Details

analyze605.0ms (3.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	49.9%	50.1%	0
0%	49.9%	50.1%	1
0%	49.9%	50.1%	2
0%	49.9%	50.1%	3
0%	49.9%	50.1%	4
0%	49.9%	50.1%	5
0%	49.9%	50.1%	6
0%	49.9%	50.1%	7
0%	49.9%	50.1%	8
0.4%	49.5%	50.1%	9
0.4%	48.9%	50.7%	10
0.6%	48.2%	51.2%	11
1.1%	47.3%	51.7%	12

Compiler

Compiled 34 to 24 computations (29.4% saved)

sample9.6s (56.3%)

Results

6.2s	4210×	body	2048	valid
2.0s	2434×	body	1024	valid
459.0ms	760×	body	512	valid
240.0ms	838×	body	256	valid
235.0ms	429×	body	1024	invalid
211.0ms	256×	body	2048	invalid
168.0ms	788×	body	256	invalid
71.0ms	204×	body	512	invalid
43.0ms	14×	body	4096	valid

preprocess48.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

604×	`associate-/l/_binary64`
556×	`distribute-rgt-in_binary64`
547×	`distribute-lft-in_binary64`
333×	`div-sub_binary64`
265×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	112
1	146	112
2	314	112
3	787	112
4	3423	112
0	3	3
1	3	3

Stop Event

1×	unsound
1×	node limit

Calls

Call 1

Inputs
0
1
2

Outputs
0
1
0
2

Call 2

Inputs
(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1)))
(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 b a) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 b eps)) 1) (-.f64 (exp.f64 (*.f64 a eps)) 1)))
(/.f64 (.f64 a (-.f64 (exp.f64 (.f64 (+.f64 eps b) a)) 1)) (.f64 (-.f64 (exp.f64 (.f64 eps a)) 1) (-.f64 (exp.f64 (*.f64 b a)) 1)))
(/.f64 (.f64 b (-.f64 (exp.f64 (.f64 (+.f64 a eps) b)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a b)) 1) (-.f64 (exp.f64 (*.f64 eps b)) 1)))

Outputs
(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1)))
(.f64 (/.f64 eps (expm1.f64 (.f64 eps a))) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps b))))
(.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (/.f64 (/.f64 eps (expm1.f64 (.f64 eps a))) (expm1.f64 (.f64 eps b))))
(.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))))
(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 b a) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 b eps)) 1) (-.f64 (exp.f64 (*.f64 a eps)) 1)))
(.f64 (/.f64 eps (expm1.f64 (.f64 eps a))) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps b))))
(.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (/.f64 (/.f64 eps (expm1.f64 (.f64 eps a))) (expm1.f64 (.f64 eps b))))
(.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))))
(/.f64 (.f64 a (-.f64 (exp.f64 (.f64 (+.f64 eps b) a)) 1)) (.f64 (-.f64 (exp.f64 (.f64 eps a)) 1) (-.f64 (exp.f64 (*.f64 b a)) 1)))
(.f64 (/.f64 a (expm1.f64 (.f64 eps a))) (/.f64 (expm1.f64 (.f64 a (+.f64 eps b))) (expm1.f64 (.f64 a b))))
(.f64 (/.f64 (expm1.f64 (.f64 a (+.f64 eps b))) (expm1.f64 (.f64 eps a))) (/.f64 a (expm1.f64 (.f64 a b))))
(/.f64 (.f64 a (expm1.f64 (.f64 a (+.f64 eps b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 a b))))
(.f64 a (/.f64 (expm1.f64 (.f64 a (+.f64 eps b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 a b)))))
(/.f64 (.f64 b (-.f64 (exp.f64 (.f64 (+.f64 a eps) b)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a b)) 1) (-.f64 (exp.f64 (*.f64 eps b)) 1)))
(/.f64 (.f64 b (expm1.f64 (.f64 b (+.f64 eps a)))) (.f64 (expm1.f64 (.f64 eps b)) (expm1.f64 (*.f64 a b))))
(.f64 (/.f64 b (expm1.f64 (.f64 a b))) (/.f64 (expm1.f64 (.f64 b (+.f64 eps a))) (expm1.f64 (.f64 eps b))))
(/.f64 (/.f64 (.f64 b (expm1.f64 (.f64 b (+.f64 eps a)))) (expm1.f64 (.f64 eps b))) (expm1.f64 (.f64 a b)))
(.f64 b (/.f64 (expm1.f64 (.f64 b (+.f64 eps a))) (.f64 (expm1.f64 (.f64 eps b)) (expm1.f64 (*.f64 a b)))))

Symmetry

(sort a b)

Compiler

Compiled 30 to 22 computations (26.7% saved)

simplify26.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

986×	`times-frac_binary64`
580×	`associate-/l*_binary64`
452×	`associate-l_binary64`
435×	`associate-r_binary64`
372×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	28
1	47	28
2	108	28
3	269	28
4	989	28

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1)))

Outputs
(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1)))
(.f64 (/.f64 eps (expm1.f64 (.f64 eps a))) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps b))))
(.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))) (/.f64 eps (expm1.f64 (.f64 eps b))))
(.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (/.f64 eps (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))))
(.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))))

eval1.0ms (0%)

Compiler: Compiled 45 to 28 computations (37.8% 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

41.2b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	41.2b	(.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))))

Compiler

Compiled 21 to 13 computations (38.1% saved)

localize42.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (*.f64 eps b))
✓	0.1b	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
✓	13.2b	(/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))))
✓	29.0b	(.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))))

Compiler

Compiled 77 to 13 computations (83.1% saved)

series37.0ms (0.2%)

Counts

4 → 132

Calls

33 calls:

Time	Variable		Point	Expression
4.0ms	eps	@	0	(.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))))
4.0ms	b	@	-inf	(.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))))
3.0ms	a	@	inf	(.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))))
2.0ms	eps	@	-inf	(.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))))
2.0ms	a	@	-inf	(.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))))

rewrite100.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

889×	`prod-diff_binary64`
838×	`log-prod_binary64`
289×	`fma-def_binary64`
269×	`expm1-udef_binary64`
269×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	73
1	294	73
2	4083	73

Stop Event

1×	node limit

Counts

4 → 119

Calls

Call 1

Inputs
(.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))))
(/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))))
(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
(expm1.f64 (*.f64 eps b))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 eps) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b)))))) (cbrt.f64 (pow.f64 (exp.f64 eps) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b)))))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 eps) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 eps) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 eps) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 eps (/.f64 (expm1.f64 (.f64 eps b)) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))) (.f64 (expm1.f64 (.f64 eps b)) (neg.f64 (expm1.f64 (.f64 eps a)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (expm1.f64 (.f64 eps a))) (expm1.f64 (.f64 eps b)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (expm1.f64 (.f64 eps b))) (expm1.f64 (.f64 eps a)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) 1) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (pow.f64 (cbrt.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b)))) 2)) (cbrt.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (sqrt.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))))) (sqrt.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (neg.f64 (expm1.f64 (.f64 eps (+.f64 a b)))) eps) (.f64 (expm1.f64 (.f64 eps b)) (neg.f64 (expm1.f64 (.f64 eps a)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))) eps) (expm1.f64 (.f64 eps b)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 eps (neg.f64 (expm1.f64 (.f64 eps (+.f64 a b))))) (.f64 (expm1.f64 (.f64 eps b)) (neg.f64 (expm1.f64 (.f64 eps a)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a)))) (expm1.f64 (.f64 eps b)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b)))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b)))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 eps) (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 eps 3) (pow.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b)))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b)))) 3) (pow.f64 eps 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b)))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b)))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b)))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b)))))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b)))))) (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b)))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (expm1.f64 (.f64 eps 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simplify182.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

881×	`times-frac_binary64`
420×	`cancel-sign-sub-inv_binary64`
280×	`associate-r_binary64`
278×	`fma-def_binary64`
218×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	297	5625
1	1024	5551
2	3928	5250

Stop Event

1×	node limit

Counts

251 → 208

Calls

Call 1

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

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

eval129.0ms (0.8%)

Compiler: Compiled 8714 to 3388 computations (61.1% saved)

prune173.0ms (1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	199	9	208
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	200	9	209

Error

0.4b

Counts

209 → 9

Alt Table

Click to see full alt table

Status	Error	Program
	51.8b	(.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 a (.f64 eps (expm1.f64 (*.f64 b eps))))))
▶	16.1b	(/.f64 (+.f64 a b) (*.f64 a b))
▶	34.1b	(/.f64 1 a)
	29.1b	(/.f64 (.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))) eps) (expm1.f64 (.f64 eps b)))
▶	55.3b	(+.f64 (/.f64 eps (-.f64 1 (exp.f64 (neg.f64 (.f64 a eps))))) (+.f64 (/.f64 1 b) (.f64 eps -1/2)))
	31.7b	(/.f64 1 b)
▶	57.8b	(.f64 eps (-.f64 (+.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1)) (/.f64 1 (.f64 eps b))) 1/2))
▶	48.8b	(.f64 eps (/.f64 1 (.f64 eps b)))
	36.7b	(.f64 eps (/.f64 (+.f64 a b) (.f64 a (*.f64 b eps))))

Compiler

Compiled 262 to 172 computations (34.4% saved)

localize7.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	16.0b	(/.f64 (+.f64 a b) (*.f64 a b))

Compiler

Compiled 18 to 6 computations (66.7% saved)

series7.0ms (0%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	a	@	0	(/.f64 (+.f64 a b) (*.f64 a b))
1.0ms	a	@	inf	(/.f64 (+.f64 a b) (*.f64 a b))
1.0ms	a	@	-inf	(/.f64 (+.f64 a b) (*.f64 a b))
1.0ms	b	@	-inf	(/.f64 (+.f64 a b) (*.f64 a b))
1.0ms	b	@	inf	(/.f64 (+.f64 a b) (*.f64 a b))

rewrite57.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

872×	`pow1_binary64`
816×	`add-log-exp_binary64`
816×	`log1p-expm1-u_binary64`
816×	`expm1-log1p-u_binary64`
799×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	136	10
2	2146	10

Stop Event

1×	node limit

Counts

1 → 38

Calls

Call 1

Inputs
(/.f64 (+.f64 a b) (*.f64 a b))

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

Outputs

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

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	204
1	10	204

Stop Event

1×

saturated

Counts

62 → 42

Calls

Call 1

Inputs
(/.f64 1 a)
(+.f64 (/.f64 1 b) (/.f64 1 a))
(+.f64 (/.f64 1 b) (/.f64 1 a))
(+.f64 (/.f64 1 b) (/.f64 1 a))
(/.f64 1 b)
(+.f64 (/.f64 1 a) (/.f64 1 b))
(+.f64 (/.f64 1 a) (/.f64 1 b))
(+.f64 (/.f64 1 a) (/.f64 1 b))
(/.f64 1 b)
(+.f64 (/.f64 1 a) (/.f64 1 b))
(+.f64 (/.f64 1 a) (/.f64 1 b))
(+.f64 (/.f64 1 a) (/.f64 1 b))
(/.f64 1 b)
(+.f64 (/.f64 1 a) (/.f64 1 b))
(+.f64 (/.f64 1 a) (/.f64 1 b))
(+.f64 (/.f64 1 a) (/.f64 1 b))
(/.f64 1 a)
(+.f64 (/.f64 1 b) (/.f64 1 a))
(+.f64 (/.f64 1 b) (/.f64 1 a))
(+.f64 (/.f64 1 b) (/.f64 1 a))
(/.f64 1 a)
(+.f64 (/.f64 1 b) (/.f64 1 a))
(+.f64 (/.f64 1 b) (/.f64 1 a))
(+.f64 (/.f64 1 b) (/.f64 1 a))

Outputs
(/.f64 1 a)
(+.f64 (/.f64 1 b) (/.f64 1 a))
(+.f64 (/.f64 1 a) (/.f64 1 b))
(+.f64 (/.f64 1 b) (/.f64 1 a))
(+.f64 (/.f64 1 a) (/.f64 1 b))
(+.f64 (/.f64 1 b) (/.f64 1 a))
(+.f64 (/.f64 1 a) (/.f64 1 b))
(/.f64 1 b)
(+.f64 (/.f64 1 a) (/.f64 1 b))
(+.f64 (/.f64 1 a) (/.f64 1 b))
(+.f64 (/.f64 1 a) (/.f64 1 b))
(/.f64 1 b)
(+.f64 (/.f64 1 a) (/.f64 1 b))
(+.f64 (/.f64 1 a) (/.f64 1 b))
(+.f64 (/.f64 1 a) (/.f64 1 b))
(/.f64 1 b)
(+.f64 (/.f64 1 a) (/.f64 1 b))
(+.f64 (/.f64 1 a) (/.f64 1 b))
(+.f64 (/.f64 1 a) (/.f64 1 b))
(/.f64 1 a)
(+.f64 (/.f64 1 b) (/.f64 1 a))
(+.f64 (/.f64 1 a) (/.f64 1 b))
(+.f64 (/.f64 1 b) (/.f64 1 a))
(+.f64 (/.f64 1 a) (/.f64 1 b))
(+.f64 (/.f64 1 b) (/.f64 1 a))
(+.f64 (/.f64 1 a) (/.f64 1 b))
(/.f64 1 a)
(+.f64 (/.f64 1 b) (/.f64 1 a))
(+.f64 (/.f64 1 a) (/.f64 1 b))
(+.f64 (/.f64 1 b) (/.f64 1 a))
(+.f64 (/.f64 1 a) (/.f64 1 b))
(+.f64 (/.f64 1 b) (/.f64 1 a))
(+.f64 (/.f64 1 a) (/.f64 1 b))

localize4.0ms (0%)

Compiler: Compiled 8 to 6 computations (25% saved)

localize22.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (*.f64 eps b))
✓	19.1b	(.f64 eps (/.f64 1 (.f64 eps b)))

Compiler

Compiled 21 to 10 computations (52.4% saved)

series5.0ms (0%)

Counts

2 → 24

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	b	@	0	(/.f64 1 (*.f64 eps b))
1.0ms	eps	@	0	(/.f64 1 (*.f64 eps b))
1.0ms	eps	@	0	(.f64 eps (/.f64 1 (.f64 eps b)))
0.0ms	b	@	-inf	(/.f64 1 (*.f64 eps b))
0.0ms	eps	@	-inf	(/.f64 1 (*.f64 eps b))

rewrite52.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

678×	`pow1_binary64`
626×	`add-log-exp_binary64`
626×	`log1p-expm1-u_binary64`
626×	`expm1-log1p-u_binary64`
612×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	142	14
2	1778	14

Stop Event

1×	node limit

Counts

2 → 51

Calls

Call 1

Inputs
(.f64 eps (/.f64 1 (.f64 eps b)))
(/.f64 1 (*.f64 eps b))

Outputs

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

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

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	96
1	6	96

Stop Event

1×

saturated

Counts

75 → 52

Calls

Call 1

Inputs
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)

Outputs
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)

localize134.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 eps (-.f64 1 (exp.f64 (neg.f64 (*.f64 a eps)))))
✓	0.0b	(+.f64 (/.f64 1 b) (*.f64 eps -1/2))
✓	0.0b	(exp.f64 (neg.f64 (*.f64 a eps)))
✓	2.5b	(-.f64 1 (exp.f64 (neg.f64 (*.f64 a eps))))

Compiler

Compiled 66 to 31 computations (53% saved)

series15.0ms (0.1%)

Counts

4 → 96

Calls

24 calls:

Time	Variable		Point	Expression
3.0ms	eps	@	inf	(exp.f64 (neg.f64 (*.f64 a eps)))
1.0ms	eps	@	0	(/.f64 eps (-.f64 1 (exp.f64 (neg.f64 (*.f64 a eps)))))
1.0ms	eps	@	-inf	(/.f64 eps (-.f64 1 (exp.f64 (neg.f64 (*.f64 a eps)))))
1.0ms	eps	@	inf	(/.f64 eps (-.f64 1 (exp.f64 (neg.f64 (*.f64 a eps)))))
1.0ms	a	@	0	(-.f64 1 (exp.f64 (neg.f64 (*.f64 a eps))))

rewrite85.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

967×	`prod-diff_binary64`
362×	`fma-def_binary64`
254×	`expm1-udef_binary64`
253×	`log1p-udef_binary64`
210×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	43
1	305	35
2	4163	35

Stop Event

1×	node limit

Counts

4 → 158

Calls

Call 1

Inputs
(-.f64 1 (exp.f64 (neg.f64 (*.f64 a eps))))
(exp.f64 (neg.f64 (*.f64 a eps)))
(+.f64 (/.f64 1 b) (*.f64 eps -1/2))
(/.f64 eps (-.f64 1 (exp.f64 (neg.f64 (*.f64 a eps)))))

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

simplify70.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

760×	`fma-neg_binary64`
744×	`distribute-rgt-out_binary64`
586×	`fma-def_binary64`
550×	`associate-l_binary64`
469×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	1194
1	254	1178
2	944	1138
3	4656	1084

Stop Event

1×	node limit

Counts

254 → 191

Calls

Call 1

Inputs
(*.f64 eps a)
(+.f64 (.f64 -1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (*.f64 eps a))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 a 3))) (*.f64 eps a)))
(+.f64 (.f64 -1/24 (.f64 (pow.f64 eps 4) (pow.f64 a 4))) (+.f64 (.f64 -1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 a 3))) (*.f64 eps a))))
(-.f64 1 (exp.f64 (neg.f64 (*.f64 eps a))))
(-.f64 1 (exp.f64 (neg.f64 (*.f64 eps a))))
(-.f64 1 (exp.f64 (neg.f64 (*.f64 eps a))))
(-.f64 1 (exp.f64 (neg.f64 (*.f64 eps a))))
(-.f64 1 (exp.f64 (neg.f64 (*.f64 eps a))))
(-.f64 1 (exp.f64 (neg.f64 (*.f64 eps a))))
(-.f64 1 (exp.f64 (neg.f64 (*.f64 eps a))))
(-.f64 1 (exp.f64 (neg.f64 (*.f64 eps a))))
(*.f64 eps a)
(+.f64 (.f64 -1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (*.f64 eps a))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 a 3))) (*.f64 eps a)))
(+.f64 (.f64 -1/24 (.f64 (pow.f64 eps 4) (pow.f64 a 4))) (+.f64 (.f64 -1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 a 3))) (*.f64 eps a))))
(-.f64 1 (exp.f64 (neg.f64 (*.f64 eps a))))
(-.f64 1 (exp.f64 (neg.f64 (*.f64 eps a))))
(-.f64 1 (exp.f64 (neg.f64 (*.f64 eps a))))
(-.f64 1 (exp.f64 (neg.f64 (*.f64 eps a))))
(-.f64 1 (exp.f64 (neg.f64 (*.f64 eps a))))
(-.f64 1 (exp.f64 (neg.f64 (*.f64 eps a))))
(-.f64 1 (exp.f64 (neg.f64 (*.f64 eps a))))
(-.f64 1 (exp.f64 (neg.f64 (*.f64 eps a))))
1
(+.f64 1 (.f64 -1 (.f64 eps a)))
(+.f64 (.f64 1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (+.f64 1 (.f64 -1 (.f64 eps a))))
(+.f64 (.f64 1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (+.f64 1 (+.f64 (.f64 -1 (.f64 eps a)) (.f64 -1/6 (.f64 (pow.f64 eps 3) (pow.f64 a 3))))))
(exp.f64 (neg.f64 (*.f64 eps a)))
(exp.f64 (neg.f64 (*.f64 eps a)))
(exp.f64 (neg.f64 (*.f64 eps a)))
(exp.f64 (neg.f64 (*.f64 eps a)))
(exp.f64 (neg.f64 (*.f64 eps a)))
(exp.f64 (neg.f64 (*.f64 eps a)))
(exp.f64 (neg.f64 (*.f64 eps a)))
(exp.f64 (neg.f64 (*.f64 eps a)))
1
(+.f64 1 (.f64 -1 (.f64 eps a)))
(+.f64 (.f64 1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (+.f64 1 (.f64 -1 (.f64 eps a))))
(+.f64 (.f64 1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (+.f64 1 (+.f64 (.f64 -1 (.f64 eps a)) (.f64 -1/6 (.f64 (pow.f64 eps 3) (pow.f64 a 3))))))
(exp.f64 (neg.f64 (*.f64 eps a)))
(exp.f64 (neg.f64 (*.f64 eps a)))
(exp.f64 (neg.f64 (*.f64 eps a)))
(exp.f64 (neg.f64 (*.f64 eps a)))
(exp.f64 (neg.f64 (*.f64 eps a)))
(exp.f64 (neg.f64 (*.f64 eps a)))
(exp.f64 (neg.f64 (*.f64 eps a)))
(exp.f64 (neg.f64 (*.f64 eps a)))
(/.f64 1 b)
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(*.f64 -1/2 eps)
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(*.f64 -1/2 eps)
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(/.f64 1 b)
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(*.f64 -1/2 eps)
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(*.f64 -1/2 eps)
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(/.f64 1 a)
(+.f64 (*.f64 1/2 eps) (/.f64 1 a))
(+.f64 (.f64 -1 (.f64 (pow.f64 eps 2) (+.f64 (.f64 -1/4 a) (.f64 1/6 a)))) (+.f64 (*.f64 1/2 eps) (/.f64 1 a)))
(+.f64 (.f64 -1 (.f64 (+.f64 (.f64 1/12 (pow.f64 a 2)) (+.f64 (.f64 1/2 (.f64 (+.f64 (.f64 -1/4 a) (.f64 1/6 a)) a)) (.f64 -1/24 (pow.f64 a 2)))) (pow.f64 eps 3))) (+.f64 (.f64 -1 (.f64 (pow.f64 eps 2) (+.f64 (.f64 -1/4 a) (.f64 1/6 a)))) (+.f64 (*.f64 1/2 eps) (/.f64 1 a))))
(/.f64 eps (-.f64 1 (exp.f64 (neg.f64 (*.f64 eps a)))))
(/.f64 eps (-.f64 1 (exp.f64 (neg.f64 (*.f64 eps a)))))
(/.f64 eps (-.f64 1 (exp.f64 (neg.f64 (*.f64 eps a)))))
(/.f64 eps (-.f64 1 (exp.f64 (neg.f64 (*.f64 eps a)))))
(/.f64 eps (-.f64 1 (exp.f64 (neg.f64 (*.f64 eps a)))))
(/.f64 eps (-.f64 1 (exp.f64 (neg.f64 (*.f64 eps a)))))
(/.f64 eps (-.f64 1 (exp.f64 (neg.f64 (*.f64 eps a)))))
(/.f64 eps (-.f64 1 (exp.f64 (neg.f64 (*.f64 eps a)))))
(/.f64 1 a)
(+.f64 (*.f64 1/2 eps) (/.f64 1 a))
(+.f64 (.f64 1/2 eps) (+.f64 (.f64 -1 (.f64 (+.f64 (.f64 1/6 (pow.f64 eps 2)) (*.f64 -1/4 (pow.f64 eps 2))) a)) (/.f64 1 a)))
(+.f64 (.f64 -1 (.f64 (+.f64 (.f64 -1/24 (pow.f64 eps 3)) (+.f64 (.f64 1/2 (.f64 eps (+.f64 (.f64 1/6 (pow.f64 eps 2)) (.f64 -1/4 (pow.f64 eps 2))))) (.f64 1/12 (pow.f64 eps 3)))) (pow.f64 a 2))) (+.f64 (.f64 1/2 eps) (+.f64 (.f64 -1 (.f64 (+.f64 (.f64 1/6 (pow.f64 eps 2)) (*.f64 -1/4 (pow.f64 eps 2))) a)) (/.f64 1 a))))
(/.f64 eps (-.f64 1 (exp.f64 (neg.f64 (*.f64 eps a)))))
(/.f64 eps (-.f64 1 (exp.f64 (neg.f64 (*.f64 eps a)))))
(/.f64 eps (-.f64 1 (exp.f64 (neg.f64 (*.f64 eps a)))))
(/.f64 eps (-.f64 1 (exp.f64 (neg.f64 (*.f64 eps a)))))
(/.f64 eps (-.f64 1 (exp.f64 (neg.f64 (*.f64 eps a)))))
(/.f64 eps (-.f64 1 (exp.f64 (neg.f64 (*.f64 eps a)))))
(/.f64 eps (-.f64 1 (exp.f64 (neg.f64 (*.f64 eps a)))))
(/.f64 eps (-.f64 1 (exp.f64 (neg.f64 (*.f64 eps a)))))

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

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f64 1 (*.f64 eps b))
✓	2.5b	(-.f64 (exp.f64 (*.f64 eps a)) 1)
✓	3.1b	(.f64 eps (-.f64 (+.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1)) (/.f64 1 (.f64 eps b))) 1/2))
✓	6.6b	(+.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1)) (/.f64 1 (*.f64 eps b)))

Compiler

Compiled 97 to 38 computations (60.8% saved)

series22.0ms (0.1%)

Counts

3 → 49

Calls

24 calls:

Time	Variable		Point	Expression
7.0ms	eps	@	inf	(-.f64 (exp.f64 (*.f64 eps a)) 1)
2.0ms	eps	@	0	(.f64 eps (-.f64 (+.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1)) (/.f64 1 (.f64 eps b))) 1/2))
1.0ms	a	@	inf	(+.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1)) (/.f64 1 (*.f64 eps b)))
1.0ms	eps	@	-inf	(.f64 eps (-.f64 (+.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1)) (/.f64 1 (.f64 eps b))) 1/2))
1.0ms	eps	@	0	(+.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1)) (/.f64 1 (*.f64 eps b)))

rewrite220.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

705×	`fma-def_binary64`
398×	`fma-neg_binary64`
303×	`log1p-udef_binary64`
302×	`expm1-udef_binary64`
273×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	58
1	342	58
2	5065	58

Stop Event

1×	node limit

Counts

3 → 153

Calls

Call 1

Inputs

(+.f64 (/.f64 (exp.f64 (*.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) (/.f64 1 (*.f64 eps b)))

(*.f64 eps (-.f64 (+.f64 (/.f64 (exp.f64 (*.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) (/.f64 1 (*.f64 eps b))) 1/2))

(-.f64 (exp.f64 (*.f64 eps a)) 1)

Outputs

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

simplify123.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

768×	`fma-neg_binary64`
686×	`fma-def_binary64`
460×	`associate-l_binary64`
430×	`associate-+l+_binary64`
401×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	119	1358
1	352	1213
2	1188	1142
3	6112	1049

Stop Event

1×	node limit

Counts

202 → 195

Calls

Call 1

Inputs
(/.f64 (+.f64 (/.f64 1 a) (/.f64 1 b)) eps)
(+.f64 1/2 (+.f64 (/.f64 1 (.f64 eps b)) (/.f64 1 (.f64 eps a))))
(+.f64 1/2 (+.f64 (/.f64 1 (.f64 eps b)) (+.f64 (.f64 eps (-.f64 (.f64 1/2 a) (+.f64 (.f64 1/4 a) (.f64 1/6 a)))) (/.f64 1 (.f64 eps a)))))
(+.f64 1/2 (+.f64 (/.f64 1 (.f64 eps b)) (+.f64 (.f64 eps (-.f64 (.f64 1/2 a) (+.f64 (.f64 1/4 a) (.f64 1/6 a)))) (+.f64 (/.f64 1 (.f64 eps a)) (.f64 (-.f64 (.f64 1/6 (pow.f64 a 2)) (+.f64 (.f64 1/12 (pow.f64 a 2)) (+.f64 (.f64 1/24 (pow.f64 a 2)) (.f64 1/2 (.f64 a (-.f64 (.f64 1/2 a) (+.f64 (.f64 1/4 a) (*.f64 1/6 a)))))))) (pow.f64 eps 2))))))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(/.f64 1 (*.f64 eps a))
(+.f64 1/2 (+.f64 (/.f64 1 (.f64 eps b)) (/.f64 1 (.f64 eps a))))
(+.f64 1/2 (+.f64 (/.f64 1 (.f64 eps b)) (+.f64 (.f64 a (-.f64 (.f64 1/2 eps) (+.f64 (.f64 1/6 eps) (.f64 1/4 eps)))) (/.f64 1 (.f64 eps a)))))
(+.f64 1/2 (+.f64 (/.f64 1 (.f64 eps b)) (+.f64 (.f64 (-.f64 (.f64 1/6 (pow.f64 eps 2)) (+.f64 (.f64 1/24 (pow.f64 eps 2)) (+.f64 (.f64 1/2 (.f64 eps (-.f64 (.f64 1/2 eps) (+.f64 (.f64 1/6 eps) (.f64 1/4 eps))))) (.f64 1/12 (pow.f64 eps 2))))) (pow.f64 a 2)) (+.f64 (.f64 a (-.f64 (.f64 1/2 eps) (+.f64 (.f64 1/6 eps) (.f64 1/4 eps)))) (/.f64 1 (*.f64 eps a))))))
(/.f64 1 (*.f64 eps b))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(+.f64 (/.f64 1 a) (/.f64 1 b))
(+.f64 (.f64 (pow.f64 eps 2) (-.f64 (.f64 1/2 a) (+.f64 (.f64 1/4 a) (.f64 1/6 a)))) (+.f64 (/.f64 1 b) (/.f64 1 a)))
(+.f64 (.f64 (pow.f64 eps 2) (-.f64 (.f64 1/2 a) (+.f64 (.f64 1/4 a) (.f64 1/6 a)))) (+.f64 (.f64 (-.f64 (.f64 1/6 (pow.f64 a 2)) (+.f64 (.f64 1/12 (pow.f64 a 2)) (+.f64 (.f64 1/24 (pow.f64 a 2)) (.f64 1/2 (.f64 a (-.f64 (.f64 1/2 a) (+.f64 (.f64 1/4 a) (*.f64 1/6 a)))))))) (pow.f64 eps 3)) (+.f64 (/.f64 1 b) (/.f64 1 a))))
(+.f64 (.f64 (pow.f64 eps 2) (-.f64 (.f64 1/2 a) (+.f64 (.f64 1/4 a) (.f64 1/6 a)))) (+.f64 (.f64 (pow.f64 eps 4) (-.f64 (.f64 1/24 (pow.f64 a 3)) (+.f64 (.f64 1/2 (.f64 (-.f64 (.f64 1/6 (pow.f64 a 2)) (+.f64 (.f64 1/12 (pow.f64 a 2)) (+.f64 (.f64 1/24 (pow.f64 a 2)) (.f64 1/2 (.f64 a (-.f64 (.f64 1/2 a) (+.f64 (.f64 1/4 a) (.f64 1/6 a)))))))) a)) (+.f64 (.f64 1/120 (pow.f64 a 3)) (+.f64 (.f64 1/48 (pow.f64 a 3)) (.f64 1/6 (.f64 (pow.f64 a 2) (-.f64 (.f64 1/2 a) (+.f64 (.f64 1/4 a) (.f64 1/6 a)))))))))) (+.f64 (.f64 (-.f64 (.f64 1/6 (pow.f64 a 2)) (+.f64 (.f64 1/12 (pow.f64 a 2)) (+.f64 (.f64 1/24 (pow.f64 a 2)) (.f64 1/2 (.f64 a (-.f64 (.f64 1/2 a) (+.f64 (.f64 1/4 a) (.f64 1/6 a)))))))) (pow.f64 eps 3)) (+.f64 (/.f64 1 b) (/.f64 1 a)))))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
(+.f64 (/.f64 1 b) (.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2)))
(+.f64 (/.f64 1 b) (.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2)))
(+.f64 (/.f64 1 b) (.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2)))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
(+.f64 (/.f64 1 b) (.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2)))
(+.f64 (/.f64 1 b) (.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2)))
(+.f64 (/.f64 1 b) (.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2)))
(/.f64 1 a)
(+.f64 (/.f64 1 b) (/.f64 1 a))
(+.f64 (.f64 eps (.f64 a (-.f64 (.f64 1/2 eps) (+.f64 (.f64 1/6 eps) (*.f64 1/4 eps))))) (+.f64 (/.f64 1 b) (/.f64 1 a)))
(+.f64 (.f64 eps (.f64 a (-.f64 (.f64 1/2 eps) (+.f64 (.f64 1/6 eps) (.f64 1/4 eps))))) (+.f64 (/.f64 1 b) (+.f64 (.f64 eps (.f64 (pow.f64 a 2) (-.f64 (.f64 1/6 (pow.f64 eps 2)) (+.f64 (.f64 1/24 (pow.f64 eps 2)) (+.f64 (.f64 1/2 (.f64 eps (-.f64 (.f64 1/2 eps) (+.f64 (.f64 1/6 eps) (.f64 1/4 eps))))) (*.f64 1/12 (pow.f64 eps 2))))))) (/.f64 1 a))))
(/.f64 1 b)
(+.f64 (.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2)) (/.f64 1 b))
(+.f64 (.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2)) (/.f64 1 b))
(+.f64 (.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2)) (/.f64 1 b))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
(+.f64 (/.f64 1 b) (.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2)))
(+.f64 (/.f64 1 b) (.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2)))
(+.f64 (/.f64 1 b) (.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2)))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
(+.f64 (/.f64 1 b) (.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2)))
(+.f64 (/.f64 1 b) (.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2)))
(+.f64 (/.f64 1 b) (.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2)))
(*.f64 eps a)
(+.f64 (.f64 1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (*.f64 eps a))
(+.f64 (.f64 1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 a 3))) (*.f64 eps a)))
(+.f64 (.f64 1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (+.f64 (.f64 1/24 (.f64 (pow.f64 eps 4) (pow.f64 a 4))) (+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 a 3))) (*.f64 eps a))))
(*.f64 eps a)
(+.f64 (.f64 1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (*.f64 eps a))
(+.f64 (.f64 1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 a 3))) (*.f64 eps a)))
(+.f64 (.f64 1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (+.f64 (.f64 1/24 (.f64 (pow.f64 eps 4) (pow.f64 a 4))) (+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 a 3))) (*.f64 eps a))))

Outputs
(/.f64 (+.f64 (/.f64 1 a) (/.f64 1 b)) eps)
(+.f64 1/2 (+.f64 (/.f64 1 (.f64 eps b)) (/.f64 1 (.f64 eps a))))
(+.f64 (+.f64 1/2 (/.f64 1 (.f64 b eps))) (/.f64 1 (.f64 a eps)))
(+.f64 (/.f64 1 (.f64 b eps)) (+.f64 (/.f64 1 (.f64 a eps)) 1/2))
(+.f64 (/.f64 1 (.f64 b eps)) (+.f64 1/2 (/.f64 1 (.f64 a eps))))
(+.f64 1/2 (+.f64 (/.f64 1 (.f64 eps b)) (+.f64 (.f64 eps (-.f64 (.f64 1/2 a) (+.f64 (.f64 1/4 a) (.f64 1/6 a)))) (/.f64 1 (.f64 eps a)))))
(+.f64 (+.f64 1/2 (/.f64 1 (.f64 b eps))) (fma.f64 eps (-.f64 (.f64 a 1/2) (.f64 a 5/12)) (/.f64 1 (.f64 a eps))))
(+.f64 1/2 (+.f64 (/.f64 1 (.f64 b eps)) (fma.f64 eps (.f64 a 1/12) (/.f64 1 (*.f64 a eps)))))
(+.f64 1/2 (+.f64 (/.f64 1 (.f64 b eps)) (fma.f64 a (.f64 eps 1/12) (/.f64 1 (*.f64 a eps)))))
(+.f64 1/2 (+.f64 (/.f64 1 (.f64 eps b)) (+.f64 (.f64 eps (-.f64 (.f64 1/2 a) (+.f64 (.f64 1/4 a) (.f64 1/6 a)))) (+.f64 (/.f64 1 (.f64 eps a)) (.f64 (-.f64 (.f64 1/6 (pow.f64 a 2)) (+.f64 (.f64 1/12 (pow.f64 a 2)) (+.f64 (.f64 1/24 (pow.f64 a 2)) (.f64 1/2 (.f64 a (-.f64 (.f64 1/2 a) (+.f64 (.f64 1/4 a) (*.f64 1/6 a)))))))) (pow.f64 eps 2))))))
(+.f64 (+.f64 1/2 (/.f64 1 (.f64 b eps))) (+.f64 (fma.f64 eps (-.f64 (.f64 a 1/2) (.f64 a 5/12)) (/.f64 1 (.f64 a eps))) (.f64 (-.f64 (.f64 1/6 (.f64 a a)) (fma.f64 1/12 (.f64 a a) (fma.f64 1/24 (.f64 a a) (.f64 (.f64 a 1/2) (-.f64 (.f64 a 1/2) (.f64 a 5/12)))))) (.f64 eps eps))))
(+.f64 (fma.f64 eps (.f64 a 1/12) (fma.f64 (-.f64 (.f64 a (.f64 a 1/12)) (fma.f64 1/2 (.f64 a (.f64 a 1/12)) (.f64 (.f64 a a) 1/24))) (.f64 eps eps) (/.f64 1 (.f64 a eps)))) (+.f64 1/2 (/.f64 1 (.f64 b eps))))
(+.f64 (fma.f64 eps (.f64 eps (+.f64 (.f64 a (.f64 a 1/24)) (.f64 -1/24 (.f64 a a)))) (/.f64 1 (.f64 a eps))) (+.f64 1/2 (fma.f64 a (.f64 eps 1/12) (/.f64 1 (.f64 b eps)))))
(+.f64 (fma.f64 eps (.f64 eps 0) (/.f64 1 (.f64 a eps))) (+.f64 1/2 (fma.f64 a (.f64 eps 1/12) (/.f64 1 (.f64 b eps)))))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (*.f64 a eps)))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (*.f64 a eps)))
(/.f64 1 (*.f64 eps a))
(/.f64 1 (*.f64 a eps))
(+.f64 1/2 (+.f64 (/.f64 1 (.f64 eps b)) (/.f64 1 (.f64 eps a))))
(+.f64 (+.f64 1/2 (/.f64 1 (.f64 b eps))) (/.f64 1 (.f64 a eps)))
(+.f64 (/.f64 1 (.f64 b eps)) (+.f64 (/.f64 1 (.f64 a eps)) 1/2))
(+.f64 (/.f64 1 (.f64 b eps)) (+.f64 1/2 (/.f64 1 (.f64 a eps))))
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(.f64 eps (+.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (.f64 a eps))) -1/2))
(+.f64 (/.f64 1 b) (.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2)))
(fma.f64 eps (+.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (*.f64 a eps))) -1/2) (/.f64 1 b))
(+.f64 (/.f64 1 b) (.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2)))
(fma.f64 eps (+.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (*.f64 a eps))) -1/2) (/.f64 1 b))
(+.f64 (/.f64 1 b) (.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2)))
(fma.f64 eps (+.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (*.f64 a eps))) -1/2) (/.f64 1 b))
(/.f64 1 a)
(+.f64 (/.f64 1 b) (/.f64 1 a))
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(+.f64 (.f64 eps (.f64 a (-.f64 (.f64 1/2 eps) (+.f64 (.f64 1/6 eps) (*.f64 1/4 eps))))) (+.f64 (/.f64 1 b) (/.f64 1 a)))
(fma.f64 (.f64 eps eps) (-.f64 (.f64 a 1/2) (*.f64 a 5/12)) (+.f64 (/.f64 1 a) (/.f64 1 b)))
(+.f64 (/.f64 1 a) (fma.f64 (.f64 a 1/12) (.f64 eps eps) (/.f64 1 b)))
(+.f64 (/.f64 1 a) (fma.f64 a (.f64 1/12 (.f64 eps eps)) (/.f64 1 b)))
(+.f64 (.f64 eps (.f64 a (-.f64 (.f64 1/2 eps) (+.f64 (.f64 1/6 eps) (.f64 1/4 eps))))) (+.f64 (/.f64 1 b) (+.f64 (.f64 eps (.f64 (pow.f64 a 2) (-.f64 (.f64 1/6 (pow.f64 eps 2)) (+.f64 (.f64 1/24 (pow.f64 eps 2)) (+.f64 (.f64 1/2 (.f64 eps (-.f64 (.f64 1/2 eps) (+.f64 (.f64 1/6 eps) (.f64 1/4 eps))))) (*.f64 1/12 (pow.f64 eps 2))))))) (/.f64 1 a))))
(fma.f64 eps (.f64 a (-.f64 (.f64 eps 1/2) (.f64 eps 5/12))) (+.f64 (/.f64 1 b) (fma.f64 eps (.f64 (.f64 a a) (-.f64 (.f64 1/6 (.f64 eps eps)) (fma.f64 1/24 (.f64 eps eps) (fma.f64 1/2 (.f64 eps (-.f64 (.f64 eps 1/2) (.f64 eps 5/12))) (.f64 1/12 (*.f64 eps eps)))))) (/.f64 1 a))))
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(+.f64 (/.f64 1 b) (fma.f64 a (.f64 1/12 (.f64 eps eps)) (fma.f64 eps (.f64 (.f64 a a) 0) (/.f64 1 a))))
(/.f64 1 b)
(+.f64 (.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2)) (/.f64 1 b))
(fma.f64 eps (+.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (*.f64 a eps))) -1/2) (/.f64 1 b))
(+.f64 (.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2)) (/.f64 1 b))
(fma.f64 eps (+.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (*.f64 a eps))) -1/2) (/.f64 1 b))
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(fma.f64 eps (+.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (*.f64 a eps))) -1/2) (/.f64 1 b))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
(.f64 eps (+.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (.f64 a eps))) -1/2))
(+.f64 (/.f64 1 b) (.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2)))
(fma.f64 eps (+.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (*.f64 a eps))) -1/2) (/.f64 1 b))
(+.f64 (/.f64 1 b) (.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2)))
(fma.f64 eps (+.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (*.f64 a eps))) -1/2) (/.f64 1 b))
(+.f64 (/.f64 1 b) (.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2)))
(fma.f64 eps (+.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (*.f64 a eps))) -1/2) (/.f64 1 b))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
(.f64 eps (+.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (.f64 a eps))) -1/2))
(+.f64 (/.f64 1 b) (.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2)))
(fma.f64 eps (+.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (*.f64 a eps))) -1/2) (/.f64 1 b))
(+.f64 (/.f64 1 b) (.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2)))
(fma.f64 eps (+.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (*.f64 a eps))) -1/2) (/.f64 1 b))
(+.f64 (/.f64 1 b) (.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2)))
(fma.f64 eps (+.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (*.f64 a eps))) -1/2) (/.f64 1 b))
(*.f64 eps a)
(*.f64 a eps)
(+.f64 (.f64 1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (*.f64 eps a))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 eps eps)) (.f64 a eps))
(fma.f64 1/2 (.f64 (.f64 a eps) (.f64 a eps)) (.f64 a eps))
(.f64 a (+.f64 eps (.f64 a (.f64 1/2 (.f64 eps eps)))))
(+.f64 (.f64 1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 a 3))) (*.f64 eps a)))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 eps eps)) (fma.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 a 3)) (*.f64 a eps)))
(fma.f64 1/2 (.f64 (.f64 a eps) (.f64 a eps)) (fma.f64 a eps (.f64 (pow.f64 eps 3) (*.f64 (pow.f64 a 3) 1/6))))
(fma.f64 a eps (.f64 (.f64 a a) (+.f64 (.f64 (pow.f64 eps 3) (.f64 a 1/6)) (.f64 1/2 (.f64 eps eps)))))
(+.f64 (.f64 1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (+.f64 (.f64 1/24 (.f64 (pow.f64 eps 4) (pow.f64 a 4))) (+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 a 3))) (*.f64 eps a))))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 eps eps)) (fma.f64 1/24 (.f64 (pow.f64 eps 4) (pow.f64 a 4)) (fma.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 a 3)) (.f64 a eps))))
(fma.f64 1/2 (.f64 (.f64 a eps) (.f64 a eps)) (fma.f64 1/24 (.f64 (pow.f64 eps 4) (pow.f64 a 4)) (fma.f64 a eps (.f64 (pow.f64 eps 3) (.f64 (pow.f64 a 3) 1/6)))))
(fma.f64 1/24 (.f64 (pow.f64 eps 4) (pow.f64 a 4)) (fma.f64 a eps (.f64 (.f64 a a) (+.f64 (.f64 (pow.f64 eps 3) (.f64 a 1/6)) (.f64 1/2 (*.f64 eps eps))))))
(*.f64 eps a)
(*.f64 a eps)
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(fma.f64 1/2 (.f64 (.f64 a a) (.f64 eps eps)) (.f64 a eps))
(fma.f64 1/2 (.f64 (.f64 a eps) (.f64 a eps)) (.f64 a eps))
(.f64 a (+.f64 eps (.f64 a (.f64 1/2 (.f64 eps eps)))))
(+.f64 (.f64 1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 a 3))) (*.f64 eps a)))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 eps eps)) (fma.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 a 3)) (*.f64 a eps)))
(fma.f64 1/2 (.f64 (.f64 a eps) (.f64 a eps)) (fma.f64 a eps (.f64 (pow.f64 eps 3) (*.f64 (pow.f64 a 3) 1/6))))
(fma.f64 a eps (.f64 (.f64 a a) (+.f64 (.f64 (pow.f64 eps 3) (.f64 a 1/6)) (.f64 1/2 (.f64 eps eps)))))
(+.f64 (.f64 1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (+.f64 (.f64 1/24 (.f64 (pow.f64 eps 4) (pow.f64 a 4))) (+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 a 3))) (*.f64 eps a))))
(fma.f64 1/2 (.f64 (.f64 a a) (.f64 eps eps)) (fma.f64 1/24 (.f64 (pow.f64 eps 4) (pow.f64 a 4)) (fma.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 a 3)) (.f64 a eps))))
(fma.f64 1/2 (.f64 (.f64 a eps) (.f64 a eps)) (fma.f64 1/24 (.f64 (pow.f64 eps 4) (pow.f64 a 4)) (fma.f64 a eps (.f64 (pow.f64 eps 3) (.f64 (pow.f64 a 3) 1/6)))))
(fma.f64 1/24 (.f64 (pow.f64 eps 4) (pow.f64 a 4)) (fma.f64 a eps (.f64 (.f64 a a) (+.f64 (.f64 (pow.f64 eps 3) (.f64 a 1/6)) (.f64 1/2 (*.f64 eps eps))))))

eval522.0ms (3.1%)

Compiler: Compiled 11272 to 5502 computations (51.2% saved)

prune276.0ms (1.6%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	495	8	503
Fresh	3	1	4
Picked	1	0	1
Done	1	3	4
Total	500	12	512

Error

Counts

512 → 12

Alt Table

Click to see full alt table

Status	Error	Program
▶	31.7b	(/.f64 1 b)
	58.9b	(+.f64 (/.f64 eps (-.f64 1 (exp.f64 (neg.f64 (.f64 a eps))))) (.f64 (-.f64 (pow.f64 b -2) (.f64 1/4 (.f64 eps eps))) (/.f64 1 (+.f64 (/.f64 1 b) (*.f64 1/2 eps)))))
✓	48.8b	(.f64 eps (/.f64 1 (.f64 eps b)))
▶	58.9b	(+.f64 (/.f64 eps (-.f64 1 (exp.f64 (neg.f64 (.f64 a eps))))) (/.f64 (-.f64 (pow.f64 b -2) (.f64 1/4 (.f64 eps eps))) (+.f64 (/.f64 1 b) (.f64 1/2 eps))))
✓	34.1b	(/.f64 1 a)
	29.1b	(/.f64 (.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))) eps) (expm1.f64 (.f64 eps b)))
	48.4b	(.f64 eps (-.f64 (/.f64 1 (.f64 eps b)) 1/2))
	47.1b	(/.f64 eps (*.f64 eps b))
✓	16.1b	(/.f64 (+.f64 a b) (*.f64 a b))
▶	47.8b	(.f64 eps (-.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (.f64 a eps))) 1/2))
▶	3.0b	(+.f64 (/.f64 1 b) (/.f64 1 a))
▶	33.5b	(/.f64 (/.f64 eps b) eps)

Compiler

Compiled 312 to 222 computations (28.8% saved)

localize8.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1 b) (/.f64 1 a))

Compiler

Compiled 19 to 13 computations (31.6% saved)

series2.0ms (0%)

Counts

1 → 15

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	b	@	0	(+.f64 (/.f64 1 b) (/.f64 1 a))
0.0ms	a	@	-inf	(+.f64 (/.f64 1 b) (/.f64 1 a))
0.0ms	a	@	0	(+.f64 (/.f64 1 b) (/.f64 1 a))
0.0ms	b	@	inf	(+.f64 (/.f64 1 b) (/.f64 1 a))
0.0ms	a	@	inf	(+.f64 (/.f64 1 b) (/.f64 1 a))

rewrite73.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

852×	`pow1_binary64`
795×	`add-log-exp_binary64`
795×	`log1p-expm1-u_binary64`
795×	`expm1-log1p-u_binary64`
777×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	156	10
2	2316	10

Stop Event

1×	node limit

Counts

1 → 44

Calls

Call 1

Inputs
(+.f64 (/.f64 1 b) (/.f64 1 a))

Outputs

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

simplify136.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	114
1	10	114

Stop Event

1×

saturated

Counts

59 → 48

Calls

Call 1

Inputs
(/.f64 1 b)
(+.f64 (/.f64 1 a) (/.f64 1 b))
(+.f64 (/.f64 1 a) (/.f64 1 b))
(+.f64 (/.f64 1 a) (/.f64 1 b))
(/.f64 1 a)
(/.f64 1 a)
(/.f64 1 a)
(/.f64 1 b)
(+.f64 (/.f64 1 a) (/.f64 1 b))
(+.f64 (/.f64 1 a) (/.f64 1 b))
(+.f64 (/.f64 1 a) (/.f64 1 b))
(/.f64 1 b)
(+.f64 (/.f64 1 a) (/.f64 1 b))
(+.f64 (/.f64 1 a) (/.f64 1 b))
(+.f64 (/.f64 1 a) (/.f64 1 b))

Outputs
(/.f64 1 b)
(+.f64 (/.f64 1 a) (/.f64 1 b))
(+.f64 (/.f64 1 b) (/.f64 1 a))
(+.f64 (/.f64 1 a) (/.f64 1 b))
(+.f64 (/.f64 1 b) (/.f64 1 a))
(+.f64 (/.f64 1 a) (/.f64 1 b))
(+.f64 (/.f64 1 b) (/.f64 1 a))
(/.f64 1 a)
(/.f64 1 a)
(/.f64 1 a)
(/.f64 1 b)
(+.f64 (/.f64 1 a) (/.f64 1 b))
(+.f64 (/.f64 1 b) (/.f64 1 a))
(+.f64 (/.f64 1 a) (/.f64 1 b))
(+.f64 (/.f64 1 b) (/.f64 1 a))
(+.f64 (/.f64 1 a) (/.f64 1 b))
(+.f64 (/.f64 1 b) (/.f64 1 a))
(/.f64 1 b)
(+.f64 (/.f64 1 a) (/.f64 1 b))
(+.f64 (/.f64 1 b) (/.f64 1 a))
(+.f64 (/.f64 1 a) (/.f64 1 b))
(+.f64 (/.f64 1 b) (/.f64 1 a))
(+.f64 (/.f64 1 a) (/.f64 1 b))
(+.f64 (/.f64 1 b) (/.f64 1 a))

localize4.0ms (0%)

Compiler: Compiled 8 to 6 computations (25% saved)

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	13.1b	(/.f64 (/.f64 eps b) eps)

Compiler

Compiled 13 to 5 computations (61.5% saved)

series2.0ms (0%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	eps	@	0	(/.f64 (/.f64 eps b) eps)
0.0ms	eps	@	-inf	(/.f64 (/.f64 eps b) eps)
0.0ms	b	@	-inf	(/.f64 (/.f64 eps b) eps)
0.0ms	eps	@	inf	(/.f64 (/.f64 eps b) eps)
0.0ms	b	@	inf	(/.f64 (/.f64 eps b) eps)

rewrite48.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

684×	`pow1_binary64`
637×	`add-log-exp_binary64`
637×	`log1p-expm1-u_binary64`
637×	`expm1-log1p-u_binary64`
622×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	111	7
2	1665	7

Stop Event

1×	node limit

Counts

1 → 38

Calls

Call 1

Inputs
(/.f64 (/.f64 eps b) eps)

Outputs

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

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	96
1	6	96

Stop Event

1×

saturated

Counts

62 → 39

Calls

Call 1

Inputs
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)

Outputs
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)

localize58.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1 b) (*.f64 1/2 eps))
	0.0b	(exp.f64 (neg.f64 (*.f64 a eps)))
	2.5b	(-.f64 1 (exp.f64 (neg.f64 (*.f64 a eps))))
✓	23.6b	(/.f64 (-.f64 (pow.f64 b -2) (.f64 1/4 (.f64 eps eps))) (+.f64 (/.f64 1 b) (*.f64 1/2 eps)))

Compiler

Compiled 115 to 60 computations (47.8% saved)

series7.0ms (0%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	b	@	0	(/.f64 (-.f64 (pow.f64 b -2) (.f64 1/4 (.f64 eps eps))) (+.f64 (/.f64 1 b) (*.f64 1/2 eps)))
1.0ms	eps	@	0	(/.f64 (-.f64 (pow.f64 b -2) (.f64 1/4 (.f64 eps eps))) (+.f64 (/.f64 1 b) (*.f64 1/2 eps)))
1.0ms	eps	@	inf	(/.f64 (-.f64 (pow.f64 b -2) (.f64 1/4 (.f64 eps eps))) (+.f64 (/.f64 1 b) (*.f64 1/2 eps)))
1.0ms	b	@	inf	(/.f64 (-.f64 (pow.f64 b -2) (.f64 1/4 (.f64 eps eps))) (+.f64 (/.f64 1 b) (*.f64 1/2 eps)))
1.0ms	b	@	-inf	(/.f64 (-.f64 (pow.f64 b -2) (.f64 1/4 (.f64 eps eps))) (+.f64 (/.f64 1 b) (*.f64 1/2 eps)))

rewrite242.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

757×	`log-prod_binary64`
641×	`fma-def_binary64`
310×	`fma-neg_binary64`
268×	`expm1-udef_binary64`
268×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	35
1	340	18
2	4715	18

Stop Event

1×	node limit

Counts

2 → 282

Calls

Call 1

Inputs
(/.f64 (-.f64 (pow.f64 b -2) (.f64 1/4 (.f64 eps eps))) (+.f64 (/.f64 1 b) (*.f64 1/2 eps)))
(+.f64 (/.f64 1 b) (*.f64 1/2 eps))

Outputs

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simplify173.0ms (1%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
2×	`+-commutative_binary64`
2×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	336
1	19	336
2	21	336

Stop Event

1×

saturated

Counts

330 → 289

Calls

Call 1

Inputs
(/.f64 1 b)
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(*.f64 -1/2 eps)
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(*.f64 -1/2 eps)
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(/.f64 1 b)
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(*.f64 -1/2 eps)
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(*.f64 -1/2 eps)
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(/.f64 1 b)
(+.f64 (*.f64 1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 1/2 eps) (/.f64 1 b))
(*.f64 1/2 eps)
(+.f64 (*.f64 1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 1/2 eps) (/.f64 1 b))
(*.f64 1/2 eps)
(+.f64 (*.f64 1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 1/2 eps) (/.f64 1 b))
(/.f64 1 b)
(+.f64 (*.f64 1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 1/2 eps) (/.f64 1 b))
(*.f64 1/2 eps)
(+.f64 (*.f64 1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 1/2 eps) (/.f64 1 b))
(*.f64 1/2 eps)
(+.f64 (*.f64 1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 1/2 eps) (/.f64 1 b))

Outputs
(/.f64 1 b)
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(fma.f64 -1/2 eps (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(fma.f64 -1/2 eps (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(fma.f64 -1/2 eps (/.f64 1 b))
(*.f64 -1/2 eps)
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(fma.f64 -1/2 eps (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(fma.f64 -1/2 eps (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(fma.f64 -1/2 eps (/.f64 1 b))
(*.f64 -1/2 eps)
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(fma.f64 -1/2 eps (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(fma.f64 -1/2 eps (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(fma.f64 -1/2 eps (/.f64 1 b))
(/.f64 1 b)
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(fma.f64 -1/2 eps (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(fma.f64 -1/2 eps (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(fma.f64 -1/2 eps (/.f64 1 b))
(*.f64 -1/2 eps)
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(fma.f64 -1/2 eps (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(fma.f64 -1/2 eps (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(fma.f64 -1/2 eps (/.f64 1 b))
(*.f64 -1/2 eps)
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(fma.f64 -1/2 eps (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(fma.f64 -1/2 eps (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(fma.f64 -1/2 eps (/.f64 1 b))
(/.f64 1 b)
(+.f64 (*.f64 1/2 eps) (/.f64 1 b))
(fma.f64 1/2 eps (/.f64 1 b))
(fma.f64 eps 1/2 (/.f64 1 b))
(+.f64 (*.f64 1/2 eps) (/.f64 1 b))
(fma.f64 1/2 eps (/.f64 1 b))
(fma.f64 eps 1/2 (/.f64 1 b))
(+.f64 (*.f64 1/2 eps) (/.f64 1 b))
(fma.f64 1/2 eps (/.f64 1 b))
(fma.f64 eps 1/2 (/.f64 1 b))
(*.f64 1/2 eps)
(*.f64 eps 1/2)
(+.f64 (*.f64 1/2 eps) (/.f64 1 b))
(fma.f64 1/2 eps (/.f64 1 b))
(fma.f64 eps 1/2 (/.f64 1 b))
(+.f64 (*.f64 1/2 eps) (/.f64 1 b))
(fma.f64 1/2 eps (/.f64 1 b))
(fma.f64 eps 1/2 (/.f64 1 b))
(+.f64 (*.f64 1/2 eps) (/.f64 1 b))
(fma.f64 1/2 eps (/.f64 1 b))
(fma.f64 eps 1/2 (/.f64 1 b))
(*.f64 1/2 eps)
(*.f64 eps 1/2)
(+.f64 (*.f64 1/2 eps) (/.f64 1 b))
(fma.f64 1/2 eps (/.f64 1 b))
(fma.f64 eps 1/2 (/.f64 1 b))
(+.f64 (*.f64 1/2 eps) (/.f64 1 b))
(fma.f64 1/2 eps (/.f64 1 b))
(fma.f64 eps 1/2 (/.f64 1 b))
(+.f64 (*.f64 1/2 eps) (/.f64 1 b))
(fma.f64 1/2 eps (/.f64 1 b))
(fma.f64 eps 1/2 (/.f64 1 b))
(/.f64 1 b)
(+.f64 (*.f64 1/2 eps) (/.f64 1 b))
(fma.f64 1/2 eps (/.f64 1 b))
(fma.f64 eps 1/2 (/.f64 1 b))
(+.f64 (*.f64 1/2 eps) (/.f64 1 b))
(fma.f64 1/2 eps (/.f64 1 b))
(fma.f64 eps 1/2 (/.f64 1 b))
(+.f64 (*.f64 1/2 eps) (/.f64 1 b))
(fma.f64 1/2 eps (/.f64 1 b))
(fma.f64 eps 1/2 (/.f64 1 b))
(*.f64 1/2 eps)
(*.f64 eps 1/2)
(+.f64 (*.f64 1/2 eps) (/.f64 1 b))
(fma.f64 1/2 eps (/.f64 1 b))
(fma.f64 eps 1/2 (/.f64 1 b))
(+.f64 (*.f64 1/2 eps) (/.f64 1 b))
(fma.f64 1/2 eps (/.f64 1 b))
(fma.f64 eps 1/2 (/.f64 1 b))
(+.f64 (*.f64 1/2 eps) (/.f64 1 b))
(fma.f64 1/2 eps (/.f64 1 b))
(fma.f64 eps 1/2 (/.f64 1 b))
(*.f64 1/2 eps)
(*.f64 eps 1/2)
(+.f64 (*.f64 1/2 eps) (/.f64 1 b))
(fma.f64 1/2 eps (/.f64 1 b))
(fma.f64 eps 1/2 (/.f64 1 b))
(+.f64 (*.f64 1/2 eps) (/.f64 1 b))
(fma.f64 1/2 eps (/.f64 1 b))
(fma.f64 eps 1/2 (/.f64 1 b))
(+.f64 (*.f64 1/2 eps) (/.f64 1 b))
(fma.f64 1/2 eps (/.f64 1 b))
(fma.f64 eps 1/2 (/.f64 1 b))

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (*.f64 a eps))
✓	0.2b	(/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (*.f64 a eps)))
✓	1.5b	(pow.f64 (exp.f64 eps) a)
✓	15.6b	(.f64 eps (-.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (.f64 a eps))) 1/2))

Compiler

Compiled 52 to 14 computations (73.1% saved)

series62.0ms (0.4%)

Counts

4 → 96

Calls

24 calls:

Time	Variable		Point	Expression
35.0ms	eps	@	inf	(.f64 eps (-.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (.f64 a eps))) 1/2))
14.0ms	eps	@	-inf	(.f64 eps (-.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (.f64 a eps))) 1/2))
3.0ms	a	@	0	(expm1.f64 (*.f64 a eps))
1.0ms	a	@	0	(.f64 eps (-.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (.f64 a eps))) 1/2))
1.0ms	eps	@	0	(.f64 eps (-.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (.f64 a eps))) 1/2))

rewrite92.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

576×	`log-prod_binary64`
368×	`pow-prod-down_binary64`
304×	`pow2_binary64`
267×	`pow-pow_binary64`
243×	`pow-unpow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	46
1	237	46
2	3053	46

Stop Event

1×	node limit

Counts

4 → 121

Calls

Call 1

Inputs
(.f64 eps (-.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (.f64 a eps))) 1/2))
(pow.f64 (exp.f64 eps) a)
(/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (*.f64 a eps)))
(expm1.f64 (*.f64 a eps))

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

simplify250.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

918×	`fma-def_binary64`
593×	`associate-l_binary64`
521×	`associate-r_binary64`
351×	`associate-+l+_binary64`
308×	`unsub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	124	1767
1	382	1580
2	1332	1463
3	7427	1445

Stop Event

1×	node limit

Counts

217 → 166

Calls

Call 1

Inputs
(/.f64 1 a)
(+.f64 (.f64 (pow.f64 eps 2) (-.f64 (.f64 1/2 a) (+.f64 (.f64 1/4 a) (.f64 1/6 a)))) (/.f64 1 a))
(+.f64 (.f64 (pow.f64 eps 2) (-.f64 (.f64 1/2 a) (+.f64 (.f64 1/4 a) (.f64 1/6 a)))) (+.f64 (.f64 (-.f64 (.f64 1/6 (pow.f64 a 2)) (+.f64 (.f64 1/12 (pow.f64 a 2)) (+.f64 (.f64 1/24 (pow.f64 a 2)) (.f64 1/2 (.f64 a (-.f64 (.f64 1/2 a) (+.f64 (.f64 1/4 a) (*.f64 1/6 a)))))))) (pow.f64 eps 3)) (/.f64 1 a)))
(+.f64 (.f64 (pow.f64 eps 2) (-.f64 (.f64 1/2 a) (+.f64 (.f64 1/4 a) (.f64 1/6 a)))) (+.f64 (.f64 (pow.f64 eps 4) (-.f64 (.f64 1/24 (pow.f64 a 3)) (+.f64 (.f64 1/2 (.f64 (-.f64 (.f64 1/6 (pow.f64 a 2)) (+.f64 (.f64 1/12 (pow.f64 a 2)) (+.f64 (.f64 1/24 (pow.f64 a 2)) (.f64 1/2 (.f64 a (-.f64 (.f64 1/2 a) (+.f64 (.f64 1/4 a) (.f64 1/6 a)))))))) a)) (+.f64 (.f64 1/120 (pow.f64 a 3)) (+.f64 (.f64 1/6 (.f64 (pow.f64 a 2) (-.f64 (.f64 1/2 a) (+.f64 (.f64 1/4 a) (.f64 1/6 a))))) (.f64 1/48 (pow.f64 a 3))))))) (+.f64 (.f64 (-.f64 (.f64 1/6 (pow.f64 a 2)) (+.f64 (.f64 1/12 (pow.f64 a 2)) (+.f64 (.f64 1/24 (pow.f64 a 2)) (.f64 1/2 (.f64 a (-.f64 (.f64 1/2 a) (+.f64 (.f64 1/4 a) (.f64 1/6 a)))))))) (pow.f64 eps 3)) (/.f64 1 a))))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
(/.f64 1 a)
(+.f64 (.f64 eps (.f64 a (-.f64 (.f64 1/2 eps) (+.f64 (.f64 1/6 eps) (*.f64 1/4 eps))))) (/.f64 1 a))
(+.f64 (.f64 eps (.f64 a (-.f64 (.f64 1/2 eps) (+.f64 (.f64 1/6 eps) (.f64 1/4 eps))))) (+.f64 (.f64 eps (.f64 (pow.f64 a 2) (-.f64 (.f64 1/6 (pow.f64 eps 2)) (+.f64 (.f64 1/24 (pow.f64 eps 2)) (+.f64 (.f64 1/2 (.f64 eps (-.f64 (.f64 1/2 eps) (+.f64 (.f64 1/6 eps) (.f64 1/4 eps))))) (*.f64 1/12 (pow.f64 eps 2))))))) (/.f64 1 a)))
(+.f64 (.f64 eps (.f64 a (-.f64 (.f64 1/2 eps) (+.f64 (.f64 1/6 eps) (.f64 1/4 eps))))) (+.f64 (.f64 eps (.f64 (pow.f64 a 3) (-.f64 (.f64 1/24 (pow.f64 eps 3)) (+.f64 (.f64 1/2 (.f64 eps (-.f64 (.f64 1/6 (pow.f64 eps 2)) (+.f64 (.f64 1/24 (pow.f64 eps 2)) (+.f64 (.f64 1/2 (.f64 eps (-.f64 (.f64 1/2 eps) (+.f64 (.f64 1/6 eps) (.f64 1/4 eps))))) (.f64 1/12 (pow.f64 eps 2))))))) (+.f64 (.f64 1/120 (pow.f64 eps 3)) (+.f64 (.f64 1/6 (.f64 (pow.f64 eps 2) (-.f64 (.f64 1/2 eps) (+.f64 (.f64 1/6 eps) (.f64 1/4 eps))))) (.f64 1/48 (pow.f64 eps 3)))))))) (+.f64 (.f64 eps (.f64 (pow.f64 a 2) (-.f64 (.f64 1/6 (pow.f64 eps 2)) (+.f64 (.f64 1/24 (pow.f64 eps 2)) (+.f64 (.f64 1/2 (.f64 eps (-.f64 (.f64 1/2 eps) (+.f64 (.f64 1/6 eps) (.f64 1/4 eps))))) (*.f64 1/12 (pow.f64 eps 2))))))) (/.f64 1 a))))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
1
(+.f64 1 (*.f64 eps a))
(+.f64 (.f64 1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (+.f64 1 (*.f64 eps a)))
(+.f64 (.f64 1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (+.f64 1 (+.f64 (.f64 eps a) (.f64 1/6 (*.f64 (pow.f64 eps 3) (pow.f64 a 3))))))
(exp.f64 (*.f64 eps a))
(exp.f64 (*.f64 eps a))
(exp.f64 (*.f64 eps a))
(exp.f64 (*.f64 eps a))
(exp.f64 (*.f64 eps a))
(exp.f64 (*.f64 eps a))
(exp.f64 (*.f64 eps a))
(exp.f64 (*.f64 eps a))
1
(+.f64 1 (*.f64 eps a))
(+.f64 (.f64 1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (+.f64 1 (*.f64 eps a)))
(+.f64 (.f64 1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (+.f64 1 (+.f64 (.f64 eps a) (.f64 1/6 (*.f64 (pow.f64 eps 3) (pow.f64 a 3))))))
(exp.f64 (*.f64 eps a))
(exp.f64 (*.f64 eps a))
(exp.f64 (*.f64 eps a))
(exp.f64 (*.f64 eps a))
(exp.f64 (*.f64 eps a))
(exp.f64 (*.f64 eps a))
(exp.f64 (*.f64 eps a))
(exp.f64 (*.f64 eps a))
(/.f64 1 (*.f64 eps a))
(+.f64 1/2 (/.f64 1 (*.f64 eps a)))
(+.f64 1/2 (+.f64 (.f64 eps (-.f64 (.f64 1/2 a) (+.f64 (.f64 1/4 a) (.f64 1/6 a)))) (/.f64 1 (*.f64 eps a))))
(+.f64 1/2 (+.f64 (.f64 eps (-.f64 (.f64 1/2 a) (+.f64 (.f64 1/4 a) (.f64 1/6 a)))) (+.f64 (/.f64 1 (.f64 eps a)) (.f64 (-.f64 (.f64 1/6 (pow.f64 a 2)) (+.f64 (.f64 1/12 (pow.f64 a 2)) (+.f64 (.f64 1/24 (pow.f64 a 2)) (.f64 1/2 (.f64 a (-.f64 (.f64 1/2 a) (+.f64 (.f64 1/4 a) (.f64 1/6 a)))))))) (pow.f64 eps 2)))))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(/.f64 1 (*.f64 eps a))
(+.f64 1/2 (/.f64 1 (*.f64 eps a)))
(+.f64 1/2 (+.f64 (.f64 a (-.f64 (.f64 1/2 eps) (+.f64 (.f64 1/6 eps) (.f64 1/4 eps)))) (/.f64 1 (*.f64 eps a))))
(+.f64 1/2 (+.f64 (.f64 (-.f64 (.f64 1/6 (pow.f64 eps 2)) (+.f64 (.f64 1/24 (pow.f64 eps 2)) (+.f64 (.f64 1/2 (.f64 eps (-.f64 (.f64 1/2 eps) (+.f64 (.f64 1/6 eps) (.f64 1/4 eps))))) (.f64 1/12 (pow.f64 eps 2))))) (pow.f64 a 2)) (+.f64 (.f64 a (-.f64 (.f64 1/2 eps) (+.f64 (.f64 1/6 eps) (.f64 1/4 eps)))) (/.f64 1 (.f64 eps a)))))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(*.f64 eps a)
(+.f64 (.f64 1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (*.f64 eps a))
(+.f64 (.f64 1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 a 3))) (*.f64 eps a)))
(+.f64 (.f64 1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (+.f64 (.f64 1/24 (.f64 (pow.f64 eps 4) (pow.f64 a 4))) (+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 a 3))) (*.f64 eps a))))
(-.f64 (exp.f64 (*.f64 eps a)) 1)
(-.f64 (exp.f64 (*.f64 eps a)) 1)
(-.f64 (exp.f64 (*.f64 eps a)) 1)
(-.f64 (exp.f64 (*.f64 eps a)) 1)
(-.f64 (exp.f64 (*.f64 eps a)) 1)
(-.f64 (exp.f64 (*.f64 eps a)) 1)
(-.f64 (exp.f64 (*.f64 eps a)) 1)
(-.f64 (exp.f64 (*.f64 eps a)) 1)
(*.f64 eps a)
(+.f64 (.f64 1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (*.f64 eps a))
(+.f64 (.f64 1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 a 3))) (*.f64 eps a)))
(+.f64 (.f64 1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (+.f64 (.f64 1/24 (.f64 (pow.f64 eps 4) (pow.f64 a 4))) (+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 a 3))) (*.f64 eps a))))
(-.f64 (exp.f64 (*.f64 eps a)) 1)
(-.f64 (exp.f64 (*.f64 eps a)) 1)
(-.f64 (exp.f64 (*.f64 eps a)) 1)
(-.f64 (exp.f64 (*.f64 eps a)) 1)
(-.f64 (exp.f64 (*.f64 eps a)) 1)
(-.f64 (exp.f64 (*.f64 eps a)) 1)
(-.f64 (exp.f64 (*.f64 eps a)) 1)
(-.f64 (exp.f64 (*.f64 eps a)) 1)

Outputs
(/.f64 1 a)
(+.f64 (.f64 (pow.f64 eps 2) (-.f64 (.f64 1/2 a) (+.f64 (.f64 1/4 a) (.f64 1/6 a)))) (/.f64 1 a))
(fma.f64 (.f64 eps eps) (-.f64 (.f64 a 1/2) (*.f64 a 5/12)) (/.f64 1 a))
(fma.f64 (.f64 eps eps) (.f64 a 1/12) (/.f64 1 a))
(fma.f64 a (.f64 eps (.f64 eps 1/12)) (/.f64 1 a))
(+.f64 (.f64 (pow.f64 eps 2) (-.f64 (.f64 1/2 a) (+.f64 (.f64 1/4 a) (.f64 1/6 a)))) (+.f64 (.f64 (-.f64 (.f64 1/6 (pow.f64 a 2)) (+.f64 (.f64 1/12 (pow.f64 a 2)) (+.f64 (.f64 1/24 (pow.f64 a 2)) (.f64 1/2 (.f64 a (-.f64 (.f64 1/2 a) (+.f64 (.f64 1/4 a) (*.f64 1/6 a)))))))) (pow.f64 eps 3)) (/.f64 1 a)))
(fma.f64 (.f64 eps eps) (-.f64 (.f64 a 1/2) (.f64 a 5/12)) (fma.f64 (-.f64 (.f64 1/6 (.f64 a a)) (fma.f64 1/12 (.f64 a a) (fma.f64 1/24 (.f64 a a) (.f64 1/2 (.f64 a (-.f64 (.f64 a 1/2) (*.f64 a 5/12))))))) (pow.f64 eps 3) (/.f64 1 a)))
(fma.f64 (.f64 eps eps) (.f64 a 1/12) (fma.f64 (-.f64 (.f64 (.f64 1/12 a) a) (fma.f64 1/2 (.f64 (.f64 1/12 a) a) (.f64 a (.f64 a 1/24)))) (pow.f64 eps 3) (/.f64 1 a)))
(fma.f64 (-.f64 (.f64 (.f64 a a) 1/24) (.f64 (.f64 a a) 1/24)) (pow.f64 eps 3) (fma.f64 a (.f64 eps (.f64 eps 1/12)) (/.f64 1 a)))
(+.f64 (.f64 (pow.f64 eps 2) (-.f64 (.f64 1/2 a) (+.f64 (.f64 1/4 a) (.f64 1/6 a)))) (+.f64 (.f64 (pow.f64 eps 4) (-.f64 (.f64 1/24 (pow.f64 a 3)) (+.f64 (.f64 1/2 (.f64 (-.f64 (.f64 1/6 (pow.f64 a 2)) (+.f64 (.f64 1/12 (pow.f64 a 2)) (+.f64 (.f64 1/24 (pow.f64 a 2)) (.f64 1/2 (.f64 a (-.f64 (.f64 1/2 a) (+.f64 (.f64 1/4 a) (.f64 1/6 a)))))))) a)) (+.f64 (.f64 1/120 (pow.f64 a 3)) (+.f64 (.f64 1/6 (.f64 (pow.f64 a 2) (-.f64 (.f64 1/2 a) (+.f64 (.f64 1/4 a) (.f64 1/6 a))))) (.f64 1/48 (pow.f64 a 3))))))) (+.f64 (.f64 (-.f64 (.f64 1/6 (pow.f64 a 2)) (+.f64 (.f64 1/12 (pow.f64 a 2)) (+.f64 (.f64 1/24 (pow.f64 a 2)) (.f64 1/2 (.f64 a (-.f64 (.f64 1/2 a) (+.f64 (.f64 1/4 a) (.f64 1/6 a)))))))) (pow.f64 eps 3)) (/.f64 1 a))))
(fma.f64 (.f64 eps eps) (-.f64 (.f64 a 1/2) (.f64 a 5/12)) (fma.f64 (pow.f64 eps 4) (-.f64 (.f64 1/24 (pow.f64 a 3)) (fma.f64 1/2 (.f64 a (-.f64 (.f64 1/6 (.f64 a a)) (fma.f64 1/12 (.f64 a a) (fma.f64 1/24 (.f64 a a) (.f64 1/2 (.f64 a (-.f64 (.f64 a 1/2) (.f64 a 5/12)))))))) (fma.f64 1/120 (pow.f64 a 3) (fma.f64 1/6 (.f64 (-.f64 (.f64 a 1/2) (.f64 a 5/12)) (.f64 a a)) (.f64 (pow.f64 a 3) 1/48))))) (fma.f64 (-.f64 (.f64 1/6 (.f64 a a)) (fma.f64 1/12 (.f64 a a) (fma.f64 1/24 (.f64 a a) (.f64 1/2 (.f64 a (-.f64 (.f64 a 1/2) (.f64 a 5/12))))))) (pow.f64 eps 3) (/.f64 1 a))))
(fma.f64 (.f64 eps eps) (.f64 a 1/12) (fma.f64 (pow.f64 eps 4) (-.f64 (.f64 1/24 (pow.f64 a 3)) (fma.f64 1/2 (.f64 a (-.f64 (.f64 (.f64 1/12 a) a) (fma.f64 1/2 (.f64 (.f64 1/12 a) a) (.f64 a (.f64 a 1/24))))) (fma.f64 (pow.f64 a 3) 1/120 (fma.f64 1/6 (.f64 a (.f64 (.f64 1/12 a) a)) (.f64 (pow.f64 a 3) 1/48))))) (fma.f64 (-.f64 (.f64 (.f64 1/12 a) a) (fma.f64 1/2 (.f64 (.f64 1/12 a) a) (.f64 a (.f64 a 1/24)))) (pow.f64 eps 3) (/.f64 1 a))))
(fma.f64 eps (.f64 a (.f64 eps 1/12)) (fma.f64 (pow.f64 eps 4) (-.f64 (.f64 1/24 (pow.f64 a 3)) (fma.f64 a (.f64 1/2 (-.f64 (.f64 (.f64 a a) 1/24) (.f64 (.f64 a a) 1/24))) (fma.f64 1/6 (.f64 1/12 (pow.f64 a 3)) (.f64 (pow.f64 a 3) 7/240)))) (fma.f64 (-.f64 (.f64 (.f64 a a) 1/24) (.f64 (.f64 a a) 1/24)) (pow.f64 eps 3) (/.f64 1 a))))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
(.f64 eps (+.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (.f64 a eps))) -1/2))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
(.f64 eps (+.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (.f64 a eps))) -1/2))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
(.f64 eps (+.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (.f64 a eps))) -1/2))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
(.f64 eps (+.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (.f64 a eps))) -1/2))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
(.f64 eps (+.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (.f64 a eps))) -1/2))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
(.f64 eps (+.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (.f64 a eps))) -1/2))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
(.f64 eps (+.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (.f64 a eps))) -1/2))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
(.f64 eps (+.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (.f64 a eps))) -1/2))
(/.f64 1 a)
(+.f64 (.f64 eps (.f64 a (-.f64 (.f64 1/2 eps) (+.f64 (.f64 1/6 eps) (*.f64 1/4 eps))))) (/.f64 1 a))
(fma.f64 (.f64 eps eps) (-.f64 (.f64 a 1/2) (*.f64 a 5/12)) (/.f64 1 a))
(fma.f64 (.f64 eps eps) (.f64 a 1/12) (/.f64 1 a))
(fma.f64 a (.f64 eps (.f64 eps 1/12)) (/.f64 1 a))
(+.f64 (.f64 eps (.f64 a (-.f64 (.f64 1/2 eps) (+.f64 (.f64 1/6 eps) (.f64 1/4 eps))))) (+.f64 (.f64 eps (.f64 (pow.f64 a 2) (-.f64 (.f64 1/6 (pow.f64 eps 2)) (+.f64 (.f64 1/24 (pow.f64 eps 2)) (+.f64 (.f64 1/2 (.f64 eps (-.f64 (.f64 1/2 eps) (+.f64 (.f64 1/6 eps) (.f64 1/4 eps))))) (*.f64 1/12 (pow.f64 eps 2))))))) (/.f64 1 a)))
(fma.f64 eps (.f64 a (-.f64 (.f64 eps 1/2) (.f64 eps 5/12))) (fma.f64 eps (.f64 (.f64 a a) (-.f64 (.f64 (.f64 eps eps) 1/6) (fma.f64 1/24 (.f64 eps eps) (fma.f64 1/2 (.f64 eps (-.f64 (.f64 eps 1/2) (.f64 eps 5/12))) (.f64 (*.f64 eps eps) 1/12))))) (/.f64 1 a)))
(+.f64 (/.f64 1 a) (.f64 eps (fma.f64 (.f64 a a) (-.f64 (.f64 (.f64 eps eps) 1/8) (fma.f64 (.f64 eps eps) 1/12 (.f64 eps (.f64 1/2 (.f64 eps 1/12))))) (.f64 a (.f64 eps 1/12)))))
(fma.f64 eps (.f64 a (+.f64 (.f64 eps 1/12) (.f64 a (+.f64 (.f64 (.f64 eps eps) 1/24) (.f64 (*.f64 eps eps) -1/24))))) (/.f64 1 a))
(+.f64 (.f64 eps (.f64 a (-.f64 (.f64 1/2 eps) (+.f64 (.f64 1/6 eps) (.f64 1/4 eps))))) (+.f64 (.f64 eps (.f64 (pow.f64 a 3) (-.f64 (.f64 1/24 (pow.f64 eps 3)) (+.f64 (.f64 1/2 (.f64 eps (-.f64 (.f64 1/6 (pow.f64 eps 2)) (+.f64 (.f64 1/24 (pow.f64 eps 2)) (+.f64 (.f64 1/2 (.f64 eps (-.f64 (.f64 1/2 eps) (+.f64 (.f64 1/6 eps) (.f64 1/4 eps))))) (.f64 1/12 (pow.f64 eps 2))))))) (+.f64 (.f64 1/120 (pow.f64 eps 3)) (+.f64 (.f64 1/6 (.f64 (pow.f64 eps 2) (-.f64 (.f64 1/2 eps) (+.f64 (.f64 1/6 eps) (.f64 1/4 eps))))) (.f64 1/48 (pow.f64 eps 3)))))))) (+.f64 (.f64 eps (.f64 (pow.f64 a 2) (-.f64 (.f64 1/6 (pow.f64 eps 2)) (+.f64 (.f64 1/24 (pow.f64 eps 2)) (+.f64 (.f64 1/2 (.f64 eps (-.f64 (.f64 1/2 eps) (+.f64 (.f64 1/6 eps) (.f64 1/4 eps))))) (*.f64 1/12 (pow.f64 eps 2))))))) (/.f64 1 a))))
(fma.f64 eps (.f64 a (-.f64 (.f64 eps 1/2) (.f64 eps 5/12))) (fma.f64 eps (.f64 (pow.f64 a 3) (-.f64 (.f64 1/24 (pow.f64 eps 3)) (fma.f64 1/2 (.f64 eps (-.f64 (.f64 (.f64 eps eps) 1/6) (fma.f64 1/24 (.f64 eps eps) (fma.f64 1/2 (.f64 eps (-.f64 (.f64 eps 1/2) (.f64 eps 5/12))) (.f64 (.f64 eps eps) 1/12))))) (fma.f64 1/120 (pow.f64 eps 3) (fma.f64 1/6 (.f64 (.f64 eps eps) (-.f64 (.f64 eps 1/2) (.f64 eps 5/12))) (.f64 (pow.f64 eps 3) 1/48)))))) (fma.f64 eps (.f64 (.f64 a a) (-.f64 (.f64 (.f64 eps eps) 1/6) (fma.f64 1/24 (.f64 eps eps) (fma.f64 1/2 (.f64 eps (-.f64 (.f64 eps 1/2) (.f64 eps 5/12))) (.f64 (*.f64 eps eps) 1/12))))) (/.f64 1 a))))
(fma.f64 eps (.f64 a (.f64 eps 1/12)) (fma.f64 eps (.f64 (pow.f64 a 3) (-.f64 (.f64 1/24 (pow.f64 eps 3)) (fma.f64 1/2 (.f64 eps (-.f64 (.f64 (.f64 eps eps) 1/8) (fma.f64 (.f64 eps eps) 1/12 (.f64 eps (.f64 1/2 (.f64 eps 1/12)))))) (fma.f64 (pow.f64 eps 3) 1/120 (fma.f64 (pow.f64 eps 3) 1/48 (.f64 (.f64 eps eps) (.f64 1/6 (.f64 eps 1/12)))))))) (fma.f64 eps (.f64 a (.f64 a (-.f64 (.f64 (.f64 eps eps) 1/8) (fma.f64 (.f64 eps eps) 1/12 (.f64 eps (.f64 1/2 (*.f64 eps 1/12))))))) (/.f64 1 a))))
(fma.f64 eps (.f64 (pow.f64 a 3) (-.f64 (.f64 1/24 (pow.f64 eps 3)) (fma.f64 (.f64 eps 1/2) (+.f64 (.f64 (.f64 eps eps) 1/24) (.f64 (.f64 eps eps) -1/24)) (fma.f64 (.f64 eps eps) (.f64 eps 1/72) (.f64 (pow.f64 eps 3) 7/240))))) (fma.f64 eps (.f64 a (+.f64 (.f64 eps 1/12) (.f64 a (+.f64 (.f64 (.f64 eps eps) 1/24) (.f64 (*.f64 eps eps) -1/24))))) (/.f64 1 a)))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
(.f64 eps (+.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (.f64 a eps))) -1/2))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
(.f64 eps (+.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (.f64 a eps))) -1/2))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
(.f64 eps (+.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (.f64 a eps))) -1/2))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
(.f64 eps (+.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (.f64 a eps))) -1/2))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
(.f64 eps (+.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (.f64 a eps))) -1/2))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
(.f64 eps (+.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (.f64 a eps))) -1/2))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
(.f64 eps (+.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (.f64 a eps))) -1/2))
(.f64 eps (-.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (*.f64 eps a)) 1)) 1/2))
(.f64 eps (+.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (.f64 a eps))) -1/2))
1
(+.f64 1 (*.f64 eps a))
(+.f64 1 (*.f64 a eps))
(fma.f64 a eps 1)
(+.f64 (.f64 1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (+.f64 1 (*.f64 eps a)))
(fma.f64 1/2 (.f64 (.f64 eps eps) (.f64 a a)) (+.f64 1 (.f64 a eps)))
(fma.f64 1/2 (.f64 a (.f64 a (*.f64 eps eps))) (fma.f64 a eps 1))
(fma.f64 a eps (fma.f64 (.f64 eps eps) (.f64 a (*.f64 a 1/2)) 1))
(+.f64 (.f64 1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (+.f64 1 (+.f64 (.f64 eps a) (.f64 1/6 (*.f64 (pow.f64 eps 3) (pow.f64 a 3))))))
(fma.f64 1/2 (.f64 (.f64 eps eps) (.f64 a a)) (+.f64 1 (fma.f64 eps a (.f64 1/6 (*.f64 (pow.f64 eps 3) (pow.f64 a 3))))))
(+.f64 1 (fma.f64 1/2 (.f64 a (.f64 a (.f64 eps eps))) (fma.f64 a eps (.f64 (pow.f64 eps 3) (*.f64 (pow.f64 a 3) 1/6)))))
(fma.f64 (.f64 eps eps) (.f64 a (.f64 a 1/2)) (fma.f64 (pow.f64 eps 3) (.f64 1/6 (pow.f64 a 3)) (fma.f64 a eps 1)))
(fma.f64 (.f64 eps eps) (.f64 a (.f64 a 1/2)) (fma.f64 a eps (fma.f64 1/6 (pow.f64 (.f64 a eps) 3) 1)))
(exp.f64 (*.f64 eps a))
(pow.f64 (exp.f64 eps) a)
(exp.f64 (*.f64 eps a))
(pow.f64 (exp.f64 eps) a)
(exp.f64 (*.f64 eps a))
(pow.f64 (exp.f64 eps) a)
(exp.f64 (*.f64 eps a))
(pow.f64 (exp.f64 eps) a)
(exp.f64 (*.f64 eps a))
(pow.f64 (exp.f64 eps) a)
(exp.f64 (*.f64 eps a))
(pow.f64 (exp.f64 eps) a)
(exp.f64 (*.f64 eps a))
(pow.f64 (exp.f64 eps) a)
(exp.f64 (*.f64 eps a))
(pow.f64 (exp.f64 eps) a)
1
(+.f64 1 (*.f64 eps a))
(+.f64 1 (*.f64 a eps))
(fma.f64 a eps 1)
(+.f64 (.f64 1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (+.f64 1 (*.f64 eps a)))
(fma.f64 1/2 (.f64 (.f64 eps eps) (.f64 a a)) (+.f64 1 (.f64 a eps)))
(fma.f64 1/2 (.f64 a (.f64 a (*.f64 eps eps))) (fma.f64 a eps 1))
(fma.f64 a eps (fma.f64 (.f64 eps eps) (.f64 a (*.f64 a 1/2)) 1))
(+.f64 (.f64 1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (+.f64 1 (+.f64 (.f64 eps a) (.f64 1/6 (*.f64 (pow.f64 eps 3) (pow.f64 a 3))))))
(fma.f64 1/2 (.f64 (.f64 eps eps) (.f64 a a)) (+.f64 1 (fma.f64 eps a (.f64 1/6 (*.f64 (pow.f64 eps 3) (pow.f64 a 3))))))
(+.f64 1 (fma.f64 1/2 (.f64 a (.f64 a (.f64 eps eps))) (fma.f64 a eps (.f64 (pow.f64 eps 3) (*.f64 (pow.f64 a 3) 1/6)))))
(fma.f64 (.f64 eps eps) (.f64 a (.f64 a 1/2)) (fma.f64 (pow.f64 eps 3) (.f64 1/6 (pow.f64 a 3)) (fma.f64 a eps 1)))
(fma.f64 (.f64 eps eps) (.f64 a (.f64 a 1/2)) (fma.f64 a eps (fma.f64 1/6 (pow.f64 (.f64 a eps) 3) 1)))
(exp.f64 (*.f64 eps a))
(pow.f64 (exp.f64 eps) a)
(exp.f64 (*.f64 eps a))
(pow.f64 (exp.f64 eps) a)
(exp.f64 (*.f64 eps a))
(pow.f64 (exp.f64 eps) a)
(exp.f64 (*.f64 eps a))
(pow.f64 (exp.f64 eps) a)
(exp.f64 (*.f64 eps a))
(pow.f64 (exp.f64 eps) a)
(exp.f64 (*.f64 eps a))
(pow.f64 (exp.f64 eps) a)
(exp.f64 (*.f64 eps a))
(pow.f64 (exp.f64 eps) a)
(exp.f64 (*.f64 eps a))
(pow.f64 (exp.f64 eps) a)
(/.f64 1 (*.f64 eps a))
(/.f64 1 (*.f64 a eps))
(+.f64 1/2 (/.f64 1 (*.f64 eps a)))
(+.f64 1/2 (/.f64 1 (*.f64 a eps)))
(+.f64 1/2 (+.f64 (.f64 eps (-.f64 (.f64 1/2 a) (+.f64 (.f64 1/4 a) (.f64 1/6 a)))) (/.f64 1 (*.f64 eps a))))
(+.f64 1/2 (fma.f64 eps (-.f64 (.f64 a 1/2) (.f64 a 5/12)) (/.f64 1 (*.f64 a eps))))
(+.f64 1/2 (fma.f64 eps (.f64 a 1/12) (/.f64 1 (.f64 a eps))))
(+.f64 (/.f64 1 (.f64 a eps)) (fma.f64 a (.f64 eps 1/12) 1/2))
(+.f64 1/2 (+.f64 (.f64 eps (-.f64 (.f64 1/2 a) (+.f64 (.f64 1/4 a) (.f64 1/6 a)))) (+.f64 (/.f64 1 (.f64 eps a)) (.f64 (-.f64 (.f64 1/6 (pow.f64 a 2)) (+.f64 (.f64 1/12 (pow.f64 a 2)) (+.f64 (.f64 1/24 (pow.f64 a 2)) (.f64 1/2 (.f64 a (-.f64 (.f64 1/2 a) (+.f64 (.f64 1/4 a) (.f64 1/6 a)))))))) (pow.f64 eps 2)))))
(+.f64 1/2 (+.f64 (fma.f64 eps (-.f64 (.f64 a 1/2) (.f64 a 5/12)) (/.f64 1 (.f64 a eps))) (.f64 (.f64 eps eps) (-.f64 (.f64 1/6 (.f64 a a)) (fma.f64 1/12 (.f64 a a) (fma.f64 1/24 (.f64 a a) (.f64 1/2 (.f64 a (-.f64 (.f64 a 1/2) (*.f64 a 5/12))))))))))
(+.f64 1/2 (fma.f64 eps (.f64 a 1/12) (fma.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 1/12 a) a) (fma.f64 1/2 (.f64 (.f64 1/12 a) a) (.f64 a (.f64 a 1/24)))) (/.f64 1 (*.f64 a eps)))))
(+.f64 (fma.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 a a) 1/24) (.f64 (.f64 a a) 1/24)) (/.f64 1 (.f64 a eps))) (fma.f64 a (*.f64 eps 1/12) 1/2))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (*.f64 a eps)))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (*.f64 a eps)))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (*.f64 a eps)))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (*.f64 a eps)))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (*.f64 a eps)))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (*.f64 a eps)))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (*.f64 a eps)))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (*.f64 a eps)))
(/.f64 1 (*.f64 eps a))
(/.f64 1 (*.f64 a eps))
(+.f64 1/2 (/.f64 1 (*.f64 eps a)))
(+.f64 1/2 (/.f64 1 (*.f64 a eps)))
(+.f64 1/2 (+.f64 (.f64 a (-.f64 (.f64 1/2 eps) (+.f64 (.f64 1/6 eps) (.f64 1/4 eps)))) (/.f64 1 (*.f64 eps a))))
(+.f64 1/2 (fma.f64 eps (-.f64 (.f64 a 1/2) (.f64 a 5/12)) (/.f64 1 (*.f64 a eps))))
(+.f64 1/2 (fma.f64 eps (.f64 a 1/12) (/.f64 1 (.f64 a eps))))
(+.f64 (/.f64 1 (.f64 a eps)) (fma.f64 a (.f64 eps 1/12) 1/2))
(+.f64 1/2 (+.f64 (.f64 (-.f64 (.f64 1/6 (pow.f64 eps 2)) (+.f64 (.f64 1/24 (pow.f64 eps 2)) (+.f64 (.f64 1/2 (.f64 eps (-.f64 (.f64 1/2 eps) (+.f64 (.f64 1/6 eps) (.f64 1/4 eps))))) (.f64 1/12 (pow.f64 eps 2))))) (pow.f64 a 2)) (+.f64 (.f64 a (-.f64 (.f64 1/2 eps) (+.f64 (.f64 1/6 eps) (.f64 1/4 eps)))) (/.f64 1 (.f64 eps a)))))
(+.f64 1/2 (fma.f64 (-.f64 (.f64 (.f64 eps eps) 1/6) (fma.f64 1/24 (.f64 eps eps) (fma.f64 1/2 (.f64 eps (-.f64 (.f64 eps 1/2) (.f64 eps 5/12))) (.f64 (.f64 eps eps) 1/12)))) (.f64 a a) (fma.f64 a (-.f64 (.f64 eps 1/2) (.f64 eps 5/12)) (/.f64 1 (.f64 a eps)))))
(+.f64 1/2 (fma.f64 (.f64 a a) (-.f64 (.f64 (.f64 eps eps) 1/8) (fma.f64 (.f64 eps eps) 1/12 (.f64 eps (.f64 1/2 (.f64 eps 1/12))))) (fma.f64 a (.f64 eps 1/12) (/.f64 1 (*.f64 a eps)))))
(fma.f64 (.f64 a a) (+.f64 (.f64 (.f64 eps eps) 1/24) (.f64 (.f64 eps eps) -1/24)) (+.f64 (/.f64 1 (.f64 a eps)) (fma.f64 a (*.f64 eps 1/12) 1/2)))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (*.f64 a eps)))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (*.f64 a eps)))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (*.f64 a eps)))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (*.f64 a eps)))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (*.f64 a eps)))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (*.f64 a eps)))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (*.f64 a eps)))
(/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1))
(/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (*.f64 a eps)))
(*.f64 eps a)
(*.f64 a eps)
(+.f64 (.f64 1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (*.f64 eps a))
(fma.f64 1/2 (.f64 (.f64 eps eps) (.f64 a a)) (.f64 a eps))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 eps eps))) (.f64 a eps))
(.f64 a (+.f64 eps (.f64 a (.f64 eps (.f64 eps 1/2)))))
(+.f64 (.f64 1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 a 3))) (*.f64 eps a)))
(fma.f64 1/2 (.f64 (.f64 eps eps) (.f64 a a)) (fma.f64 eps a (.f64 1/6 (*.f64 (pow.f64 eps 3) (pow.f64 a 3)))))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 eps eps))) (fma.f64 a eps (.f64 (pow.f64 eps 3) (*.f64 (pow.f64 a 3) 1/6))))
(fma.f64 a eps (.f64 (.f64 a a) (+.f64 (.f64 eps (.f64 eps 1/2)) (.f64 a (.f64 1/6 (pow.f64 eps 3))))))
(fma.f64 1/6 (pow.f64 (.f64 a eps) 3) (.f64 a (+.f64 eps (.f64 a (.f64 eps (*.f64 eps 1/2))))))
(+.f64 (.f64 1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (+.f64 (.f64 1/24 (.f64 (pow.f64 eps 4) (pow.f64 a 4))) (+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 a 3))) (*.f64 eps a))))
(fma.f64 1/2 (.f64 (.f64 eps eps) (.f64 a a)) (fma.f64 1/24 (.f64 (pow.f64 eps 4) (pow.f64 a 4)) (fma.f64 eps a (.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 a 3))))))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 eps eps))) (fma.f64 1/24 (.f64 (pow.f64 eps 4) (pow.f64 a 4)) (fma.f64 a eps (.f64 (pow.f64 eps 3) (.f64 (pow.f64 a 3) 1/6)))))
(fma.f64 1/24 (.f64 (pow.f64 eps 4) (pow.f64 a 4)) (fma.f64 a eps (.f64 (.f64 a a) (+.f64 (.f64 eps (.f64 eps 1/2)) (.f64 a (*.f64 1/6 (pow.f64 eps 3)))))))
(fma.f64 1/24 (.f64 (pow.f64 eps 4) (pow.f64 a 4)) (fma.f64 1/6 (pow.f64 (.f64 a eps) 3) (.f64 a (+.f64 eps (.f64 a (.f64 eps (.f64 eps 1/2)))))))
(-.f64 (exp.f64 (*.f64 eps a)) 1)
(expm1.f64 (*.f64 a eps))
(-.f64 (exp.f64 (*.f64 eps a)) 1)
(expm1.f64 (*.f64 a eps))
(-.f64 (exp.f64 (*.f64 eps a)) 1)
(expm1.f64 (*.f64 a eps))
(-.f64 (exp.f64 (*.f64 eps a)) 1)
(expm1.f64 (*.f64 a eps))
(-.f64 (exp.f64 (*.f64 eps a)) 1)
(expm1.f64 (*.f64 a eps))
(-.f64 (exp.f64 (*.f64 eps a)) 1)
(expm1.f64 (*.f64 a eps))
(-.f64 (exp.f64 (*.f64 eps a)) 1)
(expm1.f64 (*.f64 a eps))
(-.f64 (exp.f64 (*.f64 eps a)) 1)
(expm1.f64 (*.f64 a eps))
(*.f64 eps a)
(*.f64 a eps)
(+.f64 (.f64 1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (*.f64 eps a))
(fma.f64 1/2 (.f64 (.f64 eps eps) (.f64 a a)) (.f64 a eps))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 eps eps))) (.f64 a eps))
(.f64 a (+.f64 eps (.f64 a (.f64 eps (.f64 eps 1/2)))))
(+.f64 (.f64 1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 a 3))) (*.f64 eps a)))
(fma.f64 1/2 (.f64 (.f64 eps eps) (.f64 a a)) (fma.f64 eps a (.f64 1/6 (*.f64 (pow.f64 eps 3) (pow.f64 a 3)))))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 eps eps))) (fma.f64 a eps (.f64 (pow.f64 eps 3) (*.f64 (pow.f64 a 3) 1/6))))
(fma.f64 a eps (.f64 (.f64 a a) (+.f64 (.f64 eps (.f64 eps 1/2)) (.f64 a (.f64 1/6 (pow.f64 eps 3))))))
(fma.f64 1/6 (pow.f64 (.f64 a eps) 3) (.f64 a (+.f64 eps (.f64 a (.f64 eps (*.f64 eps 1/2))))))
(+.f64 (.f64 1/2 (.f64 (pow.f64 eps 2) (pow.f64 a 2))) (+.f64 (.f64 1/24 (.f64 (pow.f64 eps 4) (pow.f64 a 4))) (+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 a 3))) (*.f64 eps a))))
(fma.f64 1/2 (.f64 (.f64 eps eps) (.f64 a a)) (fma.f64 1/24 (.f64 (pow.f64 eps 4) (pow.f64 a 4)) (fma.f64 eps a (.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 a 3))))))
(fma.f64 1/2 (.f64 a (.f64 a (.f64 eps eps))) (fma.f64 1/24 (.f64 (pow.f64 eps 4) (pow.f64 a 4)) (fma.f64 a eps (.f64 (pow.f64 eps 3) (.f64 (pow.f64 a 3) 1/6)))))
(fma.f64 1/24 (.f64 (pow.f64 eps 4) (pow.f64 a 4)) (fma.f64 a eps (.f64 (.f64 a a) (+.f64 (.f64 eps (.f64 eps 1/2)) (.f64 a (*.f64 1/6 (pow.f64 eps 3)))))))
(fma.f64 1/24 (.f64 (pow.f64 eps 4) (pow.f64 a 4)) (fma.f64 1/6 (pow.f64 (.f64 a eps) 3) (.f64 a (+.f64 eps (.f64 a (.f64 eps (.f64 eps 1/2)))))))
(-.f64 (exp.f64 (*.f64 eps a)) 1)
(expm1.f64 (*.f64 a eps))
(-.f64 (exp.f64 (*.f64 eps a)) 1)
(expm1.f64 (*.f64 a eps))
(-.f64 (exp.f64 (*.f64 eps a)) 1)
(expm1.f64 (*.f64 a eps))
(-.f64 (exp.f64 (*.f64 eps a)) 1)
(expm1.f64 (*.f64 a eps))
(-.f64 (exp.f64 (*.f64 eps a)) 1)
(expm1.f64 (*.f64 a eps))
(-.f64 (exp.f64 (*.f64 eps a)) 1)
(expm1.f64 (*.f64 a eps))
(-.f64 (exp.f64 (*.f64 eps a)) 1)
(expm1.f64 (*.f64 a eps))
(-.f64 (exp.f64 (*.f64 eps a)) 1)
(expm1.f64 (*.f64 a eps))

eval973.0ms (5.7%)

Compiler: Compiled 17318 to 10035 computations (42.1% saved)

prune144.0ms (0.8%)

Pruning

10 alts after pruning (4 fresh and 6 done)

	Pruned	Kept	Total
New	628	1	629
Fresh	1	3	4
Picked	1	0	1
Done	1	6	7
Total	631	10	641

Error

Counts

641 → 10

Alt Table

Click to see full alt table

Status	Error	Program
✓	34.1b	(/.f64 1 a)
▶	29.1b	(/.f64 (.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))) eps) (expm1.f64 (.f64 eps b)))
✓	31.7b	(/.f64 1 b)
▶	48.4b	(.f64 eps (-.f64 (/.f64 1 (.f64 eps b)) 1/2))
▶	47.1b	(/.f64 eps (*.f64 eps b))
▶	47.8b	(.f64 eps (-.f64 (/.f64 1 (expm1.f64 (.f64 a eps))) 1/2))
✓	16.1b	(/.f64 (+.f64 a b) (*.f64 a b))
✓	48.8b	(.f64 eps (/.f64 1 (.f64 eps b)))
✓	3.0b	(+.f64 (/.f64 1 b) (/.f64 1 a))
✓	33.5b	(/.f64 (/.f64 eps b) eps)

Compiler

Compiled 104 to 73 computations (29.8% saved)

localize48.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(expm1.f64 (*.f64 a eps))
✓	0.2b	(/.f64 1 (expm1.f64 (*.f64 a eps)))
✓	15.6b	(.f64 eps (-.f64 (/.f64 1 (expm1.f64 (.f64 a eps))) 1/2))

Compiler

Compiled 38 to 18 computations (52.6% saved)

series8.0ms (0%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	eps	@	-inf	(.f64 eps (-.f64 (/.f64 1 (expm1.f64 (.f64 a eps))) 1/2))
1.0ms	eps	@	0	(.f64 eps (-.f64 (/.f64 1 (expm1.f64 (.f64 a eps))) 1/2))
1.0ms	a	@	-inf	(.f64 eps (-.f64 (/.f64 1 (expm1.f64 (.f64 a eps))) 1/2))
1.0ms	eps	@	inf	(.f64 eps (-.f64 (/.f64 1 (expm1.f64 (.f64 a eps))) 1/2))
1.0ms	a	@	inf	(.f64 eps (-.f64 (/.f64 1 (expm1.f64 (.f64 a eps))) 1/2))

rewrite67.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

454×	`log-prod_binary64`
356×	`prod-exp_binary64`
351×	`exp-prod_binary64`
295×	`pow-prod-down_binary64`
274×	`cbrt-unprod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	209	24
2	2529	24

Stop Event

1×	node limit

Counts

2 → 65

Calls

Call 1

Inputs
(.f64 eps (-.f64 (/.f64 1 (expm1.f64 (.f64 a eps))) 1/2))
(/.f64 1 (expm1.f64 (*.f64 a eps)))

Outputs

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

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

simplify55.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

663×	`fma-def_binary64`
486×	`distribute-rgt-neg-in_binary64`
443×	`associate-l_binary64`
443×	`distribute-lft-neg-in_binary64`
370×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	83	606
1	282	592
2	1092	576
3	5897	576

Stop Event

1×	node limit

Counts

113 → 87

Calls

Call 1

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

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

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 1 (*.f64 eps b)) 1/2)
	0.2b	(/.f64 1 (*.f64 eps b))
✓	19.1b	(.f64 eps (-.f64 (/.f64 1 (.f64 eps b)) 1/2))

Compiler

Compiled 31 to 17 computations (45.2% saved)

series8.0ms (0%)

Counts

2 → 30

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	eps	@	0	(.f64 eps (-.f64 (/.f64 1 (.f64 eps b)) 1/2))
1.0ms	b	@	-inf	(.f64 eps (-.f64 (/.f64 1 (.f64 eps b)) 1/2))
1.0ms	b	@	inf	(.f64 eps (-.f64 (/.f64 1 (.f64 eps b)) 1/2))
1.0ms	b	@	0	(.f64 eps (-.f64 (/.f64 1 (.f64 eps b)) 1/2))
1.0ms	eps	@	-inf	(.f64 eps (-.f64 (/.f64 1 (.f64 eps b)) 1/2))

rewrite128.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

960×	`pow1_binary64`
893×	`add-log-exp_binary64`
893×	`log1p-expm1-u_binary64`
893×	`expm1-log1p-u_binary64`
96×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	193	23
2	2419	23

Stop Event

1×	node limit

Counts

2 → 51

Calls

Call 1

Inputs
(.f64 eps (-.f64 (/.f64 1 (.f64 eps b)) 1/2))
(-.f64 (/.f64 1 (*.f64 eps b)) 1/2)

Outputs

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

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

simplify105.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
2×	`associate-/r*_binary64`
2×	`fma-def_binary64`
1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	186
1	18	186
2	20	186

Stop Event

1×

saturated

Counts

81 → 58

Calls

Call 1

Inputs
(/.f64 1 b)
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(*.f64 -1/2 eps)
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(*.f64 -1/2 eps)
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(/.f64 1 b)
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(*.f64 -1/2 eps)
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(*.f64 -1/2 eps)
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(/.f64 1 (*.f64 eps b))
-1/2
-1/2
(/.f64 1 (*.f64 eps b))
-1/2
-1/2

Outputs
(/.f64 1 b)
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(fma.f64 -1/2 eps (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(fma.f64 -1/2 eps (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(fma.f64 -1/2 eps (/.f64 1 b))
(*.f64 -1/2 eps)
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(fma.f64 -1/2 eps (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(fma.f64 -1/2 eps (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(fma.f64 -1/2 eps (/.f64 1 b))
(*.f64 -1/2 eps)
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(fma.f64 -1/2 eps (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(fma.f64 -1/2 eps (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(fma.f64 -1/2 eps (/.f64 1 b))
(/.f64 1 b)
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(fma.f64 -1/2 eps (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(fma.f64 -1/2 eps (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(fma.f64 -1/2 eps (/.f64 1 b))
(*.f64 -1/2 eps)
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(fma.f64 -1/2 eps (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(fma.f64 -1/2 eps (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(fma.f64 -1/2 eps (/.f64 1 b))
(*.f64 -1/2 eps)
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(fma.f64 -1/2 eps (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(fma.f64 -1/2 eps (/.f64 1 b))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(fma.f64 -1/2 eps (/.f64 1 b))
(/.f64 1 (*.f64 eps b))
(/.f64 1 (*.f64 b eps))
-1/2
-1/2
(/.f64 1 (*.f64 eps b))
(/.f64 1 (*.f64 b eps))
-1/2
-1/2

localize48.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	17.3b	(/.f64 eps (*.f64 eps b))

Compiler

Compiled 13 to 5 computations (61.5% saved)

series3.0ms (0%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	eps	@	0	(/.f64 eps (*.f64 eps b))
0.0ms	eps	@	inf	(/.f64 eps (*.f64 eps b))
0.0ms	eps	@	-inf	(/.f64 eps (*.f64 eps b))
0.0ms	b	@	-inf	(/.f64 eps (*.f64 eps b))
0.0ms	b	@	0	(/.f64 eps (*.f64 eps b))

rewrite52.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

593×	`pow1_binary64`
550×	`add-log-exp_binary64`
550×	`log1p-expm1-u_binary64`
550×	`expm1-log1p-u_binary64`
537×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	106	4
2	1507	4

Stop Event

1×	node limit

Counts

1 → 35

Calls

Call 1

Inputs
(/.f64 eps (*.f64 eps b))

Outputs

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

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	96
1	6	96

Stop Event

1×

saturated

Counts

59 → 36

Calls

Call 1

Inputs
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)

Outputs
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)
(/.f64 1 b)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(expm1.f64 (*.f64 eps b))
✓	2.7b	(.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (*.f64 eps a))) eps)
✓	12.3b	(/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a)))
✓	17.2b	(/.f64 (.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))) eps) (expm1.f64 (.f64 eps b)))

Compiler

Compiled 76 to 13 computations (82.9% saved)

series48.0ms (0.3%)

Counts

3 → 108

Calls

27 calls:

Time	Variable		Point	Expression
27.0ms	eps	@	inf	(.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (*.f64 eps a))) eps)
3.0ms	a	@	0	(.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (*.f64 eps a))) eps)
1.0ms	eps	@	0	(/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a)))
1.0ms	a	@	0	(/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a)))
1.0ms	eps	@	0	(/.f64 (.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))) eps) (expm1.f64 (.f64 eps b)))

rewrite145.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

907×	`prod-diff_binary64`
286×	`fma-def_binary64`
277×	`expm1-udef_binary64`
277×	`log1p-udef_binary64`
238×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	65
1	300	65
2	4300	65

Stop Event

1×	node limit

Counts

3 → 102

Calls

Call 1

Inputs

(/.f64 (*.f64 (/.f64 (expm1.f64 (*.f64 eps (+.f64 a b))) (expm1.f64 (*.f64 eps a))) eps) (expm1.f64 (*.f64 eps b)))

(/.f64 (expm1.f64 (*.f64 eps (+.f64 a b))) (expm1.f64 (*.f64 eps a)))

(*.f64 (/.f64 (expm1.f64 (*.f64 eps (+.f64 a b))) (expm1.f64 (*.f64 eps a))) eps)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (expm1.f64 (*.f64 eps (+.f64 a b))) (*.f64 (/.f64 (expm1.f64 (*.f64 eps b)) eps) (expm1.f64 (*.f64 eps a)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 eps (*.f64 (/.f64 (expm1.f64 (*.f64 eps (+.f64 a b))) (expm1.f64 (*.f64 eps a))) (/.f64 1 (expm1.f64 (*.f64 eps b)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (expm1.f64 (*.f64 eps (+.f64 a b))) (expm1.f64 (*.f64 eps a))) (/.f64 1 (/.f64 (expm1.f64 (*.f64 eps b)) eps)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (expm1.f64 (*.f64 eps (+.f64 a b))) (expm1.f64 (*.f64 eps a))) (*.f64 eps (/.f64 1 (expm1.f64 (*.f64 eps b)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 eps (/.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps (+.f64 a b))))) (/.f64 1 (expm1.f64 (*.f64 eps b))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (expm1.f64 (*.f64 eps (+.f64 a b))) (*.f64 (/.f64 (expm1.f64 (*.f64 eps b)) eps) (expm1.f64 (*.f64 eps a)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (expm1.f64 (*.f64 eps (+.f64 a b))) (*.f64 (/.f64 (expm1.f64 (*.f64 eps b)) eps) (expm1.f64 (*.f64 eps a)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (expm1.f64 (*.f64 eps (+.f64 a b))) (*.f64 (/.f64 (expm1.f64 (*.f64 eps b)) eps) (expm1.f64 (*.f64 eps a))))) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (*.f64 eps (+.f64 a b))) (*.f64 (/.f64 (expm1.f64 (*.f64 eps b)) eps) (expm1.f64 (*.f64 eps a))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (*.f64 eps (+.f64 a b))) (*.f64 (/.f64 (expm1.f64 (*.f64 eps b)) eps) (expm1.f64 (*.f64 eps a))))) 2) (cbrt.f64 (/.f64 (expm1.f64 (*.f64 eps (+.f64 a b))) (*.f64 (/.f64 (expm1.f64 (*.f64 eps b)) eps) (expm1.f64 (*.f64 eps a))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 eps (/.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps (+.f64 a b)))))) 2) (*.f64 (cbrt.f64 (/.f64 eps (/.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps (+.f64 a b)))))) (/.f64 1 (expm1.f64 (*.f64 eps b)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (expm1.f64 (*.f64 eps (+.f64 a b))) (*.f64 (/.f64 (expm1.f64 (*.f64 eps b)) eps) (expm1.f64 (*.f64 eps a))))) (sqrt.f64 (/.f64 (expm1.f64 (*.f64 eps (+.f64 a b))) (*.f64 (/.f64 (expm1.f64 (*.f64 eps b)) eps) (expm1.f64 (*.f64 eps a))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 eps (/.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps (+.f64 a b)))))) (*.f64 (sqrt.f64 (/.f64 eps (/.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps (+.f64 a b)))))) (/.f64 1 (expm1.f64 (*.f64 eps b)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (neg.f64 (*.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))) (expm1.f64 (*.f64 eps a))) (/.f64 1 (neg.f64 (expm1.f64 (*.f64 eps b)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (expm1.f64 (*.f64 eps b))) (/.f64 eps (/.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps (+.f64 a b))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 eps 1) (/.f64 (/.f64 (expm1.f64 (*.f64 eps (+.f64 a b))) (expm1.f64 (*.f64 eps a))) (expm1.f64 (*.f64 eps b))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (expm1.f64 (*.f64 eps (+.f64 a b))) (expm1.f64 (*.f64 eps a))) (expm1.f64 (*.f64 eps b))) eps)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (expm1.f64 (*.f64 eps (+.f64 a b))) (expm1.f64 (*.f64 eps a))) 1) (/.f64 eps (expm1.f64 (*.f64 eps b))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 eps (/.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps (+.f64 a b)))))) 2) 1) (/.f64 (cbrt.f64 (/.f64 eps (/.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps (+.f64 a b)))))) (expm1.f64 (*.f64 eps b))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (/.f64 eps (/.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps (+.f64 a 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simplify161.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

959×	`times-frac_binary64`
552×	`cancel-sign-sub-inv_binary64`
245×	`fma-neg_binary64`
240×	`fma-def_binary64`
238×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	320	4915
1	1070	4800
2	3987	4684

Stop Event

1×	node limit

Counts

210 → 181

Calls

Call 1

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

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

eval171.0ms (1%)

Compiler: Compiled 12006 to 5171 computations (56.9% saved)

prune87.0ms (0.5%)

Pruning

11 alts after pruning (4 fresh and 7 done)

	Pruned	Kept	Total
New	460	4	464
Fresh	0	0	0
Picked	1	0	1
Done	2	7	9
Total	463	11	474

Error

Counts

474 → 11

Alt Table

Click to see full alt table

Status	Error	Program
	31.3b	(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
✓	3.0b	(+.f64 (/.f64 1 b) (/.f64 1 a))
✓	34.1b	(/.f64 1 a)
	32.7b	(-.f64 (/.f64 1 a) eps)
✓	31.7b	(/.f64 1 b)
✓	48.4b	(.f64 eps (-.f64 (/.f64 1 (.f64 eps b)) 1/2))
✓	47.1b	(/.f64 eps (*.f64 eps b))
	44.1b	(/.f64 eps (expm1.f64 (*.f64 eps b)))
✓	16.1b	(/.f64 (+.f64 a b) (*.f64 a b))
	62.0b	(*.f64 eps -1/2)
✓	33.5b	(/.f64 (/.f64 eps b) eps)

Compiler

Compiled 93 to 68 computations (26.9% saved)

regimes79.0ms (0.5%)

Counts

24 → 3

Calls

Call 1

Inputs
(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1)))
(/.f64 (.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))) eps) (expm1.f64 (.f64 eps b)))
(.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))))
(.f64 eps (-.f64 (/.f64 (pow.f64 (exp.f64 eps) a) (expm1.f64 (.f64 a eps))) 1/2))
(+.f64 (/.f64 eps (-.f64 1 (exp.f64 (neg.f64 (.f64 a eps))))) (.f64 (-.f64 (pow.f64 b -2) (.f64 1/4 (.f64 eps eps))) (/.f64 1 (+.f64 (/.f64 1 b) (*.f64 1/2 eps)))))
(+.f64 (/.f64 eps (-.f64 1 (exp.f64 (neg.f64 (.f64 a eps))))) (/.f64 (-.f64 (pow.f64 b -2) (.f64 1/4 (.f64 eps eps))) (+.f64 (/.f64 1 b) (.f64 1/2 eps))))
(.f64 eps (-.f64 (+.f64 (/.f64 (exp.f64 (.f64 eps a)) (-.f64 (exp.f64 (.f64 eps a)) 1)) (/.f64 1 (.f64 eps b))) 1/2))
(.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (.f64 a (.f64 eps (expm1.f64 (*.f64 b eps))))))
(+.f64 (/.f64 eps (-.f64 1 (exp.f64 (neg.f64 (.f64 a eps))))) (+.f64 (/.f64 1 b) (.f64 eps -1/2)))
(.f64 eps (-.f64 (/.f64 1 (expm1.f64 (.f64 a eps))) 1/2))
(/.f64 eps (expm1.f64 (*.f64 eps b)))
(.f64 eps (/.f64 (+.f64 a b) (.f64 a (*.f64 b eps))))
(.f64 eps (-.f64 (/.f64 1 (.f64 eps b)) 1/2))
(+.f64 (*.f64 -1/2 eps) (/.f64 1 b))
(+.f64 (/.f64 1 b) (/.f64 1 a))
(/.f64 (+.f64 a b) (*.f64 a b))
(.f64 eps (/.f64 1 (.f64 eps b)))
(-.f64 (/.f64 1 a) eps)
(/.f64 eps (*.f64 eps b))
(/.f64 (/.f64 eps b) eps)
(*.f64 eps -1/2)
(/.f64 1 b)
(/.f64 1 a)
(/.f64 1 b)

Outputs
(+.f64 (/.f64 1 b) (/.f64 1 a))
(/.f64 (.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))) eps) (expm1.f64 (.f64 eps b)))
(+.f64 (/.f64 1 b) (/.f64 1 a))

Calls

4 calls:

29.0ms	b
15.0ms	eps
13.0ms	a
8.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1)))

Results

Error	Segments	Branch
3.0b	1	`a`
1.7b	2	`b`
3.0b	1	`eps`
0.0b	3	`(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1)))`

Compiler

Compiled 317 to 168 computations (47% saved)

bsearch1.0ms (0%)

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	6.6560530696886145e-15	+inf
0.0ms	-inf	-5.355126716949767e-54

Compiler

Compiled 33 to 24 computations (27.3% saved)

regimes69.0ms (0.4%)

Accuracy

Total -51.8b remaining (-467.6%)

Threshold costs -51.8b (-467.6%)

Counts

7 → 4

Calls

Call 1

Inputs
(-.f64 (/.f64 1 a) eps)
(/.f64 eps (*.f64 eps b))
(/.f64 (/.f64 eps b) eps)
(*.f64 eps -1/2)
(/.f64 1 b)
(/.f64 1 a)
(/.f64 1 b)

Outputs
(/.f64 1 b)
(-.f64 (/.f64 1 a) eps)
(/.f64 1 b)
(-.f64 (/.f64 1 a) eps)

Calls

3 calls:

30.0ms	eps
21.0ms	b
15.0ms	a

Results

Error	Segments	Branch
12.0b	2	`a`
11.1b	4	`b`
21.4b	6	`eps`

Compiler

Compiled 42 to 27 computations (35.7% saved)

bsearch579.0ms (3.4%)

Algorithm

3×	binary-search

Steps

Time	Left	Right
183.0ms	3.441177802647287e-68	1.560910780767229e-67
196.0ms	2.8936542360497844e-104	5.060386368645919e-101
199.0ms	6.205766968624342e-118	1.7066676272307171e-115

Compiler

Compiled 33 to 24 computations (27.3% saved)

simplify9.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
7×	`*-commutative_binary64`
5×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	176
1	64	176
2	70	176
3	72	176
4	73	176

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs

(if (<=.f64 (/.f64 (*.f64 eps (-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)) (*.f64 (-.f64 (exp.f64 (*.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))) -inf.0) (+.f64 (/.f64 1 b) (/.f64 1 a)) (if (<=.f64 (/.f64 (*.f64 eps (-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)) (*.f64 (-.f64 (exp.f64 (*.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))) 6338253001141147/633825300114114700748351602688) (/.f64 (*.f64 (/.f64 (expm1.f64 (*.f64 eps (+.f64 a b))) (expm1.f64 (*.f64 eps a))) eps) (expm1.f64 (*.f64 eps b))) (+.f64 (/.f64 1 b) (/.f64 1 a))))

(if (<=.f64 b 451059174675073216/726838724295606890549323807888004534353641360687318060281490199180639288113397923326191050713763565560762521606266177933534601628614656) (/.f64 1 b) (if (<=.f64 b 1167521609103941/40347654345107946713373737062547060536401653012956617387979052445947619094013143666088208645002153616185987062074179584) (-.f64 (/.f64 1 a) eps) (if (<=.f64 b 17113776818740668416/497323236409786642155382248146820840100456150797347717440463976893159497012533375533056) (/.f64 1 b) (-.f64 (/.f64 1 a) eps))))

(/.f64 1 b)

Outputs
(if (<=.f64 (/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (.f64 b eps)) 1))) -inf.0) (+.f64 (/.f64 1 b) (/.f64 1 a)) (if (<=.f64 (/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (.f64 b eps)) 1))) 6338253001141147/633825300114114700748351602688) (/.f64 (.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))) eps) (expm1.f64 (.f64 eps b))) (+.f64 (/.f64 1 b) (/.f64 1 a))))
(if (<=.f64 (/.f64 (.f64 eps (+.f64 (exp.f64 (.f64 eps (+.f64 a b))) -1)) (.f64 (+.f64 (exp.f64 (.f64 eps a)) -1) (+.f64 (exp.f64 (.f64 eps b)) -1))) -inf.0) (+.f64 (/.f64 1 b) (/.f64 1 a)) (if (<=.f64 (/.f64 (.f64 eps (+.f64 (exp.f64 (.f64 eps (+.f64 a b))) -1)) (.f64 (+.f64 (exp.f64 (.f64 eps a)) -1) (+.f64 (exp.f64 (.f64 eps b)) -1))) 6338253001141147/633825300114114700748351602688) (/.f64 (.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a)))) (expm1.f64 (.f64 eps b))) (+.f64 (/.f64 1 b) (/.f64 1 a))))
(if (<=.f64 b 451059174675073216/726838724295606890549323807888004534353641360687318060281490199180639288113397923326191050713763565560762521606266177933534601628614656) (/.f64 1 b) (if (<=.f64 b 1167521609103941/40347654345107946713373737062547060536401653012956617387979052445947619094013143666088208645002153616185987062074179584) (-.f64 (/.f64 1 a) eps) (if (<=.f64 b 17113776818740668416/497323236409786642155382248146820840100456150797347717440463976893159497012533375533056) (/.f64 1 b) (-.f64 (/.f64 1 a) eps))))
(if (<=.f64 b 7047799604298019/11356855067118857664833184498250070849275646260739344691898284362197488876771842551971735167402555711886914400097909030211478150447104) (/.f64 1 b) (if (<=.f64 b 1167521609103941/40347654345107946713373737062547060536401653012956617387979052445947619094013143666088208645002153616185987062074179584) (-.f64 (/.f64 1 a) eps) (if (<=.f64 b 8356336337275717/242833611528216133864932738352939863330300854881517440156476551217363035650651062272) (/.f64 1 b) (-.f64 (/.f64 1 a) eps))))
(/.f64 1 b)

Compiler

Compiled 126 to 77 computations (38.9% saved)

soundness113.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

986×	`times-frac_binary64`
986×	`times-frac_binary64`
580×	`associate-/l*_binary64`
580×	`associate-/l*_binary64`
452×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	28
1	47	28
2	108	28
3	269	28
4	989	28
0	18	28
1	47	28
2	108	28
3	269	28
4	989	28

Stop Event

1×	node limit
1×	node limit

Compiler

Compiled 384 to 256 computations (33.3% saved)

end109.0ms (0.6%)

Remove: (sort a b)
Compiler: Compiled 298 to 171 computations (42.6% saved)

Details

analyze605.0ms (3.5%)

sample9.6s (56.3%)

preprocess48.0ms (0.3%)

simplify26.0ms (0.2%)

eval1.0ms (0%)

prune1.0ms (0%)

localize42.0ms (0.2%)

series37.0ms (0.2%)

rewrite100.0ms (0.6%)

simplify182.0ms (1.1%)

eval129.0ms (0.8%)

prune173.0ms (1%)

localize7.0ms (0%)

series7.0ms (0%)

rewrite57.0ms (0.3%)

simplify8.0ms (0%)

localize4.0ms (0%)

localize22.0ms (0.1%)

series5.0ms (0%)

rewrite52.0ms (0.3%)

simplify8.0ms (0%)

localize134.0ms (0.8%)

series15.0ms (0.1%)

rewrite85.0ms (0.5%)

simplify70.0ms (0.4%)

localize29.0ms (0.2%)

series22.0ms (0.1%)

rewrite220.0ms (1.3%)

simplify123.0ms (0.7%)

eval522.0ms (3.1%)

prune276.0ms (1.6%)

localize8.0ms (0%)

series2.0ms (0%)

rewrite73.0ms (0.4%)

simplify136.0ms (0.8%)

localize4.0ms (0%)

localize5.0ms (0%)

series2.0ms (0%)

rewrite48.0ms (0.3%)

simplify9.0ms (0.1%)

localize58.0ms (0.3%)

series7.0ms (0%)

rewrite242.0ms (1.4%)

simplify173.0ms (1%)

localize16.0ms (0.1%)

series62.0ms (0.4%)

rewrite92.0ms (0.5%)

simplify250.0ms (1.5%)

eval973.0ms (5.7%)

prune144.0ms (0.8%)

localize48.0ms (0.3%)

series8.0ms (0%)

rewrite67.0ms (0.4%)

simplify55.0ms (0.3%)

localize11.0ms (0.1%)

series8.0ms (0%)

rewrite128.0ms (0.7%)

simplify105.0ms (0.6%)

localize48.0ms (0.3%)

series3.0ms (0%)

rewrite52.0ms (0.3%)

simplify9.0ms (0.1%)

localize22.0ms (0.1%)

series48.0ms (0.3%)

rewrite145.0ms (0.9%)

simplify161.0ms (0.9%)

eval171.0ms (1%)

prune87.0ms (0.5%)

regimes79.0ms (0.5%)

bsearch1.0ms (0%)

regimes69.0ms (0.4%)

bsearch579.0ms (3.4%)

simplify9.0ms (0%)

soundness113.0ms (0.7%)

end109.0ms (0.6%)

Profiling