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)

sample4.1s (40.5%)

Results

3.0s	4287×	body	2048	valid
787.0ms	2046×	body	1024	valid
201.0ms	1037×	body	512	valid
96.0ms	886×	body	256	valid
1.0ms	8×	body	256	invalid

preprocess118.0ms (1.2%)

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)

simplify73.0ms (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

31.9b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	31.9b	(+.f64 -2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	31.9b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
✓	2.1b	(+.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)))

rewrite104.0ms (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 exp.f64 (log.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 .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 exp.f64 (log.f64 (.f64 2 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.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 exp.f64 (log.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 *.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 exp.f64 (log.f64 (*.f64 2 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 2 (cosh.f64 x))))))))

simplify65.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node limit

Counts

47 → 43

Calls

Call 1

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

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

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (exp.f64 x) 2)
✓	2.8b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Compiler

Compiled 22 to 10 computations (54.5% saved)

series2.0ms (0%)

Counts

2 → 16

Calls

6 calls:

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

rewrite136.0ms (1.3%)

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 exp.f64 (log.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 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 exp.f64 (log.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 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 exp.f64 (log.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 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 exp.f64 (log.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 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)))))

simplify38.0ms (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))

eval52.0ms (0.5%)

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

prune24.0ms (0.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	127	8	135
Fresh	0	0	0
Picked	0	1	1
Done	1	0	1
Total	128	9	137

Error

Counts

137 → 9

Alt Table

Click to see full alt table

Status	Error	Program
▶	31.9b	(+.f64 -2 (*.f64 2 (cosh.f64 x)))
	1.1b	(fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))
▶	0.9b	(+.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)))))
▶	1.0b	(fma.f64 x x (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4))))
▶	1.0b	(+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (.f64 1/12 (pow.f64 x 4))))
✓	31.9b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
▶	1.5b	(*.f64 x x)
	33.7b	(+.f64 -1 (exp.f64 (neg.f64 x)))
	31.9b	(/.f64 (-.f64 4 (.f64 (.f64 2 (cosh.f64 x)) (.f64 2 (cosh.f64 x)))) (-.f64 -2 (.f64 2 (cosh.f64 x))))

Compiler

Compiled 203 to 155 computations (23.6% saved)

localize48.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 x 2) (+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/20160 (pow.f64 x 8))))
✓	0.0b	(*.f64 1/20160 (pow.f64 x 8))
✓	0.1b	(*.f64 1/360 (pow.f64 x 6))
✓	0.1b	(*.f64 1/12 (pow.f64 x 4))

Compiler

Compiled 83 to 66 computations (20.5% saved)

series6.0ms (0.1%)

Counts

4 → 6

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(+.f64 (pow.f64 x 2) (+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/20160 (pow.f64 x 8))))
1.0ms	x	@	0	(*.f64 1/12 (pow.f64 x 4))
1.0ms	x	@	0	(*.f64 1/360 (pow.f64 x 6))
1.0ms	x	@	inf	(+.f64 (pow.f64 x 2) (+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/20160 (pow.f64 x 8))))
1.0ms	x	@	0	(*.f64 1/20160 (pow.f64 x 8))

rewrite98.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

707×	`log-prod_binary64`
670×	`fma-def_binary64`
366×	`fma-neg_binary64`
292×	`expm1-udef_binary64`
292×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	41
1	398	39
2	4689	39

Stop Event

1×	node limit

Counts

4 → 135

Calls

Call 1

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

Outputs
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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 1/360 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 6)) 1/360)) (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 6)) 1/360)))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 6)) 1/360))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 x 6)) 1/360))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 x 6)) 1/360))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 1/360 (pow.f64 x 6)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/360 (pow.f64 x 6)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 1/360 (pow.f64 x 6)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (.f64 x x) (cbrt.f64 1/360)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 x 3) (sqrt.f64 1/360)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (pow.f64 x 12) 1/129600))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 x 6)) 1/360))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 1/360 (pow.f64 x 6)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 1/360 (pow.f64 x 6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 1/360 (pow.f64 x 6))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (fma.f64 6 (log.f64 x) (log.f64 1/360)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (fma.f64 6 (log.f64 x) (log.f64 1/360)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 1/360 (pow.f64 x 6))))))))
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expm1.f64 (log1p.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/20160 (pow.f64 x 8) (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/20160 (pow.f64 x 8) (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/20160 (pow.f64 x 8) (.f64 x x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/20160 (pow.f64 x 8) (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/20160 (pow.f64 x 8) (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (.f64 1/20160 (pow.f64 x 8))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 4) 1/12 (fma.f64 1/20160 (pow.f64 x 8) (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 4) (.f64 (pow.f64 x 4) 1/20160) (fma.f64 1/12 (pow.f64 x 4) (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 1/12 (pow.f64 x 4)) 1 (fma.f64 1/20160 (pow.f64 x 8) (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/20160 (pow.f64 x 8) (fma.f64 1/12 (pow.f64 x 4) (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 8) 1/20160 (fma.f64 1/12 (pow.f64 x 4) (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 1/20160 (pow.f64 x 8)) 1 (fma.f64 1/12 (pow.f64 x 4) (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x x) 1 (fma.f64 1/12 (pow.f64 x 4) (.f64 1/20160 (pow.f64 x 8))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x x) (.f64 (.f64 x x) 1/12) (fma.f64 1/20160 (pow.f64 x 8) (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 1/12 (pow.f64 x 4) (.f64 1/20160 (pow.f64 x 8))) 1 (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 1/12 (pow.f64 x 4)) (fma.f64 1/20160 (pow.f64 x 8) (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 1/20160 (pow.f64 x 8)) (fma.f64 1/12 (pow.f64 x 4) (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 x x) (fma.f64 1/12 (pow.f64 x 4) (.f64 1/20160 (pow.f64 x 8))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 1/12 (pow.f64 x 4) (.f64 1/20160 (pow.f64 x 8))) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 1/12 (pow.f64 x 4) (.f64 x x)) (.f64 1/20160 (pow.f64 x 8)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 1/12 (pow.f64 x 4))) (cbrt.f64 (.f64 (pow.f64 x 8) 1/144)) (fma.f64 1/20160 (pow.f64 x 8) (.f64 x x)))))) (#(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))) (fma.f64 1/20160 (pow.f64 x 8) (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (.f64 1/20160 (pow.f64 x 8)))) (pow.f64 (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (.f64 1/20160 (pow.f64 x 8)))) 2) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (.f64 1/20160 (pow.f64 x 8)))) 2) (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (.f64 1/20160 (pow.f64 x 8)))) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 1/20160 (pow.f64 x 8))) (cbrt.f64 (.f64 1/406425600 (pow.f64 x 16))) (fma.f64 1/12 (pow.f64 x 4) (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 1/406425600 (pow.f64 x 16))) (cbrt.f64 (.f64 1/20160 (pow.f64 x 8))) (fma.f64 1/12 (pow.f64 x 4) (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 8)) (.f64 (cbrt.f64 (pow.f64 x 4)) 1/12) (fma.f64 1/20160 (pow.f64 x 8) (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 x x)) (cbrt.f64 (pow.f64 x 4)) (fma.f64 1/12 (pow.f64 x 4) (.f64 1/20160 (pow.f64 x 8))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 x) x) (fma.f64 1/12 (pow.f64 x 4) (.f64 1/20160 (pow.f64 x 8))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (cbrt.f64 (.f64 x x)) (fma.f64 1/12 (pow.f64 x 4) (.f64 1/20160 (pow.f64 x 8))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 16)) (.f64 (cbrt.f64 (pow.f64 x 8)) 1/20160) (fma.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)) (fma.f64 1/20160 (pow.f64 x 8) (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) x) (fma.f64 1/12 (pow.f64 x 4) (.f64 1/20160 (pow.f64 x 8))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 1/12 (pow.f64 x 4) (.f64 1/20160 (pow.f64 x 8)))) (sqrt.f64 (fma.f64 1/12 (pow.f64 x 4) (.f64 1/20160 (pow.f64 x 8)))) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (.f64 1/20160 (pow.f64 x 8))) (sqrt.f64 (.f64 1/20160 (pow.f64 x 8))) (fma.f64 1/12 (pow.f64 x 4) (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 1/8193540096000 (pow.f64 (pow.f64 x 8) 3) (.f64 (pow.f64 x 12) 1/1728)) (/.f64 1 (-.f64 (fma.f64 (pow.f64 x 8) 1/144 (.f64 1/406425600 (pow.f64 x 16))) (.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 1/20160 (pow.f64 x 8))))) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (.f64 (pow.f64 x 8) 1/144) (.f64 1/406425600 (pow.f64 x 16))) (/.f64 1 (fma.f64 1/12 (pow.f64 x 4) (.f64 -1/20160 (pow.f64 x 8)))) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 1/12 (pow.f64 x 4) (.f64 x x)) 1 (.f64 1/20160 (pow.f64 x 8)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x) (fma.f64 1/12 (pow.f64 x 4) (.f64 1/20160 (pow.f64 x 8))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (.f64 x x))) (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (.f64 x x)))) (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (.f64 x x))) (.f64 1/20160 (pow.f64 x 8)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (cbrt.f64 (pow.f64 x 8))) (sqrt.f64 (cbrt.f64 (pow.f64 x 4))) (fma.f64 1/12 (pow.f64 x 4) (.f64 1/20160 (pow.f64 x 8))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 x (.f64 (.f64 x x) (sqrt.f64 1/12))) (hypot.f64 x (.f64 (.f64 x x) (sqrt.f64 1/12))) (.f64 1/20160 (pow.f64 x 8)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 1/20160 (pow.f64 x 4)) (pow.f64 x 4) (fma.f64 1/12 (pow.f64 x 4) (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 1/20160 (cbrt.f64 (pow.f64 x 16))) (cbrt.f64 (pow.f64 x 8)) (fma.f64 1/12 (pow.f64 x 4) (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 1/12 (.f64 x x)) (.f64 x x) (fma.f64 1/20160 (pow.f64 x 8) (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 1/12 (cbrt.f64 (pow.f64 x 8))) (cbrt.f64 (pow.f64 x 4)) (fma.f64 1/20160 (pow.f64 x 8) (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x (cbrt.f64 (.f64 x x))) (cbrt.f64 x) (fma.f64 1/12 (pow.f64 x 4) (.f64 1/20160 (pow.f64 x 8))))))))

simplify130.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

842×	`unswap-sqr_binary64`
724×	`sqr-pow_binary64`
559×	`fma-def_binary64`
545×	`cube-prod_binary64`
428×	`pow-sqr_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	59
1	28	57
2	60	57
3	186	57
4	871	57
5	1847	57
6	3594	57
7	3853	57
8	4218	57
9	4576	57
10	5009	57
11	5536	57
12	6186	57
13	6938	57
14	7527	57
15	7931	57

Stop Event

1×	node limit

Counts

141 → 142

Calls

Call 1

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

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

localize2.0ms (0%)

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

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.1b	(+.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)))

rewrite66.0ms (0.7%)

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 exp.f64 (log.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 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)))))

simplify76.0ms (0.8%)

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))

localize51.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 x 2) (*.f64 1/12 (pow.f64 x 4)))
✓	0.0b	(+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (.f64 1/12 (pow.f64 x 4))))
	0.1b	(*.f64 1/360 (pow.f64 x 6))
	0.1b	(*.f64 1/12 (pow.f64 x 4))

Compiler

Compiled 50 to 39 computations (22% saved)

series2.0ms (0%)

Counts

2 → 9

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(+.f64 (pow.f64 x 2) (*.f64 1/12 (pow.f64 x 4)))
0.0ms	x	@	inf	(+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (.f64 1/12 (pow.f64 x 4))))
0.0ms	x	@	0	(+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (.f64 1/12 (pow.f64 x 4))))
0.0ms	x	@	-inf	(+.f64 (pow.f64 x 2) (*.f64 1/12 (pow.f64 x 4)))
0.0ms	x	@	0	(+.f64 (pow.f64 x 2) (*.f64 1/12 (pow.f64 x 4)))

rewrite79.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

639×	`fma-def_binary64`
575×	`log-prod_binary64`
352×	`pow2_binary64`
344×	`fma-neg_binary64`
238×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	33
1	318	29
2	3895	29

Stop Event

1×	node limit

Counts

2 → 147

Calls

Call 1

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

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(*.f64 x x)) 3) (*.f64 (pow.f64 x 12) 1/1728)) (+.f64 (pow.f64 (fma.f64 1/360 (pow.f64 x 6) (*.f64 x x)) 2) (-.f64 (*.f64 (pow.f64 x 8) 1/144) (*.f64 (fma.f64 1/360 (pow.f64 x 6) (*.f64 x x)) (*.f64 1/12 (pow.f64 x 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 1/12 (pow.f64 x 4) (*.f64 x x)) 2) (*.f64 (pow.f64 x 12) 1/129600)) (-.f64 (fma.f64 1/12 (pow.f64 x 4) (*.f64 x x)) (*.f64 1/360 (pow.f64 x 6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 1/360 (pow.f64 x 6) (*.f64 x x)) 2) (*.f64 (pow.f64 x 8) 1/144)) (-.f64 (fma.f64 1/360 (pow.f64 x 6) (*.f64 x x)) (*.f64 1/12 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 1/360 (pow.f64 x 6) (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 1/360 (pow.f64 x 6) (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 1/360 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#<rule egg-rr> (2) ((x log.f64 (*.f64 (pow.f64 (exp.f64 (pow.f64 x 4)) 1/12) (*.f64 (pow.f64 (exp.f64 1/360) (pow.f64 x 6)) (pow.f64 (exp.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 1/12 (pow.f64 x 4)))) (*.f64 (pow.f64 (exp.f64 1/360) (pow.f64 x 6)) (pow.f64 (exp.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (fma.f64 1/12 (pow.f64 x 4) (*.f64 x x)))) (pow.f64 (exp.f64 1/360) (pow.f64 x 6))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))) (+.f64 1 (expm1.f64 (*.f64 1/360 (pow.f64 x 6))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (fma.f64 1/12 (pow.f64 x 4) (*.f64 x x)))) (+.f64 1 (expm1.f64 (*.f64 1/360 (pow.f64 x 6))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (*.f64 (pow.f64 (exp.f64 1/360) (pow.f64 x 6)) (pow.f64 (exp.f64 x) x)) (pow.f64 (exp.f64 (pow.f64 x 4)) 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (fma.f64 1/360 (pow.f64 x 6) (*.f64 x x))) (+.f64 1 (expm1.f64 (*.f64 1/12 (pow.f64 x 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (*.f64 (pow.f64 (exp.f64 1/360) (pow.f64 x 6)) (pow.f64 (exp.f64 x) x)) (+.f64 1 (expm1.f64 (*.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) (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 1/360 (pow.f64 x 6) (fma.f64 1/12 (pow.f64 x 4) (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 1/12 (pow.f64 x 4) (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 1/12 (pow.f64 x 4) (*.f64 x x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 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simplify166.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1124×	`sqr-pow_binary64`
653×	`pow-sqr_binary64`
603×	`cube-prod_binary64`
565×	`fma-def_binary64`
382×	`unpow3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	77
1	30	75
2	62	75
3	166	75
4	768	75
5	1989	75
6	2489	75
7	2734	75
8	2945	75
9	3214	75
10	3536	75
11	3946	75
12	4378	75
13	4869	75
14	5484	75
15	5745	75
16	5991	75
17	6255	75
18	6527	75
19	6789	75

Stop Event

1×	node limit

Counts

156 → 155

Calls

Call 1

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

localize20.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 40 to 30 computations (25% saved)

series3.0ms (0%)

Counts

2 → 24

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)))
0.0ms	x	@	0	(fma.f64 x x (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4))))
0.0ms	x	@	0	(fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4)))
0.0ms	x	@	inf	(fma.f64 x x (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4))))

rewrite86.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	32
1	234	32
2	2498	32

Stop Event

1×	node limit

Counts

2 → 43

Calls

Call 1

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

Outputs

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

simplify183.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

67 → 52

Calls

Call 1

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

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

eval282.0ms (2.8%)

Compiler: Compiled 9329 to 6855 computations (26.5% saved)

prune64.0ms (0.6%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	435	4	439
Fresh	2	1	3
Picked	1	0	1
Done	1	4	5
Total	439	9	448

Error

Counts

448 → 9

Alt Table

Click to see full alt table

Status	Error	Program
✓	31.9b	(+.f64 -2 (*.f64 2 (cosh.f64 x)))
▶	1.0b	(+.f64 (+.f64 (.f64 x x) (.f64 1/360 (pow.f64 x 6))) (*.f64 1/12 (pow.f64 x 4)))
✓	0.9b	(+.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)))))
✓	31.9b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
✓	1.5b	(*.f64 x x)
▶	31.9b	(/.f64 (-.f64 (.f64 4 (pow.f64 (cosh.f64 x) 2)) 4) (-.f64 (.f64 2 (cosh.f64 x)) -2))
▶	33.5b	(*.f64 1/360 (pow.f64 x 6))
▶	1.1b	(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))
▶	33.7b	(+.f64 -1 (exp.f64 (neg.f64 x)))

Compiler

Compiled 148 to 115 computations (22.3% saved)

localize21.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 49 to 33 computations (32.7% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time

Variable

Point

Expression

0.0ms

inf

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

0.0ms

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

0.0ms

-inf

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

rewrite66.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

686×	`fma-def_binary64`
558×	`log-prod_binary64`
337×	`pow2_binary64`
335×	`fma-neg_binary64`
227×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	296	18
2	3814	18

Stop Event

1×	node limit

Counts

1 → 99

Calls

Call 1

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

Outputs

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

simplify178.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

1287×	`fma-def_binary64`
726×	`sqr-pow_binary64`
487×	`cube-prod_binary64`
356×	`*-commutative_binary64`
336×	`unpow3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	179
1	35	165
2	75	165
3	192	165
4	847	165
5	2348	165
6	3458	165
7	3691	165
8	3891	165
9	4142	165
10	4457	165
11	4903	165
12	5670	165
13	6171	165
14	6834	165
15	7120	165
16	7368	165
17	7630	165
18	7900	165

Stop Event

1×	node limit

Counts

111 → 108

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

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

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
	0.1b	(*.f64 1/360 (pow.f64 x 6))

Compiler

Compiled 12 to 9 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.9b	(+.f64 -1 (exp.f64 (neg.f64 x)))

Compiler

Compiled 13 to 6 computations (53.8% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(+.f64 -1 (exp.f64 (neg.f64 x)))
0.0ms	x	@	0	(+.f64 -1 (exp.f64 (neg.f64 x)))
0.0ms	x	@	inf	(+.f64 -1 (exp.f64 (neg.f64 x)))

rewrite54.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 31

Calls

Call 1

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

Outputs

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

simplify56.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

43 → 42

Calls

Call 1

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

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

localize9.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))

Compiler

Compiled 21 to 14 computations (33.3% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))
1.0ms	x	@	0	(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))
1.0ms	x	@	inf	(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))

rewrite76.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

624×	`pow1_binary64`
585×	`add-log-exp_binary64`
585×	`log1p-expm1-u_binary64`
585×	`expm1-log1p-u_binary64`
573×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	150	11
2	1601	11

Stop Event

1×	node limit

Counts

1 → 13

Calls

Call 1

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

Outputs

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

simplify189.0ms (1.9%)

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

25 → 18

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))

localize25.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (cosh.f64 x) 2)
✓	0.0b	(/.f64 (-.f64 (.f64 4 (pow.f64 (cosh.f64 x) 2)) 4) (-.f64 (.f64 2 (cosh.f64 x)) -2))
✓	2.0b	(-.f64 (*.f64 4 (pow.f64 (cosh.f64 x) 2)) 4)

Compiler

Compiled 50 to 34 computations (32% saved)

series6.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

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

rewrite300.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	35
1	280	23
2	3699	23

Stop Event

1×	node limit

Counts

3 → 256

Calls

Call 1

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

Outputs

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

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

simplify111.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

924×	`distribute-rgt-out_binary64`
826×	`fma-def_binary64`
723×	`associate-l_binary64`
557×	`associate-r_binary64`
437×	`unswap-sqr_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	52	685
1	127	673
2	318	669
3	1041	669
4	4809	669
5	7798	669

Stop Event

1×	node limit

Counts

292 → 285

Calls

Call 1

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

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

eval950.0ms (9.4%)

Compiler: Compiled 13965 to 10186 computations (27.1% saved)

prune148.0ms (1.5%)

Pruning

11 alts after pruning (3 fresh and 8 done)

	Pruned	Kept	Total
New	498	3	501
Fresh	0	0	0
Picked	0	1	1
Done	1	7	8
Total	499	11	510

Error

Counts

510 → 11

Alt Table

Click to see full alt table

Status	Error	Program
✓	31.9b	(+.f64 -2 (*.f64 2 (cosh.f64 x)))
▶	1.1b	(+.f64 (.f64 (.f64 1/12 (pow.f64 x 3)) x) (*.f64 x x))
✓	1.0b	(+.f64 (+.f64 (.f64 x x) (.f64 1/360 (pow.f64 x 6))) (*.f64 1/12 (pow.f64 x 4)))
▶	60.4b	(neg.f64 x)
✓	1.1b	(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))
✓	0.9b	(+.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)))))
✓	31.9b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
✓	1.5b	(*.f64 x x)
✓	31.9b	(/.f64 (-.f64 (.f64 4 (pow.f64 (cosh.f64 x) 2)) 4) (-.f64 (.f64 2 (cosh.f64 x)) -2))
✓	33.5b	(*.f64 1/360 (pow.f64 x 6))
▶	60.3b	(expm1.f64 (neg.f64 x))

Compiler

Compiled 108 to 82 computations (24.1% saved)

localize7.0ms (0.1%)

Compiler: Compiled 7 to 3 computations (57.1% saved)

localize4.0ms (0%)

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

localize63.0ms (0.6%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (.f64 1/12 (pow.f64 x 3)) x) (*.f64 x x))
✓	0.1b	(.f64 (.f64 1/12 (pow.f64 x 3)) x)
✓	0.1b	(*.f64 1/12 (pow.f64 x 3))

Compiler

Compiled 33 to 21 computations (36.4% saved)

series6.0ms (0.1%)

Counts

3 → 24

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(*.f64 1/12 (pow.f64 x 3))
1.0ms	x	@	inf	(*.f64 1/12 (pow.f64 x 3))
1.0ms	x	@	0	(*.f64 1/12 (pow.f64 x 3))
1.0ms	x	@	inf	(+.f64 (.f64 (.f64 1/12 (pow.f64 x 3)) x) (*.f64 x x))
0.0ms	x	@	-inf	(+.f64 (.f64 (.f64 1/12 (pow.f64 x 3)) x) (*.f64 x x))

rewrite126.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

934×	`pow1_binary64`
876×	`add-log-exp_binary64`
876×	`log1p-expm1-u_binary64`
876×	`expm1-log1p-u_binary64`
97×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	30
1	203	25
2	2538	25

Stop Event

1×	node limit

Counts

3 → 65

Calls

Call 1

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

Outputs

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

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

simplify208.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	219
1	18	201
2	38	201
3	84	201
4	290	201
5	1175	201
6	2524	201
7	3205	201
8	3416	201
9	3657	201
10	3954	201
11	4338	201
12	4799	201
13	5336	201
14	5968	201
15	6719	201
16	7031	201
17	7259	201
18	7455	201
19	7511	201
20	7533	201

Stop Event

1×	node limit

Counts

89 → 69

Calls

Call 1

Inputs
(*.f64 1/12 (pow.f64 x 4))
(*.f64 1/12 (pow.f64 x 4))
(*.f64 1/12 (pow.f64 x 4))
(*.f64 1/12 (pow.f64 x 4))
(*.f64 1/12 (pow.f64 x 4))
(*.f64 1/12 (pow.f64 x 4))
(*.f64 1/12 (pow.f64 x 4))
(*.f64 1/12 (pow.f64 x 4))
(*.f64 1/12 (pow.f64 x 4))
(*.f64 1/12 (pow.f64 x 4))
(*.f64 1/12 (pow.f64 x 4))
(*.f64 1/12 (pow.f64 x 4))
(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
(*.f64 1/12 (pow.f64 x 4))
(*.f64 1/12 (pow.f64 x 4))
(*.f64 1/12 (pow.f64 x 4))
(*.f64 1/12 (pow.f64 x 4))
(*.f64 1/12 (pow.f64 x 4))
(*.f64 1/12 (pow.f64 x 4))
(*.f64 1/12 (pow.f64 x 4))
(*.f64 1/12 (pow.f64 x 4))
(*.f64 1/12 (pow.f64 x 4))
(*.f64 1/12 (pow.f64 x 4))
(*.f64 1/12 (pow.f64 x 4))
(*.f64 1/12 (pow.f64 x 4))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (pow.f64 x 2) (*.f64 1/12 (pow.f64 x 4)))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 x x))
(fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))
(+.f64 (pow.f64 x 2) (*.f64 1/12 (pow.f64 x 4)))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 x x))
(fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))
(+.f64 (pow.f64 x 2) (*.f64 1/12 (pow.f64 x 4)))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 x x))
(fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))
(*.f64 1/12 (pow.f64 x 4))
(+.f64 (pow.f64 x 2) (*.f64 1/12 (pow.f64 x 4)))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 x x))
(fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))
(+.f64 (pow.f64 x 2) (*.f64 1/12 (pow.f64 x 4)))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 x x))
(fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))
(+.f64 (pow.f64 x 2) (*.f64 1/12 (pow.f64 x 4)))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 x x))
(fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))
(*.f64 1/12 (pow.f64 x 4))
(+.f64 (pow.f64 x 2) (*.f64 1/12 (pow.f64 x 4)))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 x x))
(fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))
(+.f64 (pow.f64 x 2) (*.f64 1/12 (pow.f64 x 4)))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 x x))
(fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))
(+.f64 (pow.f64 x 2) (*.f64 1/12 (pow.f64 x 4)))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 x x))
(fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))

eval75.0ms (0.7%)

Compiler: Compiled 976 to 653 computations (33.1% saved)

prune28.0ms (0.3%)

Pruning

11 alts after pruning (1 fresh and 10 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	0	0	0
Picked	1	0	1
Done	0	10	10
Total	69	11	80

Error

Counts

80 → 11

Alt Table

Click to see full alt table

Status	Error	Program
✓	31.9b	(+.f64 -2 (*.f64 2 (cosh.f64 x)))
✓	1.0b	(+.f64 (+.f64 (.f64 x x) (.f64 1/360 (pow.f64 x 6))) (*.f64 1/12 (pow.f64 x 4)))
✓	60.4b	(neg.f64 x)
✓	1.1b	(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))
✓	0.9b	(+.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)))))
✓	31.9b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
	1.1b	(+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 x x))
✓	1.5b	(*.f64 x x)
✓	31.9b	(/.f64 (-.f64 (.f64 4 (pow.f64 (cosh.f64 x) 2)) 4) (-.f64 (.f64 2 (cosh.f64 x)) -2))
✓	33.5b	(*.f64 1/360 (pow.f64 x 6))
✓	60.3b	(expm1.f64 (neg.f64 x))

Compiler

Compiled 106 to 81 computations (23.6% saved)

regimes58.0ms (0.6%)

Counts

18 → 1

Calls

Call 1

Inputs
(neg.f64 x)
(*.f64 x x)
(expm1.f64 (neg.f64 x))
(*.f64 1/360 (pow.f64 x 6))
(+.f64 -1 (exp.f64 (neg.f64 x)))
(+.f64 -2 (*.f64 2 (cosh.f64 x)))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 x x))
(+.f64 (.f64 (.f64 1/12 (pow.f64 x 3)) x) (*.f64 x x))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))
(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)))
(+.f64 (+.f64 (.f64 x x) (.f64 1/360 (pow.f64 x 6))) (*.f64 1/12 (pow.f64 x 4)))
(/.f64 (-.f64 (.f64 4 (pow.f64 (cosh.f64 x) 2)) 4) (-.f64 (.f64 2 (cosh.f64 x)) -2))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (.f64 1/12 (pow.f64 x 4))))
(/.f64 (-.f64 4 (.f64 (.f64 2 (cosh.f64 x)) (.f64 2 (cosh.f64 x)))) (-.f64 -2 (.f64 2 (cosh.f64 x))))
(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)))))

Outputs
(+.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)))))

Calls

2 calls:

23.0ms	x
5.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Results

Error	Segments	Branch
0.9b	1	`x`
0.9b	1	`(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))`

Compiler

Compiled 185 to 122 computations (34.1% saved)

regimes168.0ms (1.7%)

Counts

17 → 1

Calls

Call 1

Inputs
(neg.f64 x)
(*.f64 x x)
(expm1.f64 (neg.f64 x))
(*.f64 1/360 (pow.f64 x 6))
(+.f64 -1 (exp.f64 (neg.f64 x)))
(+.f64 -2 (*.f64 2 (cosh.f64 x)))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 x x))
(+.f64 (.f64 (.f64 1/12 (pow.f64 x 3)) x) (*.f64 x x))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))
(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)))
(+.f64 (+.f64 (.f64 x x) (.f64 1/360 (pow.f64 x 6))) (*.f64 1/12 (pow.f64 x 4)))
(/.f64 (-.f64 (.f64 4 (pow.f64 (cosh.f64 x) 2)) 4) (-.f64 (.f64 2 (cosh.f64 x)) -2))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (.f64 1/12 (pow.f64 x 4))))
(/.f64 (-.f64 4 (.f64 (.f64 2 (cosh.f64 x)) (.f64 2 (cosh.f64 x)))) (-.f64 -2 (.f64 2 (cosh.f64 x))))
(fma.f64 x x (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4))))

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

Calls

2 calls:

18.0ms	x
5.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Results

Error	Segments	Branch
1.0b	1	`x`
1.0b	1	`(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))`

Compiler

Compiled 164 to 105 computations (36% saved)

regimes44.0ms (0.4%)

Counts

16 → 1

Calls

Call 1

Inputs
(neg.f64 x)
(*.f64 x x)
(expm1.f64 (neg.f64 x))
(*.f64 1/360 (pow.f64 x 6))
(+.f64 -1 (exp.f64 (neg.f64 x)))
(+.f64 -2 (*.f64 2 (cosh.f64 x)))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 x x))
(+.f64 (.f64 (.f64 1/12 (pow.f64 x 3)) x) (*.f64 x x))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))
(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)))
(+.f64 (+.f64 (.f64 x x) (.f64 1/360 (pow.f64 x 6))) (*.f64 1/12 (pow.f64 x 4)))
(/.f64 (-.f64 (.f64 4 (pow.f64 (cosh.f64 x) 2)) 4) (-.f64 (.f64 2 (cosh.f64 x)) -2))
(+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (pow.f64 x 2) (.f64 1/12 (pow.f64 x 4))))
(/.f64 (-.f64 4 (.f64 (.f64 2 (cosh.f64 x)) (.f64 2 (cosh.f64 x)))) (-.f64 -2 (.f64 2 (cosh.f64 x))))

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

Calls

2 calls:

31.0ms	x
5.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Results

Error	Segments	Branch
1.0b	1	`x`
1.0b	1	`(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))`

Compiler

Compiled 151 to 96 computations (36.4% saved)

regimes42.0ms (0.4%)

Counts

12 → 2

Calls

Call 1

Inputs
(neg.f64 x)
(*.f64 x x)
(expm1.f64 (neg.f64 x))
(*.f64 1/360 (pow.f64 x 6))
(+.f64 -1 (exp.f64 (neg.f64 x)))
(+.f64 -2 (*.f64 2 (cosh.f64 x)))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 x x))
(+.f64 (.f64 (.f64 1/12 (pow.f64 x 3)) x) (*.f64 x x))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))
(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
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))
(+.f64 -2 (*.f64 2 (cosh.f64 x)))

Calls

2 calls:

7.0ms	x
4.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Results

Error	Segments	Branch
1.1b	1	`x`
0.1b	2	`(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))`

Compiler

Compiled 88 to 51 computations (42% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.3062420765375116e-5	0.0020489455933945244

Compiler

Compiled 13 to 10 computations (23.1% saved)

regimes122.0ms (1.2%)

Counts

8 → 1

Calls

Call 1

Inputs
(neg.f64 x)
(*.f64 x x)
(expm1.f64 (neg.f64 x))
(*.f64 1/360 (pow.f64 x 6))
(+.f64 -1 (exp.f64 (neg.f64 x)))
(+.f64 -2 (*.f64 2 (cosh.f64 x)))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 x x))
(+.f64 (.f64 (.f64 1/12 (pow.f64 x 3)) x) (*.f64 x x))

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

Calls

1 calls:

120.0ms

Results

Error	Segments	Branch
1.1b	1	`x`

Compiler

Compiled 47 to 28 computations (40.4% saved)

regimes7.0ms (0.1%)

Accuracy

Total -59.2b remaining (-4006.3%)

Threshold costs -59.2b (-4006.3%)

Counts

6 → 1

Calls

Call 1

Inputs
(neg.f64 x)
(*.f64 x x)
(expm1.f64 (neg.f64 x))
(*.f64 1/360 (pow.f64 x 6))
(+.f64 -1 (exp.f64 (neg.f64 x)))
(+.f64 -2 (*.f64 2 (cosh.f64 x)))

Outputs
(*.f64 x x)

Calls

1 calls:

6.0ms

Results

Error	Segments	Branch
1.5b	1	`x`

Compiler

Compiled 27 to 17 computations (37% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	129
1	61	129
2	64	129
3	65	129

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(+.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 x x (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4))))
(+.f64 (+.f64 (.f64 x x) (.f64 1/360 (pow.f64 x 6))) (*.f64 1/12 (pow.f64 x 4)))
(if (<=.f64 (+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))) 5902958103587057/295147905179352825856) (.f64 x (fma.f64 1/12 (pow.f64 x 3) x)) (+.f64 -2 (.f64 2 (cosh.f64 x))))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 x x))
(*.f64 x x)
(neg.f64 x)

Outputs
(+.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 x x (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4))))
(+.f64 (+.f64 (.f64 x x) (.f64 1/360 (pow.f64 x 6))) (*.f64 1/12 (pow.f64 x 4)))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 x x)))
(if (<=.f64 (+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))) 5902958103587057/295147905179352825856) (.f64 x (fma.f64 1/12 (pow.f64 x 3) x)) (+.f64 -2 (.f64 2 (cosh.f64 x))))
(if (<=.f64 (+.f64 (+.f64 (exp.f64 x) -2) (exp.f64 (neg.f64 x))) 5902958103587057/295147905179352825856) (.f64 x (fma.f64 1/12 (pow.f64 x 3) x)) (+.f64 -2 (.f64 2 (cosh.f64 x))))
(+.f64 (.f64 1/12 (pow.f64 x 4)) (.f64 x x))
(*.f64 x x)
(neg.f64 x)

Compiler

Compiled 95 to 71 computations (25.3% saved)

soundness581.0ms (5.8%)

Algorithm

3×	egg-herbie

Rules

1124×	`sqr-pow_binary64`
801×	`associate-/l*_binary64`
801×	`associate-/l*_binary64`
653×	`pow-sqr_binary64`
624×	`fma-def_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	14	77
1	30	75
2	62	75
3	166	75
4	768	75
5	1989	75
6	2489	75
7	2734	75
8	2945	75
9	3214	75
10	3536	75
11	3946	75
12	4378	75
13	4869	75
14	5484	75
15	5745	75
16	5991	75
17	6255	75
18	6527	75
19	6789	75
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
1×	node limit
1×	node limit

Compiler

Compiled 290 to 215 computations (25.9% saved)

end250.0ms (2.5%)

Compiler: Compiled 89 to 62 computations (30.3% saved)

Details

analyze4.0ms (0%)

sample4.1s (40.5%)

preprocess118.0ms (1.2%)

simplify73.0ms (0.7%)

eval1.0ms (0%)

prune1.0ms (0%)

localize8.0ms (0.1%)

series2.0ms (0%)

rewrite104.0ms (1%)

simplify65.0ms (0.6%)

localize9.0ms (0.1%)

series2.0ms (0%)

rewrite136.0ms (1.3%)

simplify38.0ms (0.4%)

eval52.0ms (0.5%)

prune24.0ms (0.2%)

localize48.0ms (0.5%)

series6.0ms (0.1%)

rewrite98.0ms (1%)

simplify130.0ms (1.3%)

localize2.0ms (0%)

localize6.0ms (0.1%)

series3.0ms (0%)

rewrite66.0ms (0.7%)

simplify76.0ms (0.8%)

localize51.0ms (0.5%)

series2.0ms (0%)

rewrite79.0ms (0.8%)

simplify166.0ms (1.6%)

localize20.0ms (0.2%)

series3.0ms (0%)

rewrite86.0ms (0.9%)

simplify183.0ms (1.8%)

eval282.0ms (2.8%)

prune64.0ms (0.6%)

localize21.0ms (0.2%)

series1.0ms (0%)

rewrite66.0ms (0.7%)

simplify178.0ms (1.8%)

localize6.0ms (0.1%)

localize5.0ms (0.1%)

series2.0ms (0%)

rewrite54.0ms (0.5%)

simplify56.0ms (0.6%)

localize9.0ms (0.1%)

series2.0ms (0%)

rewrite76.0ms (0.8%)

simplify189.0ms (1.9%)

localize25.0ms (0.3%)

series6.0ms (0.1%)

rewrite300.0ms (3%)

simplify111.0ms (1.1%)

eval950.0ms (9.4%)

prune148.0ms (1.5%)

localize7.0ms (0.1%)

localize4.0ms (0%)

localize63.0ms (0.6%)

series6.0ms (0.1%)

rewrite126.0ms (1.2%)

simplify208.0ms (2.1%)

eval75.0ms (0.7%)

prune28.0ms (0.3%)

regimes58.0ms (0.6%)

regimes168.0ms (1.7%)

regimes44.0ms (0.4%)

regimes42.0ms (0.4%)

bsearch0.0ms (0%)

regimes122.0ms (1.2%)

regimes7.0ms (0.1%)

simplify9.0ms (0.1%)

soundness581.0ms (5.8%)

end250.0ms (2.5%)

Profiling