Details

analyze6.0ms (0.1%)

Algorithm

1×

Search

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

Compiler

Compiled 10 to 8 computations (20% saved)

sample7.8s (79.8%)

Results

6.1s	4332×	body	2048	valid
1.3s	1999×	body	1024	valid
255.0ms	1032×	body	512	valid
113.0ms	893×	body	256	valid
1.0ms	8×	body	256	invalid

preprocess83.0ms (0.9%)

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)

simplify92.0ms (0.9%)

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)

prune2.0ms (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

33.5b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	33.5b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
▶	33.5b	(+.f64 -2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize18.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 24 to 8 computations (66.7% saved)

series3.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite45.0ms (0.5%)

Algorithm

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

Rules

96×	`add-sqr-sqrt_binary64`
92×	`add-log-exp_binary64`
90×	`*-un-lft-identity_binary64`
90×	`add-exp-log_binary64`
90×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	9
1	182	9
2	3153	9
0	8	9

Stop Event

1×	iter limit
1×	unsound

Counts

1 → 11

Calls

Call 1

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

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

Outputs

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

simplify57.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

23 → 22

Calls

Call 1

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

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

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (exp.f64 x) 2)
✓	5.2b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Compiler

Compiled 22 to 10 computations (54.5% saved)

series2.0ms (0%)

Counts

2 → 16

Calls

6 calls:

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

rewrite68.0ms (0.7%)

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

Outputs

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

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

simplify39.0ms (0.4%)

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))

eval32.0ms (0.3%)

Compiler: Compiled 1637 to 934 computations (42.9% saved)

prune18.0ms (0.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	108	6	114
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	110	6	116

Error

0.0b

Counts

116 → 6

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.1b	(fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))
▶	0.5b	(*.f64 x x)
▶	33.5b	(.f64 1 (+.f64 -2 (.f64 2 (cosh.f64 x))))
	0.0b	(+.f64 (.f64 1/360 (pow.f64 x 6)) (+.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 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/20160 (pow.f64 x 8)))))
▶	33.5b	(exp.f64 (log.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))))

Compiler

Compiled 138 to 110 computations (20.3% saved)

localize32.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.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)

series7.0ms (0.1%)

Counts

4 → 3

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(+.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	@	0	(*.f64 1/20160 (pow.f64 x 8))
1.0ms	x	@	inf	(*.f64 1/12 (pow.f64 x 4))

rewrite99.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

586×	`log-prod_binary64`
354×	`pow2_binary64`
330×	`pow-prod-down_binary64`
320×	`fma-def_binary64`
244×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	35
1	328	35
2	3690	35

Stop Event

1×	node limit

Counts

4 → 111

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

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

simplify179.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

1329×	`sqr-pow_binary64`
671×	`pow-sqr_binary64`
493×	`cube-prod_binary64`
398×	`fabs-mul_binary64`
394×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	18	21
2	37	21
3	87	21
4	289	21
5	1190	21
6	1888	21
7	1985	21
8	2139	21
9	2329	21
10	2599	21
11	2952	21
12	3398	21
13	3929	21
14	4540	21
15	5265	21
16	5543	21
17	5775	21
18	5957	21
19	6085	21
20	6151	21
21	7041	21
22	7953	21

Stop Event

1×	node limit

Counts

114 → 113

Calls

Call 1

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

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

localize2.0ms (0%)

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

localize9.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 25 to 17 computations (32% saved)

series4.0ms (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)))

rewrite55.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 32

Calls

Call 1

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

Outputs

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

simplify72.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

44 → 42

Calls

Call 1

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

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

localize8.0ms (0.1%)

Compiler: Compiled 18 to 10 computations (44.4% saved)

localize12.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(exp.f64 (log.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))))
	3.3b	(+.f64 -2 (*.f64 2 (cosh.f64 x)))

Compiler

Compiled 31 to 21 computations (32.3% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite49.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

823×	`pow1_binary64`
766×	`add-log-exp_binary64`
764×	`log1p-expm1-u_binary64`
764×	`expm1-log1p-u_binary64`
752×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	9
1	178	7
2	2074	7

Stop Event

1×	node limit

Counts

1 → 37

Calls

Call 1

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

Outputs

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

simplify96.0ms (1%)

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

49 → 47

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))

eval141.0ms (1.4%)

Compiler: Compiled 4725 to 3744 computations (20.8% saved)

prune31.0ms (0.3%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	242	2	244
Fresh	0	1	1
Picked	0	1	1
Done	1	3	4
Total	243	7	250

Error

0.0b

Counts

250 → 7

Alt Table

Click to see full alt table

Status	Error	Program
▶	3.7b	(exp.f64 (log.f64 (*.f64 x x)))
✓	0.5b	(*.f64 x x)
✓	33.5b	(exp.f64 (log.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))))
▶	33.5b	(+.f64 (*.f64 2 (cosh.f64 x)) -2)
✓	0.1b	(fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))
▶	0.0b	(+.f64 (.f64 1/360 (pow.f64 x 6)) (+.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 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/20160 (pow.f64 x 8)))))

Compiler

Compiled 73 to 57 computations (21.9% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	3.3b	(exp.f64 (log.f64 (*.f64 x x)))
✓	26.5b	(log.f64 (*.f64 x x))

Compiler

Compiled 14 to 4 computations (71.4% saved)

series31.0ms (0.3%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
24.0ms	x	@	0	(log.f64 (*.f64 x x))
6.0ms	x	@	inf	(log.f64 (*.f64 x x))
0.0ms	x	@	-inf	(log.f64 (*.f64 x x))
0.0ms	x	@	0	(exp.f64 (log.f64 (*.f64 x x)))
0.0ms	x	@	inf	(exp.f64 (log.f64 (*.f64 x x)))

rewrite50.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

326×	`pow1_binary64`
312×	`add-sqr-sqrt_binary64`
306×	`*-un-lft-identity_binary64`
301×	`add-log-exp_binary64`
301×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	5	10
1	84	10
2	885	4

Stop Event

1×	node limit

Counts

2 → 130

Calls

Call 1

Inputs
(log.f64 (*.f64 x x))
(exp.f64 (log.f64 (*.f64 x x)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 x) (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 x) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (log.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 0 (log.f64 x)) (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (log.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (log.f64 x) 0) (/.f64 (log.f64 x) 0))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log.f64 x) (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log.f64 x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log.f64 x) 4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log.f64 x) 3)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log.f64 x) (pow.f64 1 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log.f64 x) (pow.f64 1 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 0 (/.f64 1 0))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 8 (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 2) (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 3 (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/3 (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (log.f64 x) (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (log.f64 x) (+.f64 0 (-.f64 (log.f64 x) (*.f64 0 (log.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 0 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 0) (sqrt.f64 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (log.f64 x)) (neg.f64 (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 0 (log.f64 x)) (*.f64 0 (log.f64 x))) (*.f64 0 (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 1 (log.f64 x)) 3) 1) (+.f64 (*.f64 (+.f64 1 (log.f64 x)) (+.f64 1 (log.f64 x))) (+.f64 1 (*.f64 (+.f64 1 (log.f64 x)) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (+.f64 1 (log.f64 x)) (+.f64 1 (log.f64 x))) 1) (+.f64 (+.f64 1 (log.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (log.f64 x) 0) (-.f64 (log.f64 x) 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 0 (log.f64 x)) (-.f64 0 (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 0 (log.f64 x)) (*.f64 0 (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log.f64 x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log.f64 x) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log.f64 x) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log.f64 x) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log.f64 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log.f64 x) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log.f64 x) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log.f64 x) 9)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log.f64 x) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log.f64 x) 6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log.f64 x) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log.f64 x) 4/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log.f64 x) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log.f64 x) 5)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log.f64 x) 5/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (log.f64 x))) 2)) (cbrt.f64 (log.f64 (log.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (log.f64 x)))) (sqrt.f64 (log.f64 (log.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (neg.f64 (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 (log.f64 x) (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (+.f64 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (log.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (log.f64 x)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (log.f64 x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (log.f64 x) (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (log.f64 x) 1 (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (log.f64 x) (log.f64 x) (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (log.f64 x) (log.f64 x) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 2 (log.f64 x) (log.f64 x))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (+.f64 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 x)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 2))) (log.f64 (cbrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 x))) (log.f64 (sqrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (pow.f64 1 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (pow.f64 1 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (exp.f64 (+.f64 1 (log.f64 x))) (E.f64))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (E.f64) (+.f64 1 (log.f64 x))) (E.f64))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 1 x) 3) 1) (+.f64 (*.f64 (+.f64 1 x) (+.f64 1 x)) (+.f64 1 (*.f64 (+.f64 1 x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 x -1) 3)) (+.f64 1 (-.f64 (pow.f64 (+.f64 x -1) 2) (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (+.f64 1 x) (+.f64 1 x)) 1) (+.f64 (+.f64 1 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (+.f64 x -1) 2)) (-.f64 1 (+.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x 8)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x 9)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x (*.f64 (log.f64 x) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x 6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x 4/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x 12)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x (*.f64 (log.f64 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x 5)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x 5/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x 5/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x (/.f64 (log.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (*.f64 (log.f64 x) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (*.f64 (log.f64 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (/.f64 (log.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 2) (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (E.f64) (E.f64)) (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (E.f64) 2) (log.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 x)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 x)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (-.f64 1 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 x)))) (#(struct:change #<rule egg-rr> (2) ((x . x)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 x))))))

simplify68.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

482×	`sub-neg_binary64`
434×	`unswap-sqr_binary64`
430×	`fma-neg_binary64`
290×	`associate--l+_binary64`
275×	`associate--r+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	132
1	29	132
2	41	132
3	79	132
4	178	132
5	511	132
6	1871	132
7	5839	132

Stop Event

1×	node limit

Counts

154 → 132

Calls

Call 1

Inputs
(*.f64 2 (log.f64 x))
(*.f64 2 (log.f64 x))
(*.f64 2 (log.f64 x))
(*.f64 2 (log.f64 x))
(*.f64 -2 (log.f64 (/.f64 1 x)))
(*.f64 -2 (log.f64 (/.f64 1 x)))
(*.f64 -2 (log.f64 (/.f64 1 x)))
(*.f64 -2 (log.f64 (/.f64 1 x)))
(*.f64 -2 (log.f64 (/.f64 -1 x)))
(*.f64 -2 (log.f64 (/.f64 -1 x)))
(*.f64 -2 (log.f64 (/.f64 -1 x)))
(*.f64 -2 (log.f64 (/.f64 -1 x)))
(pow.f64 x 2)
(pow.f64 x 2)
(pow.f64 x 2)
(pow.f64 x 2)
(pow.f64 x 2)
(pow.f64 x 2)
(pow.f64 x 2)
(pow.f64 x 2)
(pow.f64 x 2)
(pow.f64 x 2)
(pow.f64 x 2)
(pow.f64 x 2)

Outputs
(*.f64 2 (log.f64 x))
(*.f64 2 (log.f64 x))
(*.f64 2 (log.f64 x))
(*.f64 2 (log.f64 x))
(*.f64 -2 (log.f64 (/.f64 1 x)))
(*.f64 2 (log.f64 x))
(*.f64 -2 (log.f64 (/.f64 1 x)))
(*.f64 2 (log.f64 x))
(*.f64 -2 (log.f64 (/.f64 1 x)))
(*.f64 2 (log.f64 x))
(*.f64 -2 (log.f64 (/.f64 1 x)))
(*.f64 2 (log.f64 x))
(*.f64 -2 (log.f64 (/.f64 -1 x)))
(*.f64 -2 (log.f64 (/.f64 -1 x)))
(*.f64 -2 (log.f64 (/.f64 -1 x)))
(*.f64 -2 (log.f64 (/.f64 -1 x)))
(pow.f64 x 2)
(*.f64 x x)
(pow.f64 x 2)
(*.f64 x x)
(pow.f64 x 2)
(*.f64 x x)
(pow.f64 x 2)
(*.f64 x x)
(pow.f64 x 2)
(*.f64 x x)
(pow.f64 x 2)
(*.f64 x x)
(pow.f64 x 2)
(*.f64 x x)
(pow.f64 x 2)
(*.f64 x x)
(pow.f64 x 2)
(*.f64 x x)
(pow.f64 x 2)
(*.f64 x x)
(pow.f64 x 2)
(*.f64 x x)
(pow.f64 x 2)
(*.f64 x x)

localize20.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	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)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 16 to 10 computations (37.5% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite53.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

745×	`pow1_binary64`
695×	`add-log-exp_binary64`
693×	`log1p-expm1-u_binary64`
693×	`expm1-log1p-u_binary64`
683×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	7
1	155	7
2	1874	7

Stop Event

1×	node limit

Counts

1 → 32

Calls

Call 1

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

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

simplify92.0ms (0.9%)

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))

eval53.0ms (0.5%)

Compiler: Compiled 1946 to 1383 computations (28.9% saved)

prune55.0ms (0.6%)

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	208	0	208
Fresh	0	0	0
Picked	0	1	1
Done	0	6	6
Total	208	7	215

Error

0.0b

Counts

215 → 7

Alt Table

Click to see full alt table

Status	Error	Program
✓	3.7b	(exp.f64 (log.f64 (*.f64 x x)))
✓	0.5b	(*.f64 x x)
✓	33.5b	(exp.f64 (log.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))))
✓	33.5b	(+.f64 (*.f64 2 (cosh.f64 x)) -2)
✓	0.1b	(fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))
✓	0.0b	(+.f64 (.f64 1/360 (pow.f64 x 6)) (+.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 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/20160 (pow.f64 x 8)))))

Compiler

Compiled 73 to 57 computations (21.9% saved)

regimes11.0ms (0.1%)

Counts

10 → 1

Calls

Call 1

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

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:

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

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))`

Compiler

Compiled 102 to 71 computations (30.4% saved)

regimes13.0ms (0.1%)

Counts

9 → 1

Calls

Call 1

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

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

Calls

2 calls:

8.0ms	x
2.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))`

Compiler

Compiled 81 to 54 computations (33.3% saved)

regimes10.0ms (0.1%)

Counts

8 → 1

Calls

Call 1

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

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

Calls

2 calls:

5.0ms	x
2.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Results

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

Compiler

Compiled 66 to 42 computations (36.4% saved)

regimes8.0ms (0.1%)

Accuracy

Total -33.2b remaining (-7276.3%)

Threshold costs -33.2b (-7276.3%)

Counts

4 → 1

Calls

Call 1

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

Outputs
(*.f64 x x)

Calls

1 calls:

7.0ms

Results

Error	Segments	Branch
0.5b	1	`x`

Compiler

Compiled 25 to 16 computations (36% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	68
1	31	68

Stop Event

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

Compiler

Compiled 51 to 39 computations (23.5% saved)

soundness180.0ms (1.8%)

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

Compiler

Compiled 48 to 38 computations (20.8% saved)

end40.0ms (0.4%)

Compiler: Compiled 48 to 35 computations (27.1% saved)

Details

analyze6.0ms (0.1%)

sample7.8s (79.8%)

preprocess83.0ms (0.9%)

simplify92.0ms (0.9%)

eval1.0ms (0%)

prune2.0ms (0%)

localize18.0ms (0.2%)

series3.0ms (0%)

rewrite45.0ms (0.5%)

simplify57.0ms (0.6%)

localize11.0ms (0.1%)

series2.0ms (0%)

rewrite68.0ms (0.7%)

simplify39.0ms (0.4%)

eval32.0ms (0.3%)

prune18.0ms (0.2%)

localize32.0ms (0.3%)

series7.0ms (0.1%)

rewrite99.0ms (1%)

simplify179.0ms (1.8%)

localize2.0ms (0%)

localize9.0ms (0.1%)

series4.0ms (0%)

rewrite55.0ms (0.6%)

simplify72.0ms (0.7%)

localize8.0ms (0.1%)

localize12.0ms (0.1%)

series1.0ms (0%)

rewrite49.0ms (0.5%)

simplify96.0ms (1%)

eval141.0ms (1.4%)

prune31.0ms (0.3%)

localize8.0ms (0.1%)

series31.0ms (0.3%)

rewrite50.0ms (0.5%)

simplify68.0ms (0.7%)

localize20.0ms (0.2%)

localize6.0ms (0.1%)

series1.0ms (0%)

rewrite53.0ms (0.5%)

simplify92.0ms (0.9%)

eval53.0ms (0.5%)

prune55.0ms (0.6%)

regimes11.0ms (0.1%)

regimes13.0ms (0.1%)

regimes10.0ms (0.1%)

regimes8.0ms (0.1%)

simplify5.0ms (0.1%)

soundness180.0ms (1.8%)

end40.0ms (0.4%)

Profiling