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)

sample6.6s (68.1%)

Results

4.8s	4351×	body	2048	valid
1.4s	2042×	body	1024	valid
241.0ms	970×	body	512	valid
104.0ms	893×	body	256	valid
1.0ms	9×	body	256	invalid

preprocess67.0ms (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)

simplify64.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

801×	`associate-/l*_binary64`
624×	`fma-def_binary64`
581×	`fma-neg_binary64`
548×	`unswap-sqr_binary64`
536×	`div-sub_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	20	13
2	36	13
3	60	13
4	122	13
5	273	13
6	709	13
7	1729	13
8	3145	13
9	7605	13

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

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

prune1.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

30.0b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	30.0b	(+.f64 -2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	30.0b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
✓	2.6b	(+.f64 -2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 24 to 8 computations (66.7% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite203.0ms (2.1%)

Algorithm

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

2 → 23

Calls

Call 1

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

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

Outputs

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

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

simplify70.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node limit

Counts

47 → 43

Calls

Call 1

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

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

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

rewrite61.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 74

Calls

Call 1

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

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

Outputs

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

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

simplify37.0ms (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))

eval156.0ms (1.6%)

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

prune16.0ms (0.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	131	4	135
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	133	4	137

Error

Counts

137 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.6b	(fma.f64 x x (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4))))
▶	0.6b	(fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))
▶	30.0b	(+.f64 -2 (*.f64 2 (cosh.f64 x)))
▶	1.1b	(*.f64 x x)

Compiler

Compiled 34 to 24 computations (29.4% saved)

localize2.0ms (0%)

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

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.6b	(+.f64 -2 (*.f64 2 (cosh.f64 x)))

Compiler

Compiled 16 to 10 computations (37.5% saved)

series3.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite51.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 32

Calls

Call 1

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

Outputs

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

simplify71.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

44 → 42

Calls

Call 1

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

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

localize8.0ms (0.1%)

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)

series2.0ms (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))

rewrite43.0ms (0.4%)

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))))))))

simplify174.0ms (1.8%)

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))

localize22.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 40 to 30 computations (25% saved)

series4.0ms (0%)

Counts

2 → 12

Calls

6 calls:

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

rewrite60.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 32

Calls

Call 1

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

Outputs

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

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

simplify136.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

44 → 35

Calls

Call 1

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

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

eval34.0ms (0.4%)

Compiler: Compiled 1439 to 1030 computations (28.4% saved)

prune13.0ms (0.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	99	4	103
Fresh	0	0	0
Picked	1	0	1
Done	1	2	3
Total	101	6	107

Error

Counts

107 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	1.1b	(*.f64 x x)
▶	0.6b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
▶	0.6b	(+.f64 (.f64 x x) (.f64 1/12 (pow.f64 x 4)))
▶	31.0b	(*.f64 1/12 (pow.f64 x 4))
▶	0.6b	(fma.f64 x x (.f64 (pow.f64 x 4) (fma.f64 1/360 (.f64 x x) 1/12)))
✓	30.0b	(+.f64 -2 (*.f64 2 (cosh.f64 x)))

Compiler

Compiled 50 to 35 computations (30% saved)

localize5.0ms (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)

localize11.0ms (0.1%)

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)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite66.0ms (0.7%)

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))))))

simplify178.0ms (1.8%)

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))

localize9.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 20 to 14 computations (30% saved)

localize16.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 40 to 23 computations (42.5% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite64.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 36

Calls

Call 1

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

Outputs

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

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

simplify187.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

60 → 45

Calls

Call 1

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

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

eval49.0ms (0.5%)

Compiler: Compiled 1642 to 1083 computations (34% saved)

prune15.0ms (0.2%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	0	0	0
Picked	1	0	1
Done	0	5	5
Total	118	6	124

Error

Counts

124 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	1.1b	(*.f64 x x)
✓	0.6b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
▶	0.6b	(fma.f64 x x (.f64 (pow.f64 x 4) (+.f64 (.f64 1/360 (*.f64 x x)) 1/12)))
✓	0.6b	(+.f64 (.f64 x x) (.f64 1/12 (pow.f64 x 4)))
✓	31.0b	(*.f64 1/12 (pow.f64 x 4))
✓	30.0b	(+.f64 -2 (*.f64 2 (cosh.f64 x)))

Compiler

Compiled 51 to 36 computations (29.4% saved)

localize91.0ms (0.9%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 1/360 (.f64 x x)) 1/12)
✓	0.1b	(.f64 (pow.f64 x 4) (+.f64 (.f64 1/360 (*.f64 x x)) 1/12))
✓	0.2b	(.f64 1/360 (.f64 x x))

Compiler

Compiled 48 to 28 computations (41.7% saved)

series3.0ms (0%)

Counts

3 → 36

Calls

9 calls:

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

rewrite69.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 140

Calls

Call 1

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

Outputs

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

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

simplify184.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

176 → 148

Calls

Call 1

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

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

eval69.0ms (0.7%)

Compiler: Compiled 2779 to 1843 computations (33.7% saved)

prune28.0ms (0.3%)

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	148	6	154

Error

Counts

154 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	1.1b	(*.f64 x x)
✓	0.6b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
✓	0.6b	(fma.f64 x x (.f64 (pow.f64 x 4) (+.f64 (.f64 1/360 (*.f64 x x)) 1/12)))
✓	0.6b	(+.f64 (.f64 x x) (.f64 1/12 (pow.f64 x 4)))
✓	31.0b	(*.f64 1/12 (pow.f64 x 4))
✓	30.0b	(+.f64 -2 (*.f64 2 (cosh.f64 x)))

Compiler

Compiled 51 to 36 computations (29.4% saved)

regimes12.0ms (0.1%)

Counts

11 → 1

Calls

Call 1

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

Calls

2 calls:

6.0ms	x
2.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Results

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

Compiler

Compiled 107 to 66 computations (38.3% saved)

regimes11.0ms (0.1%)

Counts

8 → 1

Calls

Call 1

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

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

Calls

2 calls:

6.0ms	x
2.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Results

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

Compiler

Compiled 67 to 42 computations (37.3% saved)

regimes5.0ms (0.1%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

1 calls:

4.0ms

Results

Error	Segments	Branch
0.6b	1	`x`

Compiler

Compiled 26 to 17 computations (34.6% saved)

regimes5.0ms (0%)

Accuracy

Total -30.3b remaining (-2803.7%)

Threshold costs -30.3b (-2803.7%)

Counts

3 → 1

Calls

Call 1

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

Outputs
(*.f64 x x)

Calls

1 calls:

3.0ms

Results

Error	Segments	Branch
1.1b	1	`x`

Compiler

Compiled 17 to 12 computations (29.4% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	48
1	19	48

Stop Event

1×	done
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 38 to 25 computations (34.2% saved)

soundness613.0ms (6.3%)

Algorithm

3×	egg-herbie

Rules

811×	`sqr-pow_binary64`
801×	`associate-/l*_binary64`
624×	`fma-def_binary64`
581×	`fma-neg_binary64`
580×	`cube-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	20	13
2	36	13
3	60	13
4	122	13
5	273	13
6	709	13
7	1729	13
8	3145	13
9	7605	13
0	34	295
1	85	283
2	186	279
3	525	279
4	2241	279
5	4801	279
6	5972	279
0	11	147
1	23	147
2	48	147
3	117	147
4	391	147
5	1750	147
6	3196	147
7	3534	147
8	3804	147
9	4068	147
10	4414	147
11	4871	147
12	5439	147
13	6084	147
14	6848	147
15	7295	147
16	7793	147

Stop Event

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

Compiler

Compiled 385 to 309 computations (19.7% saved)

end54.0ms (0.6%)

Compiler: Compiled 35 to 20 computations (42.9% saved)

Details

analyze4.0ms (0%)

sample6.6s (68.1%)

preprocess67.0ms (0.7%)

simplify64.0ms (0.7%)

eval1.0ms (0%)

prune1.0ms (0%)

localize9.0ms (0.1%)

series2.0ms (0%)

rewrite203.0ms (2.1%)

simplify70.0ms (0.7%)

localize9.0ms (0.1%)

series2.0ms (0%)

rewrite61.0ms (0.6%)

simplify37.0ms (0.4%)

eval156.0ms (1.6%)

prune16.0ms (0.2%)

localize2.0ms (0%)

localize8.0ms (0.1%)

series3.0ms (0%)

rewrite51.0ms (0.5%)

simplify71.0ms (0.7%)

localize8.0ms (0.1%)

series2.0ms (0%)

rewrite43.0ms (0.4%)

simplify174.0ms (1.8%)

localize22.0ms (0.2%)

series4.0ms (0%)

rewrite60.0ms (0.6%)

simplify136.0ms (1.4%)

eval34.0ms (0.4%)

prune13.0ms (0.1%)

localize5.0ms (0.1%)

localize11.0ms (0.1%)

series1.0ms (0%)

rewrite66.0ms (0.7%)

simplify178.0ms (1.8%)

localize9.0ms (0.1%)

localize16.0ms (0.2%)

series2.0ms (0%)

rewrite64.0ms (0.7%)

simplify187.0ms (1.9%)

eval49.0ms (0.5%)

prune15.0ms (0.2%)

localize91.0ms (0.9%)

series3.0ms (0%)

rewrite69.0ms (0.7%)

simplify184.0ms (1.9%)

eval69.0ms (0.7%)

prune28.0ms (0.3%)

regimes12.0ms (0.1%)

regimes11.0ms (0.1%)

regimes5.0ms (0.1%)

regimes5.0ms (0%)

simplify4.0ms (0%)

soundness613.0ms (6.3%)

end54.0ms (0.6%)

Profiling