler

Compiled 95 to 59 computations (37.9% saved)

regimes8.0ms (0.1%)

Counts

8 → 1

Calls

Call 1

Inputs
0
(*.f64 x x)
(-.f64 (exp.f64 x) 1)
(*.f64 1/12 (pow.f64 x 4))
(+.f64 (*.f64 2 (cosh.f64 x)) -2)
(+.f64 -2 (*.f64 2 (cosh.f64 x)))
(+.f64 (.f64 x x) (.f64 1/12 (pow.f64 x 4)))
(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))

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

Calls

1 calls:

5.0ms

Results

Error	Segments	Branch
0.8b	1	`x`

Compiler

Compiled 45 to 30 computations (33.3% saved)

regimes7.0ms (0.1%)

Accuracy

Total -31.7b remaining (-2513%)

Threshold costs -31.7b (-2513%)

Counts

6 → 1

Calls

Call 1

Inputs
0
(*.f64 x x)
(-.f64 (exp.f64 x) 1)
(*.f64 1/12 (pow.f64 x 4))
(+.f64 (*.f64 2 (cosh.f64 x)) -2)
(+.f64 -2 (*.f64 2 (cosh.f64 x)))

Outputs
(*.f64 x x)

Calls

1 calls:

5.0ms

Results

Error	Segments	Branch
1.3b	1	`x`

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	49
1	22	49

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(fma.f64 x x (.f64 (pow.f64 x 4) (+.f64 (.f64 x (*.f64 x 1/360)) 1/12)))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(+.f64 (.f64 x x) (.f64 1/12 (pow.f64 x 4)))
(*.f64 x x)
0

Outputs
(fma.f64 x x (.f64 (pow.f64 x 4) (+.f64 (.f64 x (*.f64 x 1/360)) 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 (.f64 x x) (.f64 1/12 (pow.f64 x 4)))
(+.f64 (.f64 (pow.f64 x 4) 1/12) (.f64 x x))
(*.f64 x x)
0

Compiler

Compiled 40 to 27 computations (32.5% saved)

soundness504.0ms (4.2%)

Algorithm

3×	egg-herbie

Rules

1287×	`fma-def_binary64`
801×	`associate-/l*_binary64`
726×	`sqr-pow_binary64`
624×	`fma-def_binary64`
581×	`fma-neg_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	15	326
1	35	312
2	75	312
3	191	312
4	839	312
5	2320	312
6	3430	312
7	3668	312
8	3868	312
9	4119	312
10	4434	312
11	4879	312
12	5638	312
13	6137	312
14	6800	312
15	7088	312
16	7340	312
17	7600	312
18	7870	312

Stop Event

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

Compiler

Compiled 353 to 279 computations (21% saved)

end33.0ms (0.3%)

Compiler: Compiled 36 to 22 computations (38.9% saved)

Details

analyze4.0ms (0%)

sample6.8s (56.5%)

preprocess85.0ms (0.7%)

simplify63.0ms (0.5%)

eval1.0ms (0%)

prune1.0ms (0%)

localize9.0ms (0.1%)

series4.0ms (0%)

rewrite100.0ms (0.8%)

simplify66.0ms (0.5%)

localize38.0ms (0.3%)

series2.0ms (0%)

rewrite64.0ms (0.5%)

simplify48.0ms (0.4%)

eval38.0ms (0.3%)

prune45.0ms (0.4%)

localize63.0ms (0.5%)

series5.0ms (0%)

rewrite73.0ms (0.6%)

simplify189.0ms (1.6%)

localize6.0ms (0%)

localize19.0ms (0.2%)

series3.0ms (0%)

rewrite88.0ms (0.7%)

simplify210.0ms (1.7%)

localize14.0ms (0.1%)

series6.0ms (0%)

rewrite221.0ms (1.8%)

simplify74.0ms (0.6%)

localize15.0ms (0.1%)

series8.0ms (0.1%)

rewrite121.0ms (1%)

simplify58.0ms (0.5%)

eval209.0ms (1.7%)

prune87.0ms (0.7%)

localize45.0ms (0.4%)

series5.0ms (0%)

rewrite73.0ms (0.6%)

simplify286.0ms (2.4%)

localize12.0ms (0.1%)

localize22.0ms (0.2%)

series2.0ms (0%)

rewrite100.0ms (0.8%)

simplify179.0ms (1.5%)

localize10.0ms (0.1%)

series42.0ms (0.3%)

rewrite48.0ms (0.4%)

simplify184.0ms (1.5%)

localize14.0ms (0.1%)

series5.0ms (0%)

rewrite199.0ms (1.7%)

simplify69.0ms (0.6%)

eval166.0ms (1.4%)

prune43.0ms (0.4%)

localize17.0ms (0.1%)

series6.0ms (0%)

rewrite74.0ms (0.6%)

simplify70.0ms (0.6%)

localize7.0ms (0.1%)

localize11.0ms (0.1%)

series2.0ms (0%)

rewrite69.0ms (0.6%)

simplify61.0ms (0.5%)

localize21.0ms (0.2%)

series3.0ms (0%)

rewrite117.0ms (1%)

simplify250.0ms (2.1%)

eval268.0ms (2.2%)

prune64.0ms (0.5%)

regimes73.0ms (0.6%)

regimes16.0ms (0.1%)

regimes8.0ms (0.1%)

regimes7.0ms (0.1%)

simplify5.0ms (0%)

soundness504.0ms (4.2%)

end33.0ms (0.3%)

Profiling