Details

analyze27.0ms (0.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	31.2%	6.3%	6
68.7%	21.9%	9.5%	7
68.7%	17.2%	14.1%	8
71.8%	11.7%	16.5%	9
71.8%	9%	19.2%	10
73.4%	6%	20.6%	11
73.4%	4.6%	22%	12

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample1.8s (60.4%)

Results

736.0ms	1523×	body	2048	valid
514.0ms	1808×	body	1024	valid
353.0ms	3778×	body	256	valid
200.0ms	1147×	body	512	valid
27.0ms	300×	body	256	invalid

preprocess37.0ms (1.2%)

Algorithm

2×	egg-herbie

Rules

736×	`unswap-sqr_binary64`
572×	`associate-l_binary64`
512×	`associate-+l+_binary64`
458×	`associate-r_binary64`
376×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	12
1	22	12
2	30	12
3	48	12
4	98	12
5	256	12
6	875	12
7	3913	12
0	2	2
1	2	2

Stop Event

1×	unsound
1×	node limit

Calls

Call 1

Inputs
0
1

Outputs
0
1
0

Call 2

Inputs
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 x a)) 1)

Outputs
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 x a)) 1)
(expm1.f64 (*.f64 a x))

Symmetry

(sort a x)

Compiler

Compiled 10 to 8 computations (20% saved)

simplify39.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

571×	`fma-neg_binary64`
440×	`unswap-sqr_binary64`
421×	`cancel-sign-sub-inv_binary64`
385×	`*-commutative_binary64`
329×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	6
1	16	6
2	23	6
3	35	6
4	70	6
5	175	6
6	556	6
7	2331	6
8	5877	6

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(-.f64 (exp.f64 (*.f64 a x)) 1)

Outputs
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))

eval1.0ms (0%)

Compiler: Compiled 12 to 7 computations (41.7% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(expm1.f64 (*.f64 a x))

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series3.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	a	@	0	(expm1.f64 (*.f64 a x))
1.0ms	x	@	0	(expm1.f64 (*.f64 a x))
0.0ms	a	@	-inf	(expm1.f64 (*.f64 a x))
0.0ms	a	@	inf	(expm1.f64 (*.f64 a x))
0.0ms	x	@	inf	(expm1.f64 (*.f64 a x))

rewrite34.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

442×	`pow1_binary64`
422×	`add-sqr-sqrt_binary64`
416×	`*-un-lft-identity_binary64`
405×	`add-log-exp_binary64`
405×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	96	6
2	1113	6

Stop Event

1×	node limit

Counts

1 → 24

Calls

Call 1

Inputs
(expm1.f64 (*.f64 a x))

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

Outputs

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

simplify47.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

1324×	`distribute-lft-out_binary64`
822×	`fma-def_binary64`
421×	`associate-/l/_binary64`
365×	`associate-/r/_binary64`
344×	`associate-+l+_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	31	284
1	89	284
2	244	280
3	1019	262
4	3124	248
5	4830	248
6	6678	248

Stop Event

1×	node limit

Counts

48 → 33

Calls

Call 1

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

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

eval8.0ms (0.2%)

Compiler: Compiled 379 to 158 computations (58.3% saved)

prune6.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	30	3	33
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	30	4	34

Error

Counts

34 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	20.9b	(*.f64 a x)
▶	16.4b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))
▶	37.6b	(pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) 2)
✓	0.0b	(expm1.f64 (*.f64 a x))

Compiler

Compiled 29 to 21 computations (27.6% saved)

localize5.0ms (0.2%)

Local error

Found 6 expressions with local error:

New	Error	Program
	8.9b	(sqrt.f64 (expm1.f64 (*.f64 a x)))
	0.1b	(pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) 2)
	0.0b	(expm1.f64 (*.f64 a x))
	0.0b	(expm1.f64 (*.f64 a x))
✓	0.1b	(pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) 2)
✓	8.9b	(sqrt.f64 (expm1.f64 (*.f64 a x)))

series10.0ms (0.3%)

Counts

2 → 32

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) 2)
2.0ms	a	@	0	(pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) 2)
1.0ms	a	@	0	(sqrt.f64 (expm1.f64 (*.f64 a x)))
1.0ms	x	@	0	(sqrt.f64 (expm1.f64 (*.f64 a x)))
1.0ms	a	@	-inf	(pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) 2)

rewrite42.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

588×	`pow1_binary64`
543×	`add-log-exp_binary64`
543×	`log1p-expm1-u_binary64`
543×	`expm1-log1p-u_binary64`
529×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	161	14
2	1543	14

Stop Event

1×	node limit

Counts

2 → 39

Calls

Call 1

Inputs
(sqrt.f64 (expm1.f64 (*.f64 a x)))
(pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) 2)

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

Outputs

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

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

simplify45.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

571×	`fma-neg_binary64`
440×	`unswap-sqr_binary64`
421×	`cancel-sign-sub-inv_binary64`
375×	`*-commutative_binary64`
340×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	224
1	17	224
2	24	224
3	36	224
4	71	224
5	176	224
6	565	224
7	2399	224
8	5919	224

Stop Event

1×	node limit

Counts

71 → 42

Calls

Call 1

Inputs
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) 1))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) 1))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) 1))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) 1))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) 1))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) 1))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) 1))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) 1))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) 1))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) 1))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) 1))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) 1))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) 1))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) 1))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) 1))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) 1))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)

Outputs
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) 1))
(sqrt.f64 (expm1.f64 (*.f64 a x)))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) 1))
(sqrt.f64 (expm1.f64 (*.f64 a x)))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) 1))
(sqrt.f64 (expm1.f64 (*.f64 a x)))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) 1))
(sqrt.f64 (expm1.f64 (*.f64 a x)))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) 1))
(sqrt.f64 (expm1.f64 (*.f64 a x)))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) 1))
(sqrt.f64 (expm1.f64 (*.f64 a x)))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) 1))
(sqrt.f64 (expm1.f64 (*.f64 a x)))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) 1))
(sqrt.f64 (expm1.f64 (*.f64 a x)))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) 1))
(sqrt.f64 (expm1.f64 (*.f64 a x)))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) 1))
(sqrt.f64 (expm1.f64 (*.f64 a x)))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) 1))
(sqrt.f64 (expm1.f64 (*.f64 a x)))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) 1))
(sqrt.f64 (expm1.f64 (*.f64 a x)))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) 1))
(sqrt.f64 (expm1.f64 (*.f64 a x)))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) 1))
(sqrt.f64 (expm1.f64 (*.f64 a x)))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) 1))
(sqrt.f64 (expm1.f64 (*.f64 a x)))
(sqrt.f64 (-.f64 (exp.f64 (*.f64 a x)) 1))
(sqrt.f64 (expm1.f64 (*.f64 a x)))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))

localize6.0ms (0.2%)

Local error

Found 6 expressions with local error:

New	Error	Program
	16.4b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))
	0.2b	(pow.f64 (expm1.f64 (*.f64 a x)) 3)
	0.0b	(expm1.f64 (*.f64 a x))
	0.0b	(expm1.f64 (*.f64 a x))
✓	0.2b	(pow.f64 (expm1.f64 (*.f64 a x)) 3)
✓	16.4b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))

series9.0ms (0.3%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(pow.f64 (expm1.f64 (*.f64 a x)) 3)
1.0ms	x	@	0	(pow.f64 (expm1.f64 (*.f64 a x)) 3)
1.0ms	a	@	0	(pow.f64 (expm1.f64 (*.f64 a x)) 3)
1.0ms	a	@	inf	(pow.f64 (expm1.f64 (*.f64 a x)) 3)
1.0ms	a	@	-inf	(pow.f64 (expm1.f64 (*.f64 a x)) 3)

rewrite42.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

612×	`pow1_binary64`
573×	`add-log-exp_binary64`
573×	`log1p-expm1-u_binary64`
573×	`expm1-log1p-u_binary64`
558×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	164	15
2	1618	15

Stop Event

1×	node limit

Counts

2 → 41

Calls

Call 1

Inputs
(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))
(pow.f64 (expm1.f64 (*.f64 a x)) 3)

Outputs

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

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

simplify57.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

975×	`fma-def_binary64`
819×	`associate-l_binary64`
717×	`associate-r_binary64`
544×	`unswap-sqr_binary64`
358×	`associate-+l+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	97	763
1	319	751
2	1117	728
3	6750	716

Stop Event

1×	node limit

Counts

89 → 62

Calls

Call 1

Inputs
(*.f64 a x)
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (+.f64 (.f64 a x) (.f64 1/6 (*.f64 (pow.f64 a 3) (pow.f64 x 3)))))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (+.f64 (.f64 a x) (+.f64 (.f64 1/24 (.f64 (pow.f64 a 4) (pow.f64 x 4))) (.f64 1/6 (*.f64 (pow.f64 a 3) (pow.f64 x 3))))))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(*.f64 a x)
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (+.f64 (.f64 a x) (.f64 1/6 (*.f64 (pow.f64 a 3) (pow.f64 x 3)))))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (+.f64 (.f64 a x) (+.f64 (.f64 1/24 (.f64 (pow.f64 a 4) (pow.f64 x 4))) (.f64 1/6 (*.f64 (pow.f64 a 3) (pow.f64 x 3))))))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(*.f64 (pow.f64 a 3) (pow.f64 x 3))
(+.f64 (.f64 (+.f64 (pow.f64 x 4) (.f64 1/2 (pow.f64 x 4))) (pow.f64 a 4)) (*.f64 (pow.f64 a 3) (pow.f64 x 3)))
(+.f64 (.f64 (+.f64 (pow.f64 x 4) (.f64 1/2 (pow.f64 x 4))) (pow.f64 a 4)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 1/4 (pow.f64 x 4)) (.f64 1/3 (pow.f64 x 4))) x) (+.f64 (.f64 1/2 (pow.f64 x 5)) (.f64 1/6 (pow.f64 x 5)))) (pow.f64 a 5)) (*.f64 (pow.f64 a 3) (pow.f64 x 3))))
(+.f64 (.f64 (+.f64 (pow.f64 x 4) (.f64 1/2 (pow.f64 x 4))) (pow.f64 a 4)) (+.f64 (.f64 (pow.f64 a 6) (+.f64 (.f64 (+.f64 (.f64 1/12 (pow.f64 x 5)) (.f64 1/6 (pow.f64 x 5))) x) (+.f64 (.f64 1/2 (.f64 (+.f64 (.f64 1/4 (pow.f64 x 4)) (.f64 1/3 (pow.f64 x 4))) (pow.f64 x 2))) (+.f64 (.f64 1/6 (pow.f64 x 6)) (.f64 1/24 (pow.f64 x 6)))))) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 1/4 (pow.f64 x 4)) (.f64 1/3 (pow.f64 x 4))) x) (+.f64 (.f64 1/2 (pow.f64 x 5)) (.f64 1/6 (pow.f64 x 5)))) (pow.f64 a 5)) (*.f64 (pow.f64 a 3) (pow.f64 x 3)))))
(pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3)
(pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3)
(pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3)
(pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3)
(pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3)
(pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3)
(pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3)
(pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3)
(*.f64 (pow.f64 a 3) (pow.f64 x 3))
(+.f64 (.f64 (pow.f64 a 3) (pow.f64 x 3)) (.f64 (+.f64 (*.f64 1/2 (pow.f64 a 4)) (pow.f64 a 4)) (pow.f64 x 4)))
(+.f64 (.f64 (pow.f64 a 3) (pow.f64 x 3)) (+.f64 (.f64 (+.f64 (.f64 1/2 (pow.f64 a 4)) (pow.f64 a 4)) (pow.f64 x 4)) (.f64 (+.f64 (.f64 1/2 (pow.f64 a 5)) (+.f64 (.f64 a (+.f64 (.f64 1/3 (pow.f64 a 4)) (.f64 1/4 (pow.f64 a 4)))) (*.f64 1/6 (pow.f64 a 5)))) (pow.f64 x 5))))
(+.f64 (.f64 (pow.f64 a 3) (pow.f64 x 3)) (+.f64 (.f64 (+.f64 (.f64 a (+.f64 (.f64 1/12 (pow.f64 a 5)) (.f64 1/6 (pow.f64 a 5)))) (+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (+.f64 (.f64 1/3 (pow.f64 a 4)) (.f64 1/4 (pow.f64 a 4))))) (+.f64 (.f64 1/6 (pow.f64 a 6)) (.f64 1/24 (pow.f64 a 6))))) (pow.f64 x 6)) (+.f64 (.f64 (+.f64 (.f64 1/2 (pow.f64 a 4)) (pow.f64 a 4)) (pow.f64 x 4)) (.f64 (+.f64 (.f64 1/2 (pow.f64 a 5)) (+.f64 (.f64 a (+.f64 (.f64 1/3 (pow.f64 a 4)) (.f64 1/4 (pow.f64 a 4)))) (*.f64 1/6 (pow.f64 a 5)))) (pow.f64 x 5)))))
(pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3)
(pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3)
(pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3)
(pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3)
(pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3)
(pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3)
(pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3)
(pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3)

Outputs
(*.f64 a x)
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 (.f64 1/2 (.f64 a a)) (.f64 x x) (.f64 a x))
(.f64 x (+.f64 a (.f64 1/2 (.f64 a (.f64 a x)))))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (+.f64 (.f64 a x) (.f64 1/6 (*.f64 (pow.f64 a 3) (pow.f64 x 3)))))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (fma.f64 a x (.f64 1/6 (*.f64 (pow.f64 a 3) (pow.f64 x 3)))))
(fma.f64 1/2 (.f64 x (.f64 x (.f64 a a))) (fma.f64 a x (.f64 1/6 (*.f64 (pow.f64 a 3) (pow.f64 x 3)))))
(fma.f64 1/6 (.f64 (pow.f64 a 3) (pow.f64 x 3)) (.f64 x (+.f64 a (.f64 1/2 (.f64 a (*.f64 a x))))))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (+.f64 (.f64 a x) (+.f64 (.f64 1/24 (.f64 (pow.f64 a 4) (pow.f64 x 4))) (.f64 1/6 (*.f64 (pow.f64 a 3) (pow.f64 x 3))))))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (fma.f64 a x (fma.f64 1/24 (.f64 (pow.f64 a 4) (pow.f64 x 4)) (.f64 1/6 (.f64 (pow.f64 a 3) (pow.f64 x 3))))))
(fma.f64 1/2 (.f64 x (.f64 x (.f64 a a))) (fma.f64 a x (fma.f64 1/6 (.f64 (pow.f64 a 3) (pow.f64 x 3)) (.f64 1/24 (.f64 (pow.f64 a 4) (pow.f64 x 4))))))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (fma.f64 1/6 (.f64 (pow.f64 a 3) (pow.f64 x 3)) (fma.f64 (pow.f64 a 4) (.f64 1/24 (pow.f64 x 4)) (.f64 a x))))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(*.f64 a x)
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 (.f64 1/2 (.f64 a a)) (.f64 x x) (.f64 a x))
(.f64 x (+.f64 a (.f64 1/2 (.f64 a (.f64 a x)))))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (+.f64 (.f64 a x) (.f64 1/6 (*.f64 (pow.f64 a 3) (pow.f64 x 3)))))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (fma.f64 a x (.f64 1/6 (*.f64 (pow.f64 a 3) (pow.f64 x 3)))))
(fma.f64 1/2 (.f64 x (.f64 x (.f64 a a))) (fma.f64 a x (.f64 1/6 (*.f64 (pow.f64 a 3) (pow.f64 x 3)))))
(fma.f64 1/6 (.f64 (pow.f64 a 3) (pow.f64 x 3)) (.f64 x (+.f64 a (.f64 1/2 (.f64 a (*.f64 a x))))))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (+.f64 (.f64 a x) (+.f64 (.f64 1/24 (.f64 (pow.f64 a 4) (pow.f64 x 4))) (.f64 1/6 (*.f64 (pow.f64 a 3) (pow.f64 x 3))))))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (fma.f64 a x (fma.f64 1/24 (.f64 (pow.f64 a 4) (pow.f64 x 4)) (.f64 1/6 (.f64 (pow.f64 a 3) (pow.f64 x 3))))))
(fma.f64 1/2 (.f64 x (.f64 x (.f64 a a))) (fma.f64 a x (fma.f64 1/6 (.f64 (pow.f64 a 3) (pow.f64 x 3)) (.f64 1/24 (.f64 (pow.f64 a 4) (pow.f64 x 4))))))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (fma.f64 1/6 (.f64 (pow.f64 a 3) (pow.f64 x 3)) (fma.f64 (pow.f64 a 4) (.f64 1/24 (pow.f64 x 4)) (.f64 a x))))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(*.f64 (pow.f64 a 3) (pow.f64 x 3))
(+.f64 (.f64 (+.f64 (pow.f64 x 4) (.f64 1/2 (pow.f64 x 4))) (pow.f64 a 4)) (*.f64 (pow.f64 a 3) (pow.f64 x 3)))
(fma.f64 (.f64 3/2 (pow.f64 x 4)) (pow.f64 a 4) (.f64 (pow.f64 a 3) (pow.f64 x 3)))
(fma.f64 (pow.f64 a 3) (pow.f64 x 3) (.f64 (pow.f64 x 4) (.f64 (pow.f64 a 4) 3/2)))
(fma.f64 (pow.f64 a 3) (pow.f64 x 3) (.f64 (pow.f64 a 4) (.f64 (pow.f64 x 4) 3/2)))
(+.f64 (.f64 (+.f64 (pow.f64 x 4) (.f64 1/2 (pow.f64 x 4))) (pow.f64 a 4)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 1/4 (pow.f64 x 4)) (.f64 1/3 (pow.f64 x 4))) x) (+.f64 (.f64 1/2 (pow.f64 x 5)) (.f64 1/6 (pow.f64 x 5)))) (pow.f64 a 5)) (*.f64 (pow.f64 a 3) (pow.f64 x 3))))
(fma.f64 (.f64 3/2 (pow.f64 x 4)) (pow.f64 a 4) (fma.f64 (fma.f64 (.f64 (pow.f64 x 4) 7/12) x (.f64 (pow.f64 x 5) 2/3)) (pow.f64 a 5) (.f64 (pow.f64 a 3) (pow.f64 x 3))))
(fma.f64 (pow.f64 a 4) (.f64 (pow.f64 x 4) 3/2) (fma.f64 (pow.f64 a 3) (pow.f64 x 3) (.f64 (fma.f64 x (.f64 (pow.f64 x 4) 7/12) (.f64 (pow.f64 x 5) 2/3)) (pow.f64 a 5))))
(fma.f64 (fma.f64 x (.f64 (pow.f64 x 4) 7/12) (.f64 (pow.f64 x 5) 2/3)) (pow.f64 a 5) (fma.f64 (pow.f64 a 3) (pow.f64 x 3) (.f64 (pow.f64 a 4) (.f64 (pow.f64 x 4) 3/2))))
(fma.f64 (pow.f64 a 3) (pow.f64 x 3) (fma.f64 (pow.f64 x 5) (fma.f64 (pow.f64 a 5) 7/12 (.f64 (pow.f64 a 5) 2/3)) (.f64 (pow.f64 a 4) (*.f64 (pow.f64 x 4) 3/2))))
(+.f64 (.f64 (+.f64 (pow.f64 x 4) (.f64 1/2 (pow.f64 x 4))) (pow.f64 a 4)) (+.f64 (.f64 (pow.f64 a 6) (+.f64 (.f64 (+.f64 (.f64 1/12 (pow.f64 x 5)) (.f64 1/6 (pow.f64 x 5))) x) (+.f64 (.f64 1/2 (.f64 (+.f64 (.f64 1/4 (pow.f64 x 4)) (.f64 1/3 (pow.f64 x 4))) (pow.f64 x 2))) (+.f64 (.f64 1/6 (pow.f64 x 6)) (.f64 1/24 (pow.f64 x 6)))))) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 1/4 (pow.f64 x 4)) (.f64 1/3 (pow.f64 x 4))) x) (+.f64 (.f64 1/2 (pow.f64 x 5)) (.f64 1/6 (pow.f64 x 5)))) (pow.f64 a 5)) (*.f64 (pow.f64 a 3) (pow.f64 x 3)))))
(fma.f64 (.f64 3/2 (pow.f64 x 4)) (pow.f64 a 4) (fma.f64 (pow.f64 a 6) (fma.f64 (.f64 (pow.f64 x 5) 1/4) x (fma.f64 1/2 (.f64 (.f64 x x) (.f64 (pow.f64 x 4) 7/12)) (.f64 (pow.f64 x 6) 5/24))) (fma.f64 (fma.f64 (.f64 (pow.f64 x 4) 7/12) x (.f64 (pow.f64 x 5) 2/3)) (pow.f64 a 5) (*.f64 (pow.f64 a 3) (pow.f64 x 3)))))
(fma.f64 (pow.f64 a 4) (.f64 (pow.f64 x 4) 3/2) (fma.f64 (pow.f64 a 6) (fma.f64 x (.f64 1/4 (pow.f64 x 5)) (fma.f64 1/2 (.f64 (pow.f64 x 6) 7/12) (.f64 (pow.f64 x 6) 5/24))) (fma.f64 (pow.f64 a 3) (pow.f64 x 3) (.f64 (fma.f64 x (.f64 (pow.f64 x 4) 7/12) (*.f64 (pow.f64 x 5) 2/3)) (pow.f64 a 5)))))
(fma.f64 (pow.f64 a 4) (.f64 (pow.f64 x 4) 3/2) (fma.f64 (fma.f64 x (.f64 (pow.f64 x 4) 7/12) (.f64 (pow.f64 x 5) 2/3)) (pow.f64 a 5) (fma.f64 (pow.f64 a 6) (fma.f64 x (.f64 1/4 (pow.f64 x 5)) (fma.f64 (pow.f64 x 6) 5/24 (.f64 (pow.f64 x 6) 7/24))) (.f64 (pow.f64 a 3) (pow.f64 x 3)))))
(fma.f64 (pow.f64 a 4) (.f64 (pow.f64 x 4) 3/2) (fma.f64 (fma.f64 (pow.f64 x 5) 2/3 (.f64 (pow.f64 x 5) 7/12)) (pow.f64 a 5) (fma.f64 (pow.f64 a 6) (fma.f64 (pow.f64 x 6) 1/4 (fma.f64 (pow.f64 x 6) 5/24 (.f64 (pow.f64 x 6) 7/24))) (.f64 (pow.f64 a 3) (pow.f64 x 3)))))
(pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3)
(pow.f64 (expm1.f64 (*.f64 a x)) 3)
(pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3)
(pow.f64 (expm1.f64 (*.f64 a x)) 3)
(pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3)
(pow.f64 (expm1.f64 (*.f64 a x)) 3)
(pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3)
(pow.f64 (expm1.f64 (*.f64 a x)) 3)
(pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3)
(pow.f64 (expm1.f64 (*.f64 a x)) 3)
(pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3)
(pow.f64 (expm1.f64 (*.f64 a x)) 3)
(pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3)
(pow.f64 (expm1.f64 (*.f64 a x)) 3)
(pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3)
(pow.f64 (expm1.f64 (*.f64 a x)) 3)
(*.f64 (pow.f64 a 3) (pow.f64 x 3))
(+.f64 (.f64 (pow.f64 a 3) (pow.f64 x 3)) (.f64 (+.f64 (*.f64 1/2 (pow.f64 a 4)) (pow.f64 a 4)) (pow.f64 x 4)))
(fma.f64 (.f64 3/2 (pow.f64 x 4)) (pow.f64 a 4) (.f64 (pow.f64 a 3) (pow.f64 x 3)))
(fma.f64 (pow.f64 a 3) (pow.f64 x 3) (.f64 (pow.f64 x 4) (.f64 (pow.f64 a 4) 3/2)))
(fma.f64 (pow.f64 a 3) (pow.f64 x 3) (.f64 (pow.f64 a 4) (.f64 (pow.f64 x 4) 3/2)))
(+.f64 (.f64 (pow.f64 a 3) (pow.f64 x 3)) (+.f64 (.f64 (+.f64 (.f64 1/2 (pow.f64 a 4)) (pow.f64 a 4)) (pow.f64 x 4)) (.f64 (+.f64 (.f64 1/2 (pow.f64 a 5)) (+.f64 (.f64 a (+.f64 (.f64 1/3 (pow.f64 a 4)) (.f64 1/4 (pow.f64 a 4)))) (*.f64 1/6 (pow.f64 a 5)))) (pow.f64 x 5))))
(fma.f64 (.f64 3/2 (pow.f64 x 4)) (pow.f64 a 4) (fma.f64 (fma.f64 (.f64 (pow.f64 x 4) 7/12) x (.f64 (pow.f64 x 5) 2/3)) (pow.f64 a 5) (.f64 (pow.f64 a 3) (pow.f64 x 3))))
(fma.f64 (pow.f64 a 4) (.f64 (pow.f64 x 4) 3/2) (fma.f64 (pow.f64 a 3) (pow.f64 x 3) (.f64 (fma.f64 x (.f64 (pow.f64 x 4) 7/12) (.f64 (pow.f64 x 5) 2/3)) (pow.f64 a 5))))
(fma.f64 (fma.f64 x (.f64 (pow.f64 x 4) 7/12) (.f64 (pow.f64 x 5) 2/3)) (pow.f64 a 5) (fma.f64 (pow.f64 a 3) (pow.f64 x 3) (.f64 (pow.f64 a 4) (.f64 (pow.f64 x 4) 3/2))))
(fma.f64 (pow.f64 a 3) (pow.f64 x 3) (fma.f64 (pow.f64 x 5) (fma.f64 (pow.f64 a 5) 7/12 (.f64 (pow.f64 a 5) 2/3)) (.f64 (pow.f64 a 4) (*.f64 (pow.f64 x 4) 3/2))))
(+.f64 (.f64 (pow.f64 a 3) (pow.f64 x 3)) (+.f64 (.f64 (+.f64 (.f64 a (+.f64 (.f64 1/12 (pow.f64 a 5)) (.f64 1/6 (pow.f64 a 5)))) (+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (+.f64 (.f64 1/3 (pow.f64 a 4)) (.f64 1/4 (pow.f64 a 4))))) (+.f64 (.f64 1/6 (pow.f64 a 6)) (.f64 1/24 (pow.f64 a 6))))) (pow.f64 x 6)) (+.f64 (.f64 (+.f64 (.f64 1/2 (pow.f64 a 4)) (pow.f64 a 4)) (pow.f64 x 4)) (.f64 (+.f64 (.f64 1/2 (pow.f64 a 5)) (+.f64 (.f64 a (+.f64 (.f64 1/3 (pow.f64 a 4)) (.f64 1/4 (pow.f64 a 4)))) (*.f64 1/6 (pow.f64 a 5)))) (pow.f64 x 5)))))
(fma.f64 (pow.f64 a 3) (pow.f64 x 3) (fma.f64 (fma.f64 a (.f64 (pow.f64 a 5) 1/4) (fma.f64 1/2 (.f64 (.f64 a a) (.f64 (pow.f64 a 4) 7/12)) (.f64 (pow.f64 a 6) 5/24))) (pow.f64 x 6) (fma.f64 (.f64 3/2 (pow.f64 a 4)) (pow.f64 x 4) (.f64 (pow.f64 x 5) (fma.f64 1/2 (pow.f64 a 5) (fma.f64 a (.f64 (pow.f64 a 4) 7/12) (*.f64 1/6 (pow.f64 a 5))))))))
(fma.f64 (pow.f64 a 3) (pow.f64 x 3) (fma.f64 (pow.f64 x 6) (fma.f64 a (.f64 1/4 (pow.f64 a 5)) (fma.f64 1/2 (.f64 (pow.f64 a 6) 7/12) (.f64 (pow.f64 a 6) 5/24))) (fma.f64 (pow.f64 x 4) (.f64 (pow.f64 a 4) 3/2) (.f64 (pow.f64 x 5) (fma.f64 1/2 (pow.f64 a 5) (fma.f64 a (.f64 (pow.f64 a 4) 7/12) (*.f64 1/6 (pow.f64 a 5))))))))
(fma.f64 (pow.f64 x 6) (fma.f64 (pow.f64 a 6) 1/4 (fma.f64 (pow.f64 a 6) 5/24 (.f64 (pow.f64 a 6) 7/24))) (fma.f64 (pow.f64 a 3) (pow.f64 x 3) (fma.f64 (pow.f64 x 5) (fma.f64 (pow.f64 a 5) 7/12 (.f64 (pow.f64 a 5) 2/3)) (.f64 (pow.f64 a 4) (.f64 (pow.f64 x 4) 3/2)))))
(pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3)
(pow.f64 (expm1.f64 (*.f64 a x)) 3)
(pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3)
(pow.f64 (expm1.f64 (*.f64 a x)) 3)
(pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3)
(pow.f64 (expm1.f64 (*.f64 a x)) 3)
(pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3)
(pow.f64 (expm1.f64 (*.f64 a x)) 3)
(pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3)
(pow.f64 (expm1.f64 (*.f64 a x)) 3)
(pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3)
(pow.f64 (expm1.f64 (*.f64 a x)) 3)
(pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3)
(pow.f64 (expm1.f64 (*.f64 a x)) 3)
(pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3)
(pow.f64 (expm1.f64 (*.f64 a x)) 3)

localize2.0ms (0.1%)

eval55.0ms (1.8%)

Compiler: Compiled 2532 to 1302 computations (48.6% saved)

prune24.0ms (0.8%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	169	1	170
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	169	5	174

Error

Counts

174 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	21.4b	(.f64 x (+.f64 a (.f64 1/2 (.f64 a (.f64 a x)))))
✓	16.4b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))
✓	20.9b	(*.f64 a x)
✓	37.6b	(pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) 2)
✓	0.0b	(expm1.f64 (*.f64 a x))

Compiler

Compiled 42 to 29 computations (31% saved)

localize6.0ms (0.2%)

Local error

Found 6 expressions with local error:

New	Error	Program
	1.2b	(.f64 x (+.f64 a (.f64 1/2 (.f64 a (.f64 a x)))))
	0.1b	(.f64 a (.f64 a x))
	0.0b	(+.f64 a (.f64 1/2 (.f64 a (*.f64 a x))))
✓	0.0b	(+.f64 a (.f64 1/2 (.f64 a (*.f64 a x))))
✓	0.1b	(.f64 a (.f64 a x))
✓	1.2b	(.f64 x (+.f64 a (.f64 1/2 (.f64 a (.f64 a x)))))

series8.0ms (0.3%)

Counts

3 → 72

Calls

18 calls:

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

rewrite66.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

550×	`log-prod_binary64`
413×	`pow-prod-down_binary64`
396×	`exp-prod_binary64`
355×	`fma-def_binary64`
258×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	36
1	198	32
2	2746	32

Stop Event

1×	node limit

Counts

3 → 181

Calls

Call 1

Inputs
(.f64 x (+.f64 a (.f64 1/2 (.f64 a (.f64 a x)))))
(.f64 a (.f64 a x))
(+.f64 a (.f64 1/2 (.f64 a (*.f64 a x))))

Outputs

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

simplify212.0ms (6.9%)

Algorithm

1×	egg-herbie

Rules

1251×	`unswap-sqr_binary64`
823×	`fma-def_binary64`
764×	`sqr-pow_binary64`
358×	`*-commutative_binary64`
350×	`cube-prod_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	810
1	33	774
2	73	720
3	206	720
4	995	720
5	2023	720
6	2314	720
7	2637	720
8	2890	720
9	3059	720
10	3254	720
11	3418	720
12	3607	720
13	3822	720
14	4052	720
15	4296	720
16	4561	720
17	4840	720
18	5140	720
19	5454	720
20	5524	720
21	7472	720
22	7759	720
23	7981	720

Stop Event

1×	node limit

Counts

253 → 193

Calls

Call 1

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

Outputs
(*.f64 a x)
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (.f64 a x))
(.f64 x (fma.f64 1/2 (.f64 a (*.f64 a x)) a))
(.f64 x (fma.f64 x (.f64 a (*.f64 a 1/2)) a))
(.f64 a (.f64 (fma.f64 a (*.f64 x 1/2) 1) x))
(.f64 (.f64 a x) (fma.f64 a (*.f64 x 1/2) 1))
(.f64 a (.f64 x (fma.f64 a (*.f64 x 1/2) 1)))
(.f64 a (fma.f64 (.f64 x x) (*.f64 a 1/2) x))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (.f64 a x))
(.f64 x (fma.f64 1/2 (.f64 a (*.f64 a x)) a))
(.f64 x (fma.f64 x (.f64 a (*.f64 a 1/2)) a))
(.f64 a (.f64 (fma.f64 a (*.f64 x 1/2) 1) x))
(.f64 (.f64 a x) (fma.f64 a (*.f64 x 1/2) 1))
(.f64 a (.f64 x (fma.f64 a (*.f64 x 1/2) 1)))
(.f64 a (fma.f64 (.f64 x x) (*.f64 a 1/2) x))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (.f64 a x))
(.f64 x (fma.f64 1/2 (.f64 a (*.f64 a x)) a))
(.f64 x (fma.f64 x (.f64 a (*.f64 a 1/2)) a))
(.f64 a (.f64 (fma.f64 a (*.f64 x 1/2) 1) x))
(.f64 (.f64 a x) (fma.f64 a (*.f64 x 1/2) 1))
(.f64 a (.f64 x (fma.f64 a (*.f64 x 1/2) 1)))
(.f64 a (fma.f64 (.f64 x x) (*.f64 a 1/2) x))
(.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2)))
(.f64 1/2 (.f64 (.f64 a a) (.f64 x x)))
(.f64 1/2 (.f64 a (.f64 a (.f64 x x))))
(.f64 a (.f64 (.f64 a (.f64 x x)) 1/2))
(.f64 x (.f64 x (.f64 a (.f64 a 1/2))))
(.f64 a (.f64 a (.f64 x (.f64 x 1/2))))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (.f64 a x))
(.f64 x (fma.f64 1/2 (.f64 a (*.f64 a x)) a))
(.f64 x (fma.f64 x (.f64 a (*.f64 a 1/2)) a))
(.f64 a (.f64 (fma.f64 a (*.f64 x 1/2) 1) x))
(.f64 (.f64 a x) (fma.f64 a (*.f64 x 1/2) 1))
(.f64 a (.f64 x (fma.f64 a (*.f64 x 1/2) 1)))
(.f64 a (fma.f64 (.f64 x x) (*.f64 a 1/2) x))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (.f64 a x))
(.f64 x (fma.f64 1/2 (.f64 a (*.f64 a x)) a))
(.f64 x (fma.f64 x (.f64 a (*.f64 a 1/2)) a))
(.f64 a (.f64 (fma.f64 a (*.f64 x 1/2) 1) x))
(.f64 (.f64 a x) (fma.f64 a (*.f64 x 1/2) 1))
(.f64 a (.f64 x (fma.f64 a (*.f64 x 1/2) 1)))
(.f64 a (fma.f64 (.f64 x x) (*.f64 a 1/2) x))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (.f64 a x))
(.f64 x (fma.f64 1/2 (.f64 a (*.f64 a x)) a))
(.f64 x (fma.f64 x (.f64 a (*.f64 a 1/2)) a))
(.f64 a (.f64 (fma.f64 a (*.f64 x 1/2) 1) x))
(.f64 (.f64 a x) (fma.f64 a (*.f64 x 1/2) 1))
(.f64 a (.f64 x (fma.f64 a (*.f64 x 1/2) 1)))
(.f64 a (fma.f64 (.f64 x x) (*.f64 a 1/2) x))
(.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2)))
(.f64 1/2 (.f64 (.f64 a a) (.f64 x x)))
(.f64 1/2 (.f64 a (.f64 a (.f64 x x))))
(.f64 a (.f64 (.f64 a (.f64 x x)) 1/2))
(.f64 x (.f64 x (.f64 a (.f64 a 1/2))))
(.f64 a (.f64 a (.f64 x (.f64 x 1/2))))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (.f64 a x))
(.f64 x (fma.f64 1/2 (.f64 a (*.f64 a x)) a))
(.f64 x (fma.f64 x (.f64 a (*.f64 a 1/2)) a))
(.f64 a (.f64 (fma.f64 a (*.f64 x 1/2) 1) x))
(.f64 (.f64 a x) (fma.f64 a (*.f64 x 1/2) 1))
(.f64 a (.f64 x (fma.f64 a (*.f64 x 1/2) 1)))
(.f64 a (fma.f64 (.f64 x x) (*.f64 a 1/2) x))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (.f64 a x))
(.f64 x (fma.f64 1/2 (.f64 a (*.f64 a x)) a))
(.f64 x (fma.f64 x (.f64 a (*.f64 a 1/2)) a))
(.f64 a (.f64 (fma.f64 a (*.f64 x 1/2) 1) x))
(.f64 (.f64 a x) (fma.f64 a (*.f64 x 1/2) 1))
(.f64 a (.f64 x (fma.f64 a (*.f64 x 1/2) 1)))
(.f64 a (fma.f64 (.f64 x x) (*.f64 a 1/2) x))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (.f64 a x))
(.f64 x (fma.f64 1/2 (.f64 a (*.f64 a x)) a))
(.f64 x (fma.f64 x (.f64 a (*.f64 a 1/2)) a))
(.f64 a (.f64 (fma.f64 a (*.f64 x 1/2) 1) x))
(.f64 (.f64 a x) (fma.f64 a (*.f64 x 1/2) 1))
(.f64 a (.f64 x (fma.f64 a (*.f64 x 1/2) 1)))
(.f64 a (fma.f64 (.f64 x x) (*.f64 a 1/2) x))
(*.f64 a x)
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (.f64 a x))
(.f64 x (fma.f64 1/2 (.f64 a (*.f64 a x)) a))
(.f64 x (fma.f64 x (.f64 a (*.f64 a 1/2)) a))
(.f64 a (.f64 (fma.f64 a (*.f64 x 1/2) 1) x))
(.f64 (.f64 a x) (fma.f64 a (*.f64 x 1/2) 1))
(.f64 a (.f64 x (fma.f64 a (*.f64 x 1/2) 1)))
(.f64 a (fma.f64 (.f64 x x) (*.f64 a 1/2) x))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (.f64 a x))
(.f64 x (fma.f64 1/2 (.f64 a (*.f64 a x)) a))
(.f64 x (fma.f64 x (.f64 a (*.f64 a 1/2)) a))
(.f64 a (.f64 (fma.f64 a (*.f64 x 1/2) 1) x))
(.f64 (.f64 a x) (fma.f64 a (*.f64 x 1/2) 1))
(.f64 a (.f64 x (fma.f64 a (*.f64 x 1/2) 1)))
(.f64 a (fma.f64 (.f64 x x) (*.f64 a 1/2) x))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (.f64 a x))
(.f64 x (fma.f64 1/2 (.f64 a (*.f64 a x)) a))
(.f64 x (fma.f64 x (.f64 a (*.f64 a 1/2)) a))
(.f64 a (.f64 (fma.f64 a (*.f64 x 1/2) 1) x))
(.f64 (.f64 a x) (fma.f64 a (*.f64 x 1/2) 1))
(.f64 a (.f64 x (fma.f64 a (*.f64 x 1/2) 1)))
(.f64 a (fma.f64 (.f64 x x) (*.f64 a 1/2) x))
(.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2)))
(.f64 1/2 (.f64 (.f64 a a) (.f64 x x)))
(.f64 1/2 (.f64 a (.f64 a (.f64 x x))))
(.f64 a (.f64 (.f64 a (.f64 x x)) 1/2))
(.f64 x (.f64 x (.f64 a (.f64 a 1/2))))
(.f64 a (.f64 a (.f64 x (.f64 x 1/2))))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (.f64 a x))
(.f64 x (fma.f64 1/2 (.f64 a (*.f64 a x)) a))
(.f64 x (fma.f64 x (.f64 a (*.f64 a 1/2)) a))
(.f64 a (.f64 (fma.f64 a (*.f64 x 1/2) 1) x))
(.f64 (.f64 a x) (fma.f64 a (*.f64 x 1/2) 1))
(.f64 a (.f64 x (fma.f64 a (*.f64 x 1/2) 1)))
(.f64 a (fma.f64 (.f64 x x) (*.f64 a 1/2) x))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (.f64 a x))
(.f64 x (fma.f64 1/2 (.f64 a (*.f64 a x)) a))
(.f64 x (fma.f64 x (.f64 a (*.f64 a 1/2)) a))
(.f64 a (.f64 (fma.f64 a (*.f64 x 1/2) 1) x))
(.f64 (.f64 a x) (fma.f64 a (*.f64 x 1/2) 1))
(.f64 a (.f64 x (fma.f64 a (*.f64 x 1/2) 1)))
(.f64 a (fma.f64 (.f64 x x) (*.f64 a 1/2) x))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (.f64 a x))
(.f64 x (fma.f64 1/2 (.f64 a (*.f64 a x)) a))
(.f64 x (fma.f64 x (.f64 a (*.f64 a 1/2)) a))
(.f64 a (.f64 (fma.f64 a (*.f64 x 1/2) 1) x))
(.f64 (.f64 a x) (fma.f64 a (*.f64 x 1/2) 1))
(.f64 a (.f64 x (fma.f64 a (*.f64 x 1/2) 1)))
(.f64 a (fma.f64 (.f64 x x) (*.f64 a 1/2) x))
(.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2)))
(.f64 1/2 (.f64 (.f64 a a) (.f64 x x)))
(.f64 1/2 (.f64 a (.f64 a (.f64 x x))))
(.f64 a (.f64 (.f64 a (.f64 x x)) 1/2))
(.f64 x (.f64 x (.f64 a (.f64 a 1/2))))
(.f64 a (.f64 a (.f64 x (.f64 x 1/2))))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (.f64 a x))
(.f64 x (fma.f64 1/2 (.f64 a (*.f64 a x)) a))
(.f64 x (fma.f64 x (.f64 a (*.f64 a 1/2)) a))
(.f64 a (.f64 (fma.f64 a (*.f64 x 1/2) 1) x))
(.f64 (.f64 a x) (fma.f64 a (*.f64 x 1/2) 1))
(.f64 a (.f64 x (fma.f64 a (*.f64 x 1/2) 1)))
(.f64 a (fma.f64 (.f64 x x) (*.f64 a 1/2) x))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (.f64 a x))
(.f64 x (fma.f64 1/2 (.f64 a (*.f64 a x)) a))
(.f64 x (fma.f64 x (.f64 a (*.f64 a 1/2)) a))
(.f64 a (.f64 (fma.f64 a (*.f64 x 1/2) 1) x))
(.f64 (.f64 a x) (fma.f64 a (*.f64 x 1/2) 1))
(.f64 a (.f64 x (fma.f64 a (*.f64 x 1/2) 1)))
(.f64 a (fma.f64 (.f64 x x) (*.f64 a 1/2) x))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (.f64 a x))
(.f64 x (fma.f64 1/2 (.f64 a (*.f64 a x)) a))
(.f64 x (fma.f64 x (.f64 a (*.f64 a 1/2)) a))
(.f64 a (.f64 (fma.f64 a (*.f64 x 1/2) 1) x))
(.f64 (.f64 a x) (fma.f64 a (*.f64 x 1/2) 1))
(.f64 a (.f64 x (fma.f64 a (*.f64 x 1/2) 1)))
(.f64 a (fma.f64 (.f64 x x) (*.f64 a 1/2) x))
(*.f64 (pow.f64 a 2) x)
(.f64 x (.f64 a a))
(.f64 a (.f64 a x))
(*.f64 (pow.f64 a 2) x)
(.f64 x (.f64 a a))
(.f64 a (.f64 a x))
(*.f64 (pow.f64 a 2) x)
(.f64 x (.f64 a a))
(.f64 a (.f64 a x))
(*.f64 (pow.f64 a 2) x)
(.f64 x (.f64 a a))
(.f64 a (.f64 a x))
(*.f64 (pow.f64 a 2) x)
(.f64 x (.f64 a a))
(.f64 a (.f64 a x))
(*.f64 (pow.f64 a 2) x)
(.f64 x (.f64 a a))
(.f64 a (.f64 a x))
(*.f64 (pow.f64 a 2) x)
(.f64 x (.f64 a a))
(.f64 a (.f64 a x))
(*.f64 (pow.f64 a 2) x)
(.f64 x (.f64 a a))
(.f64 a (.f64 a x))
(*.f64 (pow.f64 a 2) x)
(.f64 x (.f64 a a))
(.f64 a (.f64 a x))
(*.f64 (pow.f64 a 2) x)
(.f64 x (.f64 a a))
(.f64 a (.f64 a x))
(*.f64 (pow.f64 a 2) x)
(.f64 x (.f64 a a))
(.f64 a (.f64 a x))
(*.f64 (pow.f64 a 2) x)
(.f64 x (.f64 a a))
(.f64 a (.f64 a x))
(*.f64 (pow.f64 a 2) x)
(.f64 x (.f64 a a))
(.f64 a (.f64 a x))
(*.f64 (pow.f64 a 2) x)
(.f64 x (.f64 a a))
(.f64 a (.f64 a x))
(*.f64 (pow.f64 a 2) x)
(.f64 x (.f64 a a))
(.f64 a (.f64 a x))
(*.f64 (pow.f64 a 2) x)
(.f64 x (.f64 a a))
(.f64 a (.f64 a x))
(*.f64 (pow.f64 a 2) x)
(.f64 x (.f64 a a))
(.f64 a (.f64 a x))
(*.f64 (pow.f64 a 2) x)
(.f64 x (.f64 a a))
(.f64 a (.f64 a x))
(*.f64 (pow.f64 a 2) x)
(.f64 x (.f64 a a))
(.f64 a (.f64 a x))
(*.f64 (pow.f64 a 2) x)
(.f64 x (.f64 a a))
(.f64 a (.f64 a x))
(*.f64 (pow.f64 a 2) x)
(.f64 x (.f64 a a))
(.f64 a (.f64 a x))
(*.f64 (pow.f64 a 2) x)
(.f64 x (.f64 a a))
(.f64 a (.f64 a x))
(*.f64 (pow.f64 a 2) x)
(.f64 x (.f64 a a))
(.f64 a (.f64 a x))
(*.f64 (pow.f64 a 2) x)
(.f64 x (.f64 a a))
(.f64 a (.f64 a x))
a
(+.f64 a (.f64 1/2 (.f64 (pow.f64 a 2) x)))
(+.f64 a (.f64 1/2 (.f64 x (*.f64 a a))))
(fma.f64 1/2 (.f64 a (.f64 a x)) a)
(fma.f64 x (.f64 a (.f64 a 1/2)) a)
(.f64 a (fma.f64 a (.f64 x 1/2) 1))
(+.f64 a (.f64 1/2 (.f64 (pow.f64 a 2) x)))
(+.f64 a (.f64 1/2 (.f64 x (*.f64 a a))))
(fma.f64 1/2 (.f64 a (.f64 a x)) a)
(fma.f64 x (.f64 a (.f64 a 1/2)) a)
(.f64 a (fma.f64 a (.f64 x 1/2) 1))
(+.f64 a (.f64 1/2 (.f64 (pow.f64 a 2) x)))
(+.f64 a (.f64 1/2 (.f64 x (*.f64 a a))))
(fma.f64 1/2 (.f64 a (.f64 a x)) a)
(fma.f64 x (.f64 a (.f64 a 1/2)) a)
(.f64 a (fma.f64 a (.f64 x 1/2) 1))
(.f64 1/2 (.f64 (pow.f64 a 2) x))
(.f64 1/2 (.f64 x (*.f64 a a)))
(.f64 x (.f64 1/2 (*.f64 a a)))
(.f64 a (.f64 a (*.f64 x 1/2)))
(.f64 x (.f64 a (*.f64 a 1/2)))
(+.f64 a (.f64 1/2 (.f64 (pow.f64 a 2) x)))
(+.f64 a (.f64 1/2 (.f64 x (*.f64 a a))))
(fma.f64 1/2 (.f64 a (.f64 a x)) a)
(fma.f64 x (.f64 a (.f64 a 1/2)) a)
(.f64 a (fma.f64 a (.f64 x 1/2) 1))
(+.f64 a (.f64 1/2 (.f64 (pow.f64 a 2) x)))
(+.f64 a (.f64 1/2 (.f64 x (*.f64 a a))))
(fma.f64 1/2 (.f64 a (.f64 a x)) a)
(fma.f64 x (.f64 a (.f64 a 1/2)) a)
(.f64 a (fma.f64 a (.f64 x 1/2) 1))
(+.f64 a (.f64 1/2 (.f64 (pow.f64 a 2) x)))
(+.f64 a (.f64 1/2 (.f64 x (*.f64 a a))))
(fma.f64 1/2 (.f64 a (.f64 a x)) a)
(fma.f64 x (.f64 a (.f64 a 1/2)) a)
(.f64 a (fma.f64 a (.f64 x 1/2) 1))
(.f64 1/2 (.f64 (pow.f64 a 2) x))
(.f64 1/2 (.f64 x (*.f64 a a)))
(.f64 x (.f64 1/2 (*.f64 a a)))
(.f64 a (.f64 a (*.f64 x 1/2)))
(.f64 x (.f64 a (*.f64 a 1/2)))
(+.f64 a (.f64 1/2 (.f64 (pow.f64 a 2) x)))
(+.f64 a (.f64 1/2 (.f64 x (*.f64 a a))))
(fma.f64 1/2 (.f64 a (.f64 a x)) a)
(fma.f64 x (.f64 a (.f64 a 1/2)) a)
(.f64 a (fma.f64 a (.f64 x 1/2) 1))
(+.f64 a (.f64 1/2 (.f64 (pow.f64 a 2) x)))
(+.f64 a (.f64 1/2 (.f64 x (*.f64 a a))))
(fma.f64 1/2 (.f64 a (.f64 a x)) a)
(fma.f64 x (.f64 a (.f64 a 1/2)) a)
(.f64 a (fma.f64 a (.f64 x 1/2) 1))
(+.f64 a (.f64 1/2 (.f64 (pow.f64 a 2) x)))
(+.f64 a (.f64 1/2 (.f64 x (*.f64 a a))))
(fma.f64 1/2 (.f64 a (.f64 a x)) a)
(fma.f64 x (.f64 a (.f64 a 1/2)) a)
(.f64 a (fma.f64 a (.f64 x 1/2) 1))
a
(+.f64 a (.f64 1/2 (.f64 (pow.f64 a 2) x)))
(+.f64 a (.f64 1/2 (.f64 x (*.f64 a a))))
(fma.f64 1/2 (.f64 a (.f64 a x)) a)
(fma.f64 x (.f64 a (.f64 a 1/2)) a)
(.f64 a (fma.f64 a (.f64 x 1/2) 1))
(+.f64 a (.f64 1/2 (.f64 (pow.f64 a 2) x)))
(+.f64 a (.f64 1/2 (.f64 x (*.f64 a a))))
(fma.f64 1/2 (.f64 a (.f64 a x)) a)
(fma.f64 x (.f64 a (.f64 a 1/2)) a)
(.f64 a (fma.f64 a (.f64 x 1/2) 1))
(+.f64 a (.f64 1/2 (.f64 (pow.f64 a 2) x)))
(+.f64 a (.f64 1/2 (.f64 x (*.f64 a a))))
(fma.f64 1/2 (.f64 a (.f64 a x)) a)
(fma.f64 x (.f64 a (.f64 a 1/2)) a)
(.f64 a (fma.f64 a (.f64 x 1/2) 1))
(.f64 1/2 (.f64 (pow.f64 a 2) x))
(.f64 1/2 (.f64 x (*.f64 a a)))
(.f64 x (.f64 1/2 (*.f64 a a)))
(.f64 a (.f64 a (*.f64 x 1/2)))
(.f64 x (.f64 a (*.f64 a 1/2)))
(+.f64 a (.f64 1/2 (.f64 (pow.f64 a 2) x)))
(+.f64 a (.f64 1/2 (.f64 x (*.f64 a a))))
(fma.f64 1/2 (.f64 a (.f64 a x)) a)
(fma.f64 x (.f64 a (.f64 a 1/2)) a)
(.f64 a (fma.f64 a (.f64 x 1/2) 1))
(+.f64 a (.f64 1/2 (.f64 (pow.f64 a 2) x)))
(+.f64 a (.f64 1/2 (.f64 x (*.f64 a a))))
(fma.f64 1/2 (.f64 a (.f64 a x)) a)
(fma.f64 x (.f64 a (.f64 a 1/2)) a)
(.f64 a (fma.f64 a (.f64 x 1/2) 1))
(+.f64 a (.f64 1/2 (.f64 (pow.f64 a 2) x)))
(+.f64 a (.f64 1/2 (.f64 x (*.f64 a a))))
(fma.f64 1/2 (.f64 a (.f64 a x)) a)
(fma.f64 x (.f64 a (.f64 a 1/2)) a)
(.f64 a (fma.f64 a (.f64 x 1/2) 1))
(.f64 1/2 (.f64 (pow.f64 a 2) x))
(.f64 1/2 (.f64 x (*.f64 a a)))
(.f64 x (.f64 1/2 (*.f64 a a)))
(.f64 a (.f64 a (*.f64 x 1/2)))
(.f64 x (.f64 a (*.f64 a 1/2)))
(+.f64 a (.f64 1/2 (.f64 (pow.f64 a 2) x)))
(+.f64 a (.f64 1/2 (.f64 x (*.f64 a a))))
(fma.f64 1/2 (.f64 a (.f64 a x)) a)
(fma.f64 x (.f64 a (.f64 a 1/2)) a)
(.f64 a (fma.f64 a (.f64 x 1/2) 1))
(+.f64 a (.f64 1/2 (.f64 (pow.f64 a 2) x)))
(+.f64 a (.f64 1/2 (.f64 x (*.f64 a a))))
(fma.f64 1/2 (.f64 a (.f64 a x)) a)
(fma.f64 x (.f64 a (.f64 a 1/2)) a)
(.f64 a (fma.f64 a (.f64 x 1/2) 1))
(+.f64 a (.f64 1/2 (.f64 (pow.f64 a 2) x)))
(+.f64 a (.f64 1/2 (.f64 x (*.f64 a a))))
(fma.f64 1/2 (.f64 a (.f64 a x)) a)
(fma.f64 x (.f64 a (.f64 a 1/2)) a)
(.f64 a (fma.f64 a (.f64 x 1/2) 1))

eval51.0ms (1.7%)

Compiler: Compiled 3152 to 1456 computations (53.8% saved)

prune25.0ms (0.8%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	192	1	193
Fresh	0	0	0
Picked	0	1	1
Done	1	3	4
Total	193	5	198

Error

Counts

198 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	20.9b	(*.f64 a x)
✓	21.4b	(.f64 x (+.f64 a (.f64 1/2 (.f64 a (.f64 a x)))))
✓	37.6b	(pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) 2)
▶	21.4b	(.f64 x (.f64 a (fma.f64 a (*.f64 x 1/2) 1)))
✓	0.0b	(expm1.f64 (*.f64 a x))

Compiler

Compiled 45 to 30 computations (33.3% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.2b	(.f64 x (.f64 a (fma.f64 a (*.f64 x 1/2) 1)))
	0.0b	(.f64 a (fma.f64 a (.f64 x 1/2) 1))
✓	0.0b	(.f64 a (fma.f64 a (.f64 x 1/2) 1))
✓	1.2b	(.f64 x (.f64 a (fma.f64 a (*.f64 x 1/2) 1)))

series10.0ms (0.3%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
3.0ms	a	@	0	(.f64 x (.f64 a (fma.f64 a (*.f64 x 1/2) 1)))
1.0ms	a	@	-inf	(.f64 x (.f64 a (fma.f64 a (*.f64 x 1/2) 1)))
1.0ms	x	@	0	(.f64 x (.f64 a (fma.f64 a (*.f64 x 1/2) 1)))
1.0ms	x	@	-inf	(.f64 x (.f64 a (fma.f64 a (*.f64 x 1/2) 1)))
1.0ms	x	@	inf	(.f64 x (.f64 a (fma.f64 a (*.f64 x 1/2) 1)))

rewrite50.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

811×	`pow1_binary64`
745×	`add-log-exp_binary64`
745×	`log1p-expm1-u_binary64`
745×	`expm1-log1p-u_binary64`
729×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	25
1	175	25
2	2011	25

Stop Event

1×	node limit

Counts

2 → 30

Calls

Call 1

Inputs
(.f64 x (.f64 a (fma.f64 a (*.f64 x 1/2) 1)))
(.f64 a (fma.f64 a (.f64 x 1/2) 1))

Outputs

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

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

simplify197.0ms (6.5%)

Algorithm

1×	egg-herbie

Rules

1251×	`unswap-sqr_binary64`
823×	`fma-def_binary64`
764×	`sqr-pow_binary64`
358×	`*-commutative_binary64`
350×	`cube-prod_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	642
1	33	606
2	73	552
3	206	552
4	995	552
5	2023	552
6	2314	552
7	2637	552
8	2890	552
9	3059	552
10	3254	552
11	3418	552
12	3607	552
13	3822	552
14	4052	552
15	4296	552
16	4561	552
17	4840	552
18	5140	552
19	5454	552
20	5524	552
21	7472	552
22	7759	552
23	7981	552

Stop Event

1×	node limit

Counts

78 → 40

Calls

Call 1

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

Outputs
(*.f64 a x)
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (.f64 a x))
(.f64 x (fma.f64 1/2 (.f64 a (*.f64 a x)) a))
(.f64 x (fma.f64 x (.f64 a (*.f64 a 1/2)) a))
(.f64 a (.f64 (fma.f64 a (*.f64 x 1/2) 1) x))
(.f64 (.f64 a x) (fma.f64 a (*.f64 x 1/2) 1))
(.f64 a (.f64 x (fma.f64 a (*.f64 x 1/2) 1)))
(.f64 a (fma.f64 (.f64 x x) (*.f64 a 1/2) x))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (.f64 a x))
(.f64 x (fma.f64 1/2 (.f64 a (*.f64 a x)) a))
(.f64 x (fma.f64 x (.f64 a (*.f64 a 1/2)) a))
(.f64 a (.f64 (fma.f64 a (*.f64 x 1/2) 1) x))
(.f64 (.f64 a x) (fma.f64 a (*.f64 x 1/2) 1))
(.f64 a (.f64 x (fma.f64 a (*.f64 x 1/2) 1)))
(.f64 a (fma.f64 (.f64 x x) (*.f64 a 1/2) x))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (.f64 a x))
(.f64 x (fma.f64 1/2 (.f64 a (*.f64 a x)) a))
(.f64 x (fma.f64 x (.f64 a (*.f64 a 1/2)) a))
(.f64 a (.f64 (fma.f64 a (*.f64 x 1/2) 1) x))
(.f64 (.f64 a x) (fma.f64 a (*.f64 x 1/2) 1))
(.f64 a (.f64 x (fma.f64 a (*.f64 x 1/2) 1)))
(.f64 a (fma.f64 (.f64 x x) (*.f64 a 1/2) x))
(.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2)))
(.f64 1/2 (.f64 (.f64 a a) (.f64 x x)))
(.f64 1/2 (.f64 a (.f64 a (.f64 x x))))
(.f64 a (.f64 (.f64 a (.f64 x x)) 1/2))
(.f64 x (.f64 x (.f64 a (.f64 a 1/2))))
(.f64 a (.f64 a (.f64 x (.f64 x 1/2))))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (.f64 a x))
(.f64 x (fma.f64 1/2 (.f64 a (*.f64 a x)) a))
(.f64 x (fma.f64 x (.f64 a (*.f64 a 1/2)) a))
(.f64 a (.f64 (fma.f64 a (*.f64 x 1/2) 1) x))
(.f64 (.f64 a x) (fma.f64 a (*.f64 x 1/2) 1))
(.f64 a (.f64 x (fma.f64 a (*.f64 x 1/2) 1)))
(.f64 a (fma.f64 (.f64 x x) (*.f64 a 1/2) x))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (.f64 a x))
(.f64 x (fma.f64 1/2 (.f64 a (*.f64 a x)) a))
(.f64 x (fma.f64 x (.f64 a (*.f64 a 1/2)) a))
(.f64 a (.f64 (fma.f64 a (*.f64 x 1/2) 1) x))
(.f64 (.f64 a x) (fma.f64 a (*.f64 x 1/2) 1))
(.f64 a (.f64 x (fma.f64 a (*.f64 x 1/2) 1)))
(.f64 a (fma.f64 (.f64 x x) (*.f64 a 1/2) x))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (.f64 a x))
(.f64 x (fma.f64 1/2 (.f64 a (*.f64 a x)) a))
(.f64 x (fma.f64 x (.f64 a (*.f64 a 1/2)) a))
(.f64 a (.f64 (fma.f64 a (*.f64 x 1/2) 1) x))
(.f64 (.f64 a x) (fma.f64 a (*.f64 x 1/2) 1))
(.f64 a (.f64 x (fma.f64 a (*.f64 x 1/2) 1)))
(.f64 a (fma.f64 (.f64 x x) (*.f64 a 1/2) x))
(.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2)))
(.f64 1/2 (.f64 (.f64 a a) (.f64 x x)))
(.f64 1/2 (.f64 a (.f64 a (.f64 x x))))
(.f64 a (.f64 (.f64 a (.f64 x x)) 1/2))
(.f64 x (.f64 x (.f64 a (.f64 a 1/2))))
(.f64 a (.f64 a (.f64 x (.f64 x 1/2))))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (.f64 a x))
(.f64 x (fma.f64 1/2 (.f64 a (*.f64 a x)) a))
(.f64 x (fma.f64 x (.f64 a (*.f64 a 1/2)) a))
(.f64 a (.f64 (fma.f64 a (*.f64 x 1/2) 1) x))
(.f64 (.f64 a x) (fma.f64 a (*.f64 x 1/2) 1))
(.f64 a (.f64 x (fma.f64 a (*.f64 x 1/2) 1)))
(.f64 a (fma.f64 (.f64 x x) (*.f64 a 1/2) x))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (.f64 a x))
(.f64 x (fma.f64 1/2 (.f64 a (*.f64 a x)) a))
(.f64 x (fma.f64 x (.f64 a (*.f64 a 1/2)) a))
(.f64 a (.f64 (fma.f64 a (*.f64 x 1/2) 1) x))
(.f64 (.f64 a x) (fma.f64 a (*.f64 x 1/2) 1))
(.f64 a (.f64 x (fma.f64 a (*.f64 x 1/2) 1)))
(.f64 a (fma.f64 (.f64 x x) (*.f64 a 1/2) x))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (.f64 a x))
(.f64 x (fma.f64 1/2 (.f64 a (*.f64 a x)) a))
(.f64 x (fma.f64 x (.f64 a (*.f64 a 1/2)) a))
(.f64 a (.f64 (fma.f64 a (*.f64 x 1/2) 1) x))
(.f64 (.f64 a x) (fma.f64 a (*.f64 x 1/2) 1))
(.f64 a (.f64 x (fma.f64 a (*.f64 x 1/2) 1)))
(.f64 a (fma.f64 (.f64 x x) (*.f64 a 1/2) x))
(*.f64 a x)
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (.f64 a x))
(.f64 x (fma.f64 1/2 (.f64 a (*.f64 a x)) a))
(.f64 x (fma.f64 x (.f64 a (*.f64 a 1/2)) a))
(.f64 a (.f64 (fma.f64 a (*.f64 x 1/2) 1) x))
(.f64 (.f64 a x) (fma.f64 a (*.f64 x 1/2) 1))
(.f64 a (.f64 x (fma.f64 a (*.f64 x 1/2) 1)))
(.f64 a (fma.f64 (.f64 x x) (*.f64 a 1/2) x))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (.f64 a x))
(.f64 x (fma.f64 1/2 (.f64 a (*.f64 a x)) a))
(.f64 x (fma.f64 x (.f64 a (*.f64 a 1/2)) a))
(.f64 a (.f64 (fma.f64 a (*.f64 x 1/2) 1) x))
(.f64 (.f64 a x) (fma.f64 a (*.f64 x 1/2) 1))
(.f64 a (.f64 x (fma.f64 a (*.f64 x 1/2) 1)))
(.f64 a (fma.f64 (.f64 x x) (*.f64 a 1/2) x))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (.f64 a x))
(.f64 x (fma.f64 1/2 (.f64 a (*.f64 a x)) a))
(.f64 x (fma.f64 x (.f64 a (*.f64 a 1/2)) a))
(.f64 a (.f64 (fma.f64 a (*.f64 x 1/2) 1) x))
(.f64 (.f64 a x) (fma.f64 a (*.f64 x 1/2) 1))
(.f64 a (.f64 x (fma.f64 a (*.f64 x 1/2) 1)))
(.f64 a (fma.f64 (.f64 x x) (*.f64 a 1/2) x))
(.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2)))
(.f64 1/2 (.f64 (.f64 a a) (.f64 x x)))
(.f64 1/2 (.f64 a (.f64 a (.f64 x x))))
(.f64 a (.f64 (.f64 a (.f64 x x)) 1/2))
(.f64 x (.f64 x (.f64 a (.f64 a 1/2))))
(.f64 a (.f64 a (.f64 x (.f64 x 1/2))))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (.f64 a x))
(.f64 x (fma.f64 1/2 (.f64 a (*.f64 a x)) a))
(.f64 x (fma.f64 x (.f64 a (*.f64 a 1/2)) a))
(.f64 a (.f64 (fma.f64 a (*.f64 x 1/2) 1) x))
(.f64 (.f64 a x) (fma.f64 a (*.f64 x 1/2) 1))
(.f64 a (.f64 x (fma.f64 a (*.f64 x 1/2) 1)))
(.f64 a (fma.f64 (.f64 x x) (*.f64 a 1/2) x))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (.f64 a x))
(.f64 x (fma.f64 1/2 (.f64 a (*.f64 a x)) a))
(.f64 x (fma.f64 x (.f64 a (*.f64 a 1/2)) a))
(.f64 a (.f64 (fma.f64 a (*.f64 x 1/2) 1) x))
(.f64 (.f64 a x) (fma.f64 a (*.f64 x 1/2) 1))
(.f64 a (.f64 x (fma.f64 a (*.f64 x 1/2) 1)))
(.f64 a (fma.f64 (.f64 x x) (*.f64 a 1/2) x))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (.f64 a x))
(.f64 x (fma.f64 1/2 (.f64 a (*.f64 a x)) a))
(.f64 x (fma.f64 x (.f64 a (*.f64 a 1/2)) a))
(.f64 a (.f64 (fma.f64 a (*.f64 x 1/2) 1) x))
(.f64 (.f64 a x) (fma.f64 a (*.f64 x 1/2) 1))
(.f64 a (.f64 x (fma.f64 a (*.f64 x 1/2) 1)))
(.f64 a (fma.f64 (.f64 x x) (*.f64 a 1/2) x))
(.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2)))
(.f64 1/2 (.f64 (.f64 a a) (.f64 x x)))
(.f64 1/2 (.f64 a (.f64 a (.f64 x x))))
(.f64 a (.f64 (.f64 a (.f64 x x)) 1/2))
(.f64 x (.f64 x (.f64 a (.f64 a 1/2))))
(.f64 a (.f64 a (.f64 x (.f64 x 1/2))))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (.f64 a x))
(.f64 x (fma.f64 1/2 (.f64 a (*.f64 a x)) a))
(.f64 x (fma.f64 x (.f64 a (*.f64 a 1/2)) a))
(.f64 a (.f64 (fma.f64 a (*.f64 x 1/2) 1) x))
(.f64 (.f64 a x) (fma.f64 a (*.f64 x 1/2) 1))
(.f64 a (.f64 x (fma.f64 a (*.f64 x 1/2) 1)))
(.f64 a (fma.f64 (.f64 x x) (*.f64 a 1/2) x))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (.f64 a x))
(.f64 x (fma.f64 1/2 (.f64 a (*.f64 a x)) a))
(.f64 x (fma.f64 x (.f64 a (*.f64 a 1/2)) a))
(.f64 a (.f64 (fma.f64 a (*.f64 x 1/2) 1) x))
(.f64 (.f64 a x) (fma.f64 a (*.f64 x 1/2) 1))
(.f64 a (.f64 x (fma.f64 a (*.f64 x 1/2) 1)))
(.f64 a (fma.f64 (.f64 x x) (*.f64 a 1/2) x))
(+.f64 (.f64 1/2 (.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 x x)) (.f64 a x))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 x x))) (.f64 a x))
(.f64 x (fma.f64 1/2 (.f64 a (*.f64 a x)) a))
(.f64 x (fma.f64 x (.f64 a (*.f64 a 1/2)) a))
(.f64 a (.f64 (fma.f64 a (*.f64 x 1/2) 1) x))
(.f64 (.f64 a x) (fma.f64 a (*.f64 x 1/2) 1))
(.f64 a (.f64 x (fma.f64 a (*.f64 x 1/2) 1)))
(.f64 a (fma.f64 (.f64 x x) (*.f64 a 1/2) x))
a
(+.f64 a (.f64 1/2 (.f64 (pow.f64 a 2) x)))
(+.f64 a (.f64 1/2 (.f64 x (*.f64 a a))))
(fma.f64 1/2 (.f64 a (.f64 a x)) a)
(fma.f64 x (.f64 a (.f64 a 1/2)) a)
(.f64 a (fma.f64 a (.f64 x 1/2) 1))
(+.f64 a (.f64 1/2 (.f64 (pow.f64 a 2) x)))
(+.f64 a (.f64 1/2 (.f64 x (*.f64 a a))))
(fma.f64 1/2 (.f64 a (.f64 a x)) a)
(fma.f64 x (.f64 a (.f64 a 1/2)) a)
(.f64 a (fma.f64 a (.f64 x 1/2) 1))
(+.f64 a (.f64 1/2 (.f64 (pow.f64 a 2) x)))
(+.f64 a (.f64 1/2 (.f64 x (*.f64 a a))))
(fma.f64 1/2 (.f64 a (.f64 a x)) a)
(fma.f64 x (.f64 a (.f64 a 1/2)) a)
(.f64 a (fma.f64 a (.f64 x 1/2) 1))
(.f64 1/2 (.f64 (pow.f64 a 2) x))
(.f64 1/2 (.f64 x (*.f64 a a)))
(.f64 x (.f64 1/2 (*.f64 a a)))
(.f64 a (.f64 a (*.f64 x 1/2)))
(.f64 x (.f64 a (*.f64 a 1/2)))
(+.f64 a (.f64 1/2 (.f64 (pow.f64 a 2) x)))
(+.f64 a (.f64 1/2 (.f64 x (*.f64 a a))))
(fma.f64 1/2 (.f64 a (.f64 a x)) a)
(fma.f64 x (.f64 a (.f64 a 1/2)) a)
(.f64 a (fma.f64 a (.f64 x 1/2) 1))
(+.f64 a (.f64 1/2 (.f64 (pow.f64 a 2) x)))
(+.f64 a (.f64 1/2 (.f64 x (*.f64 a a))))
(fma.f64 1/2 (.f64 a (.f64 a x)) a)
(fma.f64 x (.f64 a (.f64 a 1/2)) a)
(.f64 a (fma.f64 a (.f64 x 1/2) 1))
(+.f64 a (.f64 1/2 (.f64 (pow.f64 a 2) x)))
(+.f64 a (.f64 1/2 (.f64 x (*.f64 a a))))
(fma.f64 1/2 (.f64 a (.f64 a x)) a)
(fma.f64 x (.f64 a (.f64 a 1/2)) a)
(.f64 a (fma.f64 a (.f64 x 1/2) 1))
(.f64 1/2 (.f64 (pow.f64 a 2) x))
(.f64 1/2 (.f64 x (*.f64 a a)))
(.f64 x (.f64 1/2 (*.f64 a a)))
(.f64 a (.f64 a (*.f64 x 1/2)))
(.f64 x (.f64 a (*.f64 a 1/2)))
(+.f64 a (.f64 1/2 (.f64 (pow.f64 a 2) x)))
(+.f64 a (.f64 1/2 (.f64 x (*.f64 a a))))
(fma.f64 1/2 (.f64 a (.f64 a x)) a)
(fma.f64 x (.f64 a (.f64 a 1/2)) a)
(.f64 a (fma.f64 a (.f64 x 1/2) 1))
(+.f64 a (.f64 1/2 (.f64 (pow.f64 a 2) x)))
(+.f64 a (.f64 1/2 (.f64 x (*.f64 a a))))
(fma.f64 1/2 (.f64 a (.f64 a x)) a)
(fma.f64 x (.f64 a (.f64 a 1/2)) a)
(.f64 a (fma.f64 a (.f64 x 1/2) 1))
(+.f64 a (.f64 1/2 (.f64 (pow.f64 a 2) x)))
(+.f64 a (.f64 1/2 (.f64 x (*.f64 a a))))
(fma.f64 1/2 (.f64 a (.f64 a x)) a)
(fma.f64 x (.f64 a (.f64 a 1/2)) a)
(.f64 a (fma.f64 a (.f64 x 1/2) 1))
a
(+.f64 a (.f64 1/2 (.f64 (pow.f64 a 2) x)))
(+.f64 a (.f64 1/2 (.f64 x (*.f64 a a))))
(fma.f64 1/2 (.f64 a (.f64 a x)) a)
(fma.f64 x (.f64 a (.f64 a 1/2)) a)
(.f64 a (fma.f64 a (.f64 x 1/2) 1))
(+.f64 a (.f64 1/2 (.f64 (pow.f64 a 2) x)))
(+.f64 a (.f64 1/2 (.f64 x (*.f64 a a))))
(fma.f64 1/2 (.f64 a (.f64 a x)) a)
(fma.f64 x (.f64 a (.f64 a 1/2)) a)
(.f64 a (fma.f64 a (.f64 x 1/2) 1))
(+.f64 a (.f64 1/2 (.f64 (pow.f64 a 2) x)))
(+.f64 a (.f64 1/2 (.f64 x (*.f64 a a))))
(fma.f64 1/2 (.f64 a (.f64 a x)) a)
(fma.f64 x (.f64 a (.f64 a 1/2)) a)
(.f64 a (fma.f64 a (.f64 x 1/2) 1))
(.f64 1/2 (.f64 (pow.f64 a 2) x))
(.f64 1/2 (.f64 x (*.f64 a a)))
(.f64 x (.f64 1/2 (*.f64 a a)))
(.f64 a (.f64 a (*.f64 x 1/2)))
(.f64 x (.f64 a (*.f64 a 1/2)))
(+.f64 a (.f64 1/2 (.f64 (pow.f64 a 2) x)))
(+.f64 a (.f64 1/2 (.f64 x (*.f64 a a))))
(fma.f64 1/2 (.f64 a (.f64 a x)) a)
(fma.f64 x (.f64 a (.f64 a 1/2)) a)
(.f64 a (fma.f64 a (.f64 x 1/2) 1))
(+.f64 a (.f64 1/2 (.f64 (pow.f64 a 2) x)))
(+.f64 a (.f64 1/2 (.f64 x (*.f64 a a))))
(fma.f64 1/2 (.f64 a (.f64 a x)) a)
(fma.f64 x (.f64 a (.f64 a 1/2)) a)
(.f64 a (fma.f64 a (.f64 x 1/2) 1))
(+.f64 a (.f64 1/2 (.f64 (pow.f64 a 2) x)))
(+.f64 a (.f64 1/2 (.f64 x (*.f64 a a))))
(fma.f64 1/2 (.f64 a (.f64 a x)) a)
(fma.f64 x (.f64 a (.f64 a 1/2)) a)
(.f64 a (fma.f64 a (.f64 x 1/2) 1))
(.f64 1/2 (.f64 (pow.f64 a 2) x))
(.f64 1/2 (.f64 x (*.f64 a a)))
(.f64 x (.f64 1/2 (*.f64 a a)))
(.f64 a (.f64 a (*.f64 x 1/2)))
(.f64 x (.f64 a (*.f64 a 1/2)))
(+.f64 a (.f64 1/2 (.f64 (pow.f64 a 2) x)))
(+.f64 a (.f64 1/2 (.f64 x (*.f64 a a))))
(fma.f64 1/2 (.f64 a (.f64 a x)) a)
(fma.f64 x (.f64 a (.f64 a 1/2)) a)
(.f64 a (fma.f64 a (.f64 x 1/2) 1))
(+.f64 a (.f64 1/2 (.f64 (pow.f64 a 2) x)))
(+.f64 a (.f64 1/2 (.f64 x (*.f64 a a))))
(fma.f64 1/2 (.f64 a (.f64 a x)) a)
(fma.f64 x (.f64 a (.f64 a 1/2)) a)
(.f64 a (fma.f64 a (.f64 x 1/2) 1))
(+.f64 a (.f64 1/2 (.f64 (pow.f64 a 2) x)))
(+.f64 a (.f64 1/2 (.f64 x (*.f64 a a))))
(fma.f64 1/2 (.f64 a (.f64 a x)) a)
(fma.f64 x (.f64 a (.f64 a 1/2)) a)
(.f64 a (fma.f64 a (.f64 x 1/2) 1))

eval10.0ms (0.3%)

Compiler: Compiled 478 to 313 computations (34.5% saved)

prune7.0ms (0.2%)

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	40	0	40
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	40	5	45

Error

Counts

45 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	20.9b	(*.f64 a x)
✓	21.4b	(.f64 x (+.f64 a (.f64 1/2 (.f64 a (.f64 a x)))))
✓	37.6b	(pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) 2)
✓	21.4b	(.f64 x (.f64 a (fma.f64 a (*.f64 x 1/2) 1)))
✓	0.0b	(expm1.f64 (*.f64 a x))

Compiler

Compiled 45 to 30 computations (33.3% saved)

regimes24.0ms (0.8%)

Counts

7 → 1

Calls

Call 1

Inputs
(*.f64 a x)
(.f64 x (+.f64 a (.f64 1/2 (.f64 a (.f64 a x)))))
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(.f64 x (.f64 a (fma.f64 a (*.f64 x 1/2) 1)))
(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))
(pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) 2)

Outputs
(expm1.f64 (*.f64 a x))

Calls

5 calls:

5.0ms	(exp.f64 (*.f64 a x))
5.0ms	x
5.0ms	a
4.0ms	(*.f64 a x)
2.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)

Results

Error	Segments	Branch
0.0b	1	`a`
0.0b	1	`x`
0.0b	1	`(-.f64 (exp.f64 (*.f64 a x)) 1)`
0.0b	1	`(exp.f64 (*.f64 a x))`
0.0b	1	`(*.f64 a x)`

Compiler

Compiled 75 to 41 computations (45.3% saved)

regimes10.0ms (0.3%)

Accuracy

Total -0.9b remaining (-4.3%)

Threshold costs -0.9b (-4.3%)

Counts

2 → 1

Calls

Call 1

Inputs
(*.f64 a x)
(.f64 x (+.f64 a (.f64 1/2 (.f64 a (.f64 a x)))))

Outputs
(*.f64 a x)

Calls

3 calls:

3.0ms	x
3.0ms	a
3.0ms	(*.f64 a x)

Results

Error	Segments	Branch
20.9b	1	`a`
20.9b	1	`x`
20.9b	1	`(*.f64 a x)`

Compiler

Compiled 27 to 15 computations (44.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	10
1	6	10

Stop Event

1×

saturated

Calls

Call 1

Inputs
(expm1.f64 (*.f64 a x))
(*.f64 a x)

Outputs
(expm1.f64 (*.f64 a x))
(*.f64 a x)

end17.0ms (0.6%)

Stop Event

1×

done

Remove

(sort a x)

Compiler

Compiled 32 to 19 computations (40.6% saved)

Details

analyze27.0ms (0.9%)

sample1.8s (60.4%)

preprocess37.0ms (1.2%)

simplify39.0ms (1.3%)

eval1.0ms (0%)

prune1.0ms (0%)

localize3.0ms (0.1%)

series3.0ms (0.1%)

rewrite34.0ms (1.1%)

simplify47.0ms (1.5%)

eval8.0ms (0.2%)

prune6.0ms (0.2%)

localize5.0ms (0.2%)

series10.0ms (0.3%)

rewrite42.0ms (1.4%)

simplify45.0ms (1.5%)

localize6.0ms (0.2%)

series9.0ms (0.3%)

rewrite42.0ms (1.4%)

simplify57.0ms (1.9%)

localize2.0ms (0.1%)

eval55.0ms (1.8%)

prune24.0ms (0.8%)

localize6.0ms (0.2%)

series8.0ms (0.3%)

rewrite66.0ms (2.2%)

simplify212.0ms (6.9%)

eval51.0ms (1.7%)

prune25.0ms (0.8%)

localize7.0ms (0.2%)

series10.0ms (0.3%)

rewrite50.0ms (1.6%)

simplify197.0ms (6.5%)

eval10.0ms (0.3%)

prune7.0ms (0.2%)

regimes24.0ms (0.8%)

regimes10.0ms (0.3%)

simplify4.0ms (0.1%)

end17.0ms (0.6%)

Profiling