Details

analyze58.0ms (2.5%)

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
74.1%	3.1%	22.8%	13
74.1%	2.3%	23.5%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample2.0s (83.1%)

Results

730.0ms	1529×	body	2048	valid
562.0ms	1765×	body	1024	valid
274.0ms	3162×	body	128	valid
247.0ms	1143×	body	512	valid
127.0ms	657×	body	256	valid
12.0ms	138×	body	128	invalid

Compiler

Compiled 18 to 14 computations (22.2% saved)

preprocess41.0ms (1.7%)

Algorithm

2×	egg-herbie

Rules

736×	`unswap-sqr_binary64`
572×	`associate-l_binary64`
458×	`associate-r_binary64`
278×	`fma-def_binary64`
262×	`distribute-rgt-in_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 8 to 6 computations (25% saved)

simplify20.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

440×	`unswap-sqr_binary64`
329×	`associate-l_binary64`
275×	`associate-+l+_binary64`
252×	`associate-r_binary64`
201×	`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

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))

prune3.0ms (0.1%)

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

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

Compiler

Compiled 24 to 15 computations (37.5% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series6.0ms (0.3%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	a	@	0	(expm1.f64 (*.f64 a x))
1.0ms	x	@	0	(expm1.f64 (*.f64 a x))
1.0ms	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))

rewrite31.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

442×	`pow1_binary64`
405×	`add-log-exp_binary64`
405×	`log1p-expm1-u_binary64`
405×	`expm1-log1p-u_binary64`
395×	`add-exp-log_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 → 18

Calls

Call 1

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

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

Outputs

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

simplify36.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

850×	`distribute-lft-out_binary64`
815×	`fma-def_binary64`
308×	`*-commutative_binary64`
300×	`unswap-sqr_binary64`
172×	`associate-l_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	30	284
1	87	284
2	242	278
3	1018	262
4	3128	248
5	4836	248

Stop Event

1×	node limit

Counts

42 → 27

Calls

Call 1

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

prune12.0ms (0.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	26	1	27
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	26	2	28

Error

Counts

28 → 2

Alt Table

Status	Error	Program
▶	39.3b	(pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) 2)
✓	0.0b	(expm1.f64 (*.f64 a x))

Compiler

Compiled 325 to 155 computations (52.3% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(expm1.f64 (*.f64 a x))
✓	0.1b	(pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) 2)
✓	9.3b	(sqrt.f64 (expm1.f64 (*.f64 a x)))

series33.0ms (1.4%)

Counts

2 → 32

Calls

12 calls:

Time	Variable		Point	Expression
9.0ms	x	@	0	(pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) 2)
6.0ms	a	@	0	(pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) 2)
5.0ms	a	@	0	(sqrt.f64 (expm1.f64 (*.f64 a x)))
3.0ms	x	@	0	(sqrt.f64 (expm1.f64 (*.f64 a x)))
2.0ms	x	@	-inf	(pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) 2)

rewrite37.0ms (1.6%)

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 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 log1p.f64 (expm1.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 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 log1p.f64 (expm1.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 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 log1p.f64 (expm1.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 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 log1p.f64 (expm1.f64 (expm1.f64 (*.f64 a x))))))))

simplify28.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

440×	`unswap-sqr_binary64`
340×	`associate-l_binary64`
284×	`associate-r_binary64`
275×	`associate-+l+_binary64`
201×	`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

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))

prune25.0ms (1.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	69	2	71

Error

Counts

71 → 2

Alt Table

Status	Error	Program
✓	39.3b	(pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) 2)
✓	0.0b	(expm1.f64 (*.f64 a x))

Compiler

Compiled 854 to 389 computations (54.4% saved)

regimes21.0ms (0.9%)

Accuracy

Total 0.0b remaining (6.8%)

Threshold costs 0.0b (6.8%)

Counts

6 → 1

Compiler

Compiled 64 to 30 computations (53.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	6	6

Stop Event

1×

saturated

Calls

Call 1

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

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

end40.0ms (1.7%)

Stop Event

1×

done

Remove

(sort a x)

Compiler

Compiled 39 to 27 computations (30.8% saved)

Details

analyze58.0ms (2.5%)

sample2.0s (83.1%)

preprocess41.0ms (1.7%)

simplify20.0ms (0.8%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

series6.0ms (0.3%)

rewrite31.0ms (1.3%)

simplify36.0ms (1.5%)

prune12.0ms (0.5%)

localize5.0ms (0.2%)

series33.0ms (1.4%)

rewrite37.0ms (1.6%)

simplify28.0ms (1.2%)

prune25.0ms (1.1%)

regimes21.0ms (0.9%)

simplify2.0ms (0.1%)

end40.0ms (1.7%)

Profiling