Details

analyze20.0ms (0.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	12.8%	87.2%	0
0%	12.8%	87.2%	1
0%	12.8%	87.2%	2
6.4%	6.4%	87.2%	3
6.4%	4.8%	88.8%	4
7.2%	3.2%	89.6%	5
7.2%	2.4%	90.4%	6
7.6%	1.6%	90.8%	7
7.6%	1.2%	91.2%	8
7.8%	0.8%	91.4%	9
7.8%	0.6%	91.5%	10
7.9%	0.4%	91.7%	11
8%	0.3%	91.7%	12

Compiler

Compiled 25 to 17 computations (32% saved)

sample1.8s (33.6%)

Results

771.0ms	5899×	body	256	valid
504.0ms	1125×	body	1024	valid
436.0ms	1186×	body	512	valid
54.0ms	169×	body	256	invalid
16.0ms	46×	body	2048	valid

preprocess62.0ms (1.2%)

Algorithm

2×	egg-herbie

Rules

144×	`fma-neg_binary64`
96×	`fma-def_binary64`
54×	`cancel-sign-sub-inv_binary64`
44×	`sub-neg_binary64`
26×	`associate--r+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	21	24
2	35	24
3	63	24
4	102	24
5	210	24
6	353	24
7	506	24
8	608	24
9	660	24
10	670	24
0	2	2

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

Inputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 eps (sqrt.f64 (-.f64 (*.f64 eps eps) x)))

Outputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 eps (sqrt.f64 (-.f64 (*.f64 eps eps) x)))
(-.f64 eps (sqrt.f64 (fma.f64 eps eps (neg.f64 x))))

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify33.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

107×	`fma-def_binary64`
72×	`fma-neg_binary64`
29×	`cancel-sign-sub-inv_binary64`
24×	`distribute-rgt-in_binary64`
24×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	12	12
2	20	12
3	34	12
4	55	12
5	103	12
6	196	12
7	269	12
8	361	12
9	439	12
10	495	12
11	499	12

Stop Event

1×

saturated

Counts

1 → 1

Calls

Call 1

Inputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Outputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

eval1.0ms (0%)

Compiler: Compiled 10 to 6 computations (40% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

24.0b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	24.0b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 10 to 6 computations (40% saved)

localize16.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 x x) eps)
✓	3.4b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 26 to 6 computations (76.9% saved)

series14.0ms (0.3%)

Counts

2 → 40

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
2.0ms	eps	@	inf	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
2.0ms	x	@	0	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
2.0ms	eps	@	0	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
1.0ms	eps	@	-inf	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

rewrite70.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

931×	`pow1_binary64`
871×	`add-log-exp_binary64`
871×	`log1p-expm1-u_binary64`
871×	`expm1-log1p-u_binary64`
849×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	162	19
2	2429	19

Stop Event

1×	node limit

Counts

2 → 75

Calls

Call 1

Inputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 (*.f64 x x) eps)

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

Outputs

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

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

simplify67.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

676×	`unswap-sqr_binary64`
320×	`fma-def_binary64`
311×	`associate-/l/_binary64`
275×	`distribute-lft-in_binary64`
275×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	85	598
1	243	571
2	740	561
3	2994	549
4	4729	547

Stop Event

1×	node limit

Counts

115 → 106

Calls

Call 1

Inputs
(.f64 -1 (.f64 (sqrt.f64 -1) (sqrt.f64 eps)))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 -1) (sqrt.f64 eps))) x)
(+.f64 (.f64 -1 (.f64 (sqrt.f64 -1) (sqrt.f64 eps))) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))) x))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 -1) (sqrt.f64 eps))) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (+.f64 (.f64 1/8 (.f64 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3)) (sqrt.f64 (/.f64 1 (pow.f64 eps 3))))) x)))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 (+.f64 (pow.f64 (.f64 -1/8 (pow.f64 eps 2)) 2) (.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 7))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(*.f64 2 x)
(+.f64 (.f64 -1/2 (/.f64 eps x)) (.f64 2 x))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (*.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 eps 4) (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 x 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 x 6))))) x)) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(*.f64 -1 eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(*.f64 -1 eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(*.f64 -1 eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))

Outputs
(.f64 -1 (.f64 (sqrt.f64 -1) (sqrt.f64 eps)))
(neg.f64 (*.f64 (sqrt.f64 -1) (sqrt.f64 eps)))
(*.f64 (sqrt.f64 -1) (neg.f64 (sqrt.f64 eps)))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 -1) (sqrt.f64 eps))) x)
(fma.f64 -1 (*.f64 (sqrt.f64 -1) (sqrt.f64 eps)) x)
(fma.f64 (neg.f64 (sqrt.f64 -1)) (sqrt.f64 eps) x)
(fma.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 -1)) x)
(fma.f64 (sqrt.f64 -1) (neg.f64 (sqrt.f64 eps)) x)
(+.f64 (.f64 -1 (.f64 (sqrt.f64 -1) (sqrt.f64 eps))) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))) x))
(fma.f64 -1 (.f64 (sqrt.f64 -1) (sqrt.f64 eps)) (fma.f64 -1/2 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (*.f64 x x) (sqrt.f64 -1))) x))
(-.f64 (fma.f64 -1/2 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 x (/.f64 (sqrt.f64 -1) x))) x) (.f64 (sqrt.f64 -1) (sqrt.f64 eps)))
(fma.f64 (sqrt.f64 (/.f64 1 eps)) (.f64 -1/2 (.f64 (/.f64 x (sqrt.f64 -1)) x)) (fma.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 -1)) x))
(fma.f64 (sqrt.f64 (/.f64 1 eps)) (.f64 -1/2 (.f64 (/.f64 x (sqrt.f64 -1)) x)) (fma.f64 (sqrt.f64 -1) (neg.f64 (sqrt.f64 eps)) x))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 -1) (sqrt.f64 eps))) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (+.f64 (.f64 1/8 (.f64 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3)) (sqrt.f64 (/.f64 1 (pow.f64 eps 3))))) x)))
(fma.f64 -1 (.f64 (sqrt.f64 -1) (sqrt.f64 eps)) (fma.f64 -1/2 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (.f64 x x) (sqrt.f64 -1))) (fma.f64 1/8 (.f64 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3)) (sqrt.f64 (/.f64 1 (pow.f64 eps 3)))) x)))
(-.f64 (fma.f64 -1/2 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 x (/.f64 (sqrt.f64 -1) x))) (fma.f64 1/8 (.f64 (/.f64 (pow.f64 x 4) (neg.f64 (sqrt.f64 -1))) (sqrt.f64 (/.f64 1 (pow.f64 eps 3)))) x)) (*.f64 (sqrt.f64 -1) (sqrt.f64 eps)))
(-.f64 (fma.f64 -1/2 (.f64 (sqrt.f64 (/.f64 1 eps)) (.f64 (/.f64 x (sqrt.f64 -1)) x)) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 eps 3))) (.f64 -1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1))) x)) (.f64 (sqrt.f64 -1) (sqrt.f64 eps)))
(-.f64 (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 eps 3))) (.f64 -1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1))) x) (fma.f64 (sqrt.f64 -1) (sqrt.f64 eps) (.f64 (sqrt.f64 (/.f64 1 eps)) (.f64 (.f64 (/.f64 x (sqrt.f64 -1)) x) 1/2))))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (*.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 eps (.f64 eps 1/8)) (pow.f64 x 3)))
(.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (*.f64 x x))))
(*.f64 eps (+.f64 (/.f64 1/2 x) (/.f64 1/8 (/.f64 (pow.f64 x 3) eps))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 eps x) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (fma.f64 1/2 (/.f64 eps x) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (/.f64 (.f64 eps (.f64 eps 1/8)) (pow.f64 x 3))))
(fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (*.f64 x x)))))
(fma.f64 1/2 (/.f64 eps x) (.f64 (.f64 eps eps) (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/16 (/.f64 (pow.f64 x 5) eps)))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 (+.f64 (pow.f64 (.f64 -1/8 (pow.f64 eps 2)) 2) (.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 7))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 (+.f64 (pow.f64 (.f64 (.f64 eps eps) -1/8) 2) (.f64 1/16 (pow.f64 eps 4))) (pow.f64 x 7)) (fma.f64 1/2 (/.f64 eps x) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (fma.f64 1/2 (/.f64 (fma.f64 1/16 (pow.f64 eps 4) (.f64 (pow.f64 eps 4) 1/64)) (pow.f64 x 7)) (fma.f64 1/2 (/.f64 eps x) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/2 (+.f64 (/.f64 eps x) (/.f64 (.f64 (pow.f64 eps 4) 5/64) (pow.f64 x 7))) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (/.f64 (.f64 eps (*.f64 eps 1/8)) (pow.f64 x 3))))
(fma.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (/.f64 (.f64 (pow.f64 eps 4) 5/128) (pow.f64 x 7)))))
(fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (fma.f64 1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (/.f64 (*.f64 (pow.f64 eps 4) 5/128) (pow.f64 x 7)))))
(*.f64 2 x)
(*.f64 x 2)
(+.f64 (.f64 -1/2 (/.f64 eps x)) (.f64 2 x))
(fma.f64 -1/2 (/.f64 eps x) (*.f64 x 2))
(fma.f64 x 2 (/.f64 -1/2 (/.f64 x eps)))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (*.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 2 x (.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1/8)))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 x 2 (*.f64 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) -1/8)))
(fma.f64 x 2 (fma.f64 -1/2 (/.f64 eps x) (.f64 (.f64 eps eps) (/.f64 -1/8 (pow.f64 x 3)))))
(fma.f64 x 2 (.f64 (/.f64 eps x) (+.f64 (.f64 (/.f64 eps (*.f64 x x)) -1/8) -1/2)))
(fma.f64 x 2 (.f64 eps (+.f64 (/.f64 -1/2 x) (.f64 (/.f64 -1/8 (pow.f64 x 3)) eps))))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 2 x (fma.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1/8))))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 x 2 (fma.f64 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) -1/8 (*.f64 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) -1/16))))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 (.f64 (/.f64 eps (pow.f64 x 3)) eps) -1/8 (fma.f64 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) -1/16 (.f64 x 2))))
(fma.f64 x 2 (fma.f64 -1/2 (/.f64 eps x) (.f64 (.f64 eps eps) (+.f64 (/.f64 -1/8 (pow.f64 x 3)) (/.f64 -1/16 (/.f64 (pow.f64 x 5) eps))))))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (*.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 eps (.f64 eps 1/8)) (pow.f64 x 3)))
(.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (*.f64 x x))))
(*.f64 eps (+.f64 (/.f64 1/2 x) (/.f64 1/8 (/.f64 (pow.f64 x 3) eps))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 eps x) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (fma.f64 1/2 (/.f64 eps x) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (/.f64 (.f64 eps (.f64 eps 1/8)) (pow.f64 x 3))))
(fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (*.f64 x x)))))
(fma.f64 1/2 (/.f64 eps x) (.f64 (.f64 eps eps) (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/16 (/.f64 (pow.f64 x 5) eps)))))
(+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 eps 4) (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 x 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 x 6))))) x)) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/2 (/.f64 (pow.f64 eps 4) (/.f64 x (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 x 3)) 2) (/.f64 1/16 (pow.f64 x 6))))) (fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 eps x) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/2 (.f64 (/.f64 (pow.f64 eps 4) x) (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 x 3)) 2) (/.f64 1/16 (pow.f64 x 6)))) (fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (fma.f64 1/2 (/.f64 eps x) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps) (fma.f64 1/2 (.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 x 3)) 2) (/.f64 1/16 (pow.f64 x 6))) (/.f64 (pow.f64 eps 4) x)) (fma.f64 1/2 (/.f64 eps x) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(+.f64 (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (/.f64 (.f64 eps (.f64 eps 1/8)) (pow.f64 x 3))) (.f64 (/.f64 1/2 x) (+.f64 eps (.f64 (pow.f64 eps 4) (+.f64 (/.f64 1/64 (pow.f64 x 6)) (/.f64 1/16 (pow.f64 x 6)))))))
(+.f64 (.f64 (.f64 eps eps) (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/16 (/.f64 (pow.f64 x 5) eps)))) (.f64 (/.f64 1/2 x) (+.f64 eps (.f64 (pow.f64 eps 4) (+.f64 (/.f64 1/64 (pow.f64 x 6)) (/.f64 1/16 (pow.f64 x 6)))))))
(*.f64 -1 eps)
(neg.f64 eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(fma.f64 -1 eps (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(fma.f64 -1 eps (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(fma.f64 -1 eps (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(fma.f64 -1 eps (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(fma.f64 -1 eps (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(fma.f64 -1 eps (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(fma.f64 -1 eps (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(fma.f64 -1 eps (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(fma.f64 -1 eps (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(fma.f64 -1 eps (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(fma.f64 -1 eps (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(fma.f64 -1 eps (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(*.f64 -1 eps)
(neg.f64 eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(fma.f64 -1 eps (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(fma.f64 -1 eps (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(fma.f64 -1 eps (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(*.f64 -1 eps)
(neg.f64 eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(fma.f64 -1 eps (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(fma.f64 -1 eps (*.f64 x x))
(-.f64 (*.f64 x x) eps)
(+.f64 (*.f64 -1 eps) (pow.f64 x 2))
(fma.f64 -1 eps (*.f64 x x))
(-.f64 (*.f64 x x) eps)

eval33.0ms (0.6%)

Compiler: Compiled 1790 to 766 computations (57.2% saved)

prune38.0ms (0.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	101	5	106
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	101	6	107

Error

Counts

107 → 6

Alt Table

Click to see full alt table

Status	Error	Program
▶	26.5b	(-.f64 x (sqrt.f64 (neg.f64 eps)))
▶	38.4b	(*.f64 eps (+.f64 (/.f64 1/2 x) (/.f64 1/8 (/.f64 (pow.f64 x 3) eps))))
▶	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
▶	61.9b	(*.f64 x 2)
▶	36.0b	(*.f64 1/2 (/.f64 eps x))
✓	24.0b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 118 to 74 computations (37.3% saved)

localize14.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
	0.0b	(-.f64 (*.f64 x x) eps)
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))

Compiler

Compiled 60 to 9 computations (85% saved)

series10.0ms (0.2%)

Counts

2 → 32

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	eps	@	inf	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
2.0ms	eps	@	-inf	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
1.0ms	x	@	0	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
1.0ms	x	@	inf	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
1.0ms	x	@	-inf	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))

rewrite113.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

700×	`fma-def_binary64`
508×	`log-prod_binary64`
308×	`fma-neg_binary64`
272×	`pow2_binary64`
185×	`pow1/3_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	261	24
2	4073	22

Stop Event

1×	node limit

Counts

2 → 194

Calls

Call 1

Inputs
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 x (neg.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 x (.f64 -1 (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 x (.f64 (neg.f64 (cbrt.f64 (fma.f64 x x (neg.f64 eps)))) (cbrt.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 x (.f64 (neg.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) 1/4)) (pow.f64 (fma.f64 x x (neg.f64 eps)) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) (fma.f64 (neg.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) 1 (hypot.f64 x (sqrt.f64 (neg.f64 eps)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 x (hypot.f64 x (sqrt.f64 (neg.f64 eps)))) (fma.f64 (neg.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 (neg.f64 eps))))) (cbrt.f64 (fma.f64 x x 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Outputs

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

simplify95.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

776×	`fma-def_binary64`
516×	`cancel-sign-sub-inv_binary64`
392×	`fma-neg_binary64`
356×	`associate-l_binary64`
346×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	132	962
1	400	841
2	1374	803
3	6258	785

Stop Event

1×	node limit

Counts

226 → 230

Calls

Call 1

Inputs
(*.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps)) (.f64 -1 (/.f64 x (pow.f64 (sqrt.f64 -1) 2))))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps)) (+.f64 (.f64 -1 (/.f64 x (pow.f64 (sqrt.f64 -1) 2))) (.f64 -1 (.f64 (+.f64 (.f64 -1 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 1 (pow.f64 (sqrt.f64 -1) 3)))) (.f64 1/2 (.f64 (/.f64 1 (pow.f64 (sqrt.f64 -1) 3)) (sqrt.f64 (/.f64 1 eps))))) (pow.f64 x 2)))))
(+.f64 (.f64 (-.f64 (.f64 1/2 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 4) eps))) (.f64 -1 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (+.f64 (.f64 -1 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 1 (pow.f64 (sqrt.f64 -1) 3)))) (.f64 1/2 (.f64 (/.f64 1 (pow.f64 (sqrt.f64 -1) 3)) (sqrt.f64 (/.f64 1 eps))))) (sqrt.f64 -1))))) (pow.f64 x 3)) (+.f64 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps)) (+.f64 (.f64 -1 (/.f64 x (pow.f64 (sqrt.f64 -1) 2))) (.f64 -1 (.f64 (+.f64 (.f64 -1 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 1 (pow.f64 (sqrt.f64 -1) 3)))) (.f64 1/2 (*.f64 (/.f64 1 (pow.f64 (sqrt.f64 -1) 3)) (sqrt.f64 (/.f64 1 eps))))) (pow.f64 x 2))))))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -1/32 (pow.f64 eps 4)) (.f64 -1/128 (pow.f64 eps 4))) (pow.f64 x 7))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(*.f64 2 x)
(+.f64 (.f64 -1/2 (/.f64 eps x)) (.f64 2 x))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (+.f64 (.f64 -2 (/.f64 (+.f64 (pow.f64 (.f64 -1/8 (pow.f64 eps 2)) 2) (.f64 1/16 (pow.f64 eps 4))) (.f64 eps (pow.f64 x 5)))) (.f64 -1/4 (/.f64 (.f64 eps (+.f64 (.f64 -1/4 (pow.f64 eps 2)) (*.f64 1/8 (pow.f64 eps 2)))) (pow.f64 x 5)))))))))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(*.f64 (sqrt.f64 -1) (sqrt.f64 eps))
(+.f64 x (*.f64 (sqrt.f64 -1) (sqrt.f64 eps)))
(+.f64 x (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (*.f64 (sqrt.f64 -1) (sqrt.f64 eps))))
(+.f64 (.f64 -1/8 (.f64 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3)) (sqrt.f64 (/.f64 1 (pow.f64 eps 3))))) (+.f64 x (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (*.f64 (sqrt.f64 -1) (sqrt.f64 eps)))))
(*.f64 2 x)
(+.f64 (.f64 -1/2 (/.f64 eps x)) (.f64 2 x))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (*.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 1/16 (pow.f64 eps 4)) (pow.f64 (.f64 -1/8 (pow.f64 eps 2)) 2)) (pow.f64 x 7))) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(*.f64 2 x)
(+.f64 (.f64 -1/2 (/.f64 eps x)) (.f64 2 x))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (*.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))

Outputs
(*.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps))
(/.f64 (sqrt.f64 eps) (sqrt.f64 -1))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps)) (.f64 -1 (/.f64 x (pow.f64 (sqrt.f64 -1) 2))))
(fma.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps) (neg.f64 (/.f64 x (pow.f64 (sqrt.f64 -1) 2))))
(-.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 -1)) (/.f64 x -1))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 -1)) (*.f64 1 x))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
(+.f64 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps)) (+.f64 (.f64 -1 (/.f64 x (pow.f64 (sqrt.f64 -1) 2))) (.f64 -1 (.f64 (+.f64 (.f64 -1 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 1 (pow.f64 (sqrt.f64 -1) 3)))) (.f64 1/2 (.f64 (/.f64 1 (pow.f64 (sqrt.f64 -1) 3)) (sqrt.f64 (/.f64 1 eps))))) (pow.f64 x 2)))))
(fma.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps) (.f64 -1 (+.f64 (/.f64 x (pow.f64 (sqrt.f64 -1) 2)) (.f64 (fma.f64 -1 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 1 (pow.f64 (sqrt.f64 -1) 3))) (.f64 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 1 (pow.f64 (sqrt.f64 -1) 3))) 1/2)) (.f64 x x)))))
(-.f64 (-.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 -1)) (/.f64 x -1)) (.f64 (.f64 (.f64 -1 (/.f64 (sqrt.f64 (/.f64 1 eps)) (sqrt.f64 -1))) -1/2) (.f64 x x)))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 -1)) (fma.f64 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 -1/2 (sqrt.f64 -1))) (.f64 x x) (*.f64 1 x)))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 -1)) (fma.f64 (.f64 (sqrt.f64 (/.f64 1 eps)) (.f64 x x)) (/.f64 -1/2 (sqrt.f64 -1)) x))
(+.f64 (.f64 (-.f64 (.f64 1/2 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 4) eps))) (.f64 -1 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (+.f64 (.f64 -1 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 1 (pow.f64 (sqrt.f64 -1) 3)))) (.f64 1/2 (.f64 (/.f64 1 (pow.f64 (sqrt.f64 -1) 3)) (sqrt.f64 (/.f64 1 eps))))) (sqrt.f64 -1))))) (pow.f64 x 3)) (+.f64 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps)) (+.f64 (.f64 -1 (/.f64 x (pow.f64 (sqrt.f64 -1) 2))) (.f64 -1 (.f64 (+.f64 (.f64 -1 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 1 (pow.f64 (sqrt.f64 -1) 3)))) (.f64 1/2 (*.f64 (/.f64 1 (pow.f64 (sqrt.f64 -1) 3)) (sqrt.f64 (/.f64 1 eps))))) (pow.f64 x 2))))))
(fma.f64 (-.f64 (/.f64 1/2 (.f64 eps (pow.f64 (sqrt.f64 -1) 4))) (neg.f64 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (fma.f64 -1 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 1 (pow.f64 (sqrt.f64 -1) 3))) (.f64 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 1 (pow.f64 (sqrt.f64 -1) 3))) 1/2)) (sqrt.f64 -1))))) (pow.f64 x 3) (fma.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps) (.f64 -1 (+.f64 (/.f64 x (pow.f64 (sqrt.f64 -1) 2)) (.f64 (fma.f64 -1 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 1 (pow.f64 (sqrt.f64 -1) 3))) (.f64 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 1 (pow.f64 (sqrt.f64 -1) 3))) 1/2)) (*.f64 x x))))))
(fma.f64 (+.f64 (/.f64 1/2 eps) (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (.f64 (.f64 -1 (/.f64 (sqrt.f64 (/.f64 1 eps)) (sqrt.f64 -1))) -1/2) (sqrt.f64 -1)))) (pow.f64 x 3) (-.f64 (-.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 -1)) (/.f64 x -1)) (.f64 (.f64 (.f64 -1 (/.f64 (sqrt.f64 (/.f64 1 eps)) (sqrt.f64 -1))) -1/2) (*.f64 x x))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 -1)) (fma.f64 (fma.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 1 eps)) (sqrt.f64 -1)) 1/2) (sqrt.f64 -1)) (/.f64 1/2 eps)) (pow.f64 x 3) (fma.f64 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 -1/2 (sqrt.f64 -1))) (.f64 x x) (.f64 1 x))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 -1)) (fma.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 -1/2 (sqrt.f64 -1))) (.f64 x (-.f64 (/.f64 1/2 eps) (/.f64 (.f64 (/.f64 1 eps) (/.f64 -1/2 (sqrt.f64 -1))) (sqrt.f64 -1))))) x))
(*.f64 1/2 (/.f64 eps x))
(/.f64 (*.f64 eps 1/2) x)
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 eps (.f64 eps 1/8)) (pow.f64 x 3)))
(fma.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 1/16 (pow.f64 eps 3)) (pow.f64 x 5))))
(fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (fma.f64 1/2 (/.f64 eps x) (/.f64 1/16 (/.f64 (pow.f64 x 5) (pow.f64 eps 3)))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps) (.f64 (/.f64 1/16 (pow.f64 x 5)) (pow.f64 eps 3))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -1/32 (pow.f64 eps 4)) (.f64 -1/128 (pow.f64 eps 4))) (pow.f64 x 7))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 -1 (/.f64 (.f64 (pow.f64 eps 4) -5/128) (pow.f64 x 7)) (fma.f64 1/2 (/.f64 eps x) (/.f64 (*.f64 1/16 (pow.f64 eps 3)) (pow.f64 x 5)))))
(fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (-.f64 (fma.f64 1/2 (/.f64 eps x) (/.f64 1/16 (/.f64 (pow.f64 x 5) (pow.f64 eps 3)))) (/.f64 (pow.f64 eps 4) (/.f64 (pow.f64 x 7) -5/128))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (.f64 (/.f64 5/128 (pow.f64 x 7)) (pow.f64 eps 4)))))
(*.f64 2 x)
(*.f64 x 2)
(+.f64 (.f64 -1/2 (/.f64 eps x)) (.f64 2 x))
(fma.f64 -1/2 (/.f64 eps x) (*.f64 x 2))
(fma.f64 x 2 (/.f64 (*.f64 eps -1/2) x))
(fma.f64 x 2 (*.f64 (/.f64 eps x) -1/2))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 2 x (/.f64 (.f64 (.f64 eps eps) -1/8) (pow.f64 x 3))))
(fma.f64 (/.f64 eps x) -1/2 (fma.f64 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) -1/8 (*.f64 x 2)))
(fma.f64 x 2 (fma.f64 (/.f64 eps x) -1/2 (/.f64 eps (/.f64 (pow.f64 x 3) (*.f64 eps -1/8)))))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (+.f64 (.f64 -2 (/.f64 (+.f64 (pow.f64 (.f64 -1/8 (pow.f64 eps 2)) 2) (.f64 1/16 (pow.f64 eps 4))) (.f64 eps (pow.f64 x 5)))) (.f64 -1/4 (/.f64 (.f64 eps (+.f64 (.f64 -1/4 (pow.f64 eps 2)) (*.f64 1/8 (pow.f64 eps 2)))) (pow.f64 x 5)))))))))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 2 x (+.f64 (/.f64 (.f64 (.f64 eps eps) -1/8) (pow.f64 x 3)) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (fma.f64 -2 (/.f64 (fma.f64 1/16 (pow.f64 eps 4) (pow.f64 (.f64 (.f64 eps eps) -1/8) 2)) (.f64 eps (pow.f64 x 5))) (.f64 -1/4 (/.f64 eps (/.f64 (pow.f64 x 5) (.f64 (.f64 eps eps) -1/8)))))))))
(fma.f64 (/.f64 eps x) -1/2 (fma.f64 x 2 (fma.f64 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) -1/8 (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (fma.f64 -1/4 (/.f64 (.f64 (pow.f64 eps 3) -1/8) (pow.f64 x 5)) (.f64 (/.f64 -2 eps) (/.f64 (fma.f64 1/16 (pow.f64 eps 4) (*.f64 (pow.f64 eps 4) 1/64)) (pow.f64 x 5))))))))
(fma.f64 x 2 (fma.f64 (/.f64 eps x) -1/2 (fma.f64 (.f64 (/.f64 eps (pow.f64 x 3)) eps) -1/8 (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (fma.f64 -2 (/.f64 (.f64 (pow.f64 eps 4) 5/64) (.f64 eps (pow.f64 x 5))) (/.f64 (.f64 (pow.f64 eps 3) 1/32) (pow.f64 x 5)))))))
(*.f64 1/2 (/.f64 eps x))
(/.f64 (*.f64 eps 1/2) x)
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 eps (.f64 eps 1/8)) (pow.f64 x 3)))
(fma.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 1/16 (pow.f64 eps 3)) (pow.f64 x 5))))
(fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (fma.f64 1/2 (/.f64 eps x) (/.f64 1/16 (/.f64 (pow.f64 x 5) (pow.f64 eps 3)))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps) (.f64 (/.f64 1/16 (pow.f64 x 5)) (pow.f64 eps 3))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 5/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7))) (+.f64 (.f64 1/2 (/.f64 eps x)) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 -1 (/.f64 (.f64 (pow.f64 eps 4) -5/128) (pow.f64 x 7)) (fma.f64 1/2 (/.f64 eps x) (/.f64 (*.f64 1/16 (pow.f64 eps 3)) (pow.f64 x 5)))))
(fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (-.f64 (fma.f64 1/2 (/.f64 eps x) (/.f64 1/16 (/.f64 (pow.f64 x 5) (pow.f64 eps 3)))) (/.f64 (pow.f64 eps 4) (/.f64 (pow.f64 x 7) -5/128))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (.f64 (/.f64 5/128 (pow.f64 x 7)) (pow.f64 eps 4)))))
(*.f64 (sqrt.f64 -1) (sqrt.f64 eps))
(+.f64 x (*.f64 (sqrt.f64 -1) (sqrt.f64 eps)))
(fma.f64 (sqrt.f64 -1) (sqrt.f64 eps) x)
(+.f64 x (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (*.f64 (sqrt.f64 -1) (sqrt.f64 eps))))
(+.f64 x (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (.f64 x x) (sqrt.f64 -1))) (*.f64 (sqrt.f64 -1) (sqrt.f64 eps))))
(fma.f64 (sqrt.f64 (/.f64 1 eps)) (.f64 1/2 (.f64 (/.f64 x (sqrt.f64 -1)) x)) (fma.f64 (sqrt.f64 -1) (sqrt.f64 eps) x))
(fma.f64 (sqrt.f64 -1) (sqrt.f64 eps) (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 eps)) (.f64 (/.f64 x (sqrt.f64 -1)) x)) x))
(+.f64 (.f64 -1/8 (.f64 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3)) (sqrt.f64 (/.f64 1 (pow.f64 eps 3))))) (+.f64 x (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (*.f64 (sqrt.f64 -1) (sqrt.f64 eps)))))
(fma.f64 -1/8 (.f64 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3)) (sqrt.f64 (/.f64 1 (pow.f64 eps 3)))) (+.f64 x (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (.f64 x x) (sqrt.f64 -1))) (.f64 (sqrt.f64 -1) (sqrt.f64 eps)))))
(+.f64 (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (.f64 x x) (sqrt.f64 -1))) (.f64 (sqrt.f64 -1) (sqrt.f64 eps))) (fma.f64 -1/8 (.f64 (/.f64 (pow.f64 x 4) (*.f64 -1 (sqrt.f64 -1))) (sqrt.f64 (/.f64 1 (pow.f64 eps 3)))) x))
(fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 eps 3))) (.f64 1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1))) (fma.f64 (sqrt.f64 (/.f64 1 eps)) (.f64 1/2 (*.f64 (/.f64 x (sqrt.f64 -1)) x)) (fma.f64 (sqrt.f64 -1) (sqrt.f64 eps) x)))
(fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 eps 3))) (.f64 1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1))) (fma.f64 (sqrt.f64 -1) (sqrt.f64 eps) (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 eps)) (*.f64 (/.f64 x (sqrt.f64 -1)) x)) x)))
(*.f64 2 x)
(*.f64 x 2)
(+.f64 (.f64 -1/2 (/.f64 eps x)) (.f64 2 x))
(fma.f64 -1/2 (/.f64 eps x) (*.f64 x 2))
(fma.f64 x 2 (/.f64 (*.f64 eps -1/2) x))
(fma.f64 x 2 (*.f64 (/.f64 eps x) -1/2))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (*.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 2 x (/.f64 (.f64 (.f64 eps eps) -1/8) (pow.f64 x 3))))
(fma.f64 (/.f64 eps x) -1/2 (fma.f64 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) -1/8 (*.f64 x 2)))
(fma.f64 x 2 (fma.f64 (/.f64 eps x) -1/2 (/.f64 eps (/.f64 (pow.f64 x 3) (*.f64 eps -1/8)))))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 2 x (fma.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (/.f64 (.f64 (.f64 eps eps) -1/8) (pow.f64 x 3)))))
(fma.f64 (/.f64 eps x) -1/2 (fma.f64 x 2 (fma.f64 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) -1/8 (/.f64 -1/16 (/.f64 (pow.f64 x 5) (pow.f64 eps 3))))))
(fma.f64 (/.f64 eps x) -1/2 (fma.f64 x 2 (fma.f64 (*.f64 (/.f64 eps (pow.f64 x 3)) eps) -1/8 (/.f64 -1/16 (/.f64 (pow.f64 x 5) (pow.f64 eps 3))))))
(*.f64 1/2 (/.f64 eps x))
(/.f64 (*.f64 eps 1/2) x)
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 eps (.f64 eps 1/8)) (pow.f64 x 3)))
(fma.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 eps x) (/.f64 (.f64 1/16 (pow.f64 eps 3)) (pow.f64 x 5))))
(fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (fma.f64 1/2 (/.f64 eps x) (/.f64 1/16 (/.f64 (pow.f64 x 5) (pow.f64 eps 3)))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps) (.f64 (/.f64 1/16 (pow.f64 x 5)) (pow.f64 eps 3))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 1/16 (pow.f64 eps 4)) (pow.f64 (.f64 -1/8 (pow.f64 eps 2)) 2)) (pow.f64 x 7))) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))))))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 -1 (/.f64 (.f64 (pow.f64 eps 4) -5/128) (pow.f64 x 7)) (fma.f64 1/2 (/.f64 eps x) (/.f64 (*.f64 1/16 (pow.f64 eps 3)) (pow.f64 x 5)))))
(fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (-.f64 (fma.f64 1/2 (/.f64 eps x) (/.f64 1/16 (/.f64 (pow.f64 x 5) (pow.f64 eps 3)))) (/.f64 (pow.f64 eps 4) (/.f64 (pow.f64 x 7) -5/128))))
(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (.f64 (/.f64 5/128 (pow.f64 x 7)) (pow.f64 eps 4)))))
(*.f64 2 x)
(*.f64 x 2)
(+.f64 (.f64 -1/2 (/.f64 eps x)) (.f64 2 x))
(fma.f64 -1/2 (/.f64 eps x) (*.f64 x 2))
(fma.f64 x 2 (/.f64 (*.f64 eps -1/2) x))
(fma.f64 x 2 (*.f64 (/.f64 eps x) -1/2))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (*.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 2 x (/.f64 (.f64 (.f64 eps eps) -1/8) (pow.f64 x 3))))
(fma.f64 (/.f64 eps x) -1/2 (fma.f64 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) -1/8 (*.f64 x 2)))
(fma.f64 x 2 (fma.f64 (/.f64 eps x) -1/2 (/.f64 eps (/.f64 (pow.f64 x 3) (*.f64 eps -1/8)))))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
(fma.f64 -1/2 (/.f64 eps x) (fma.f64 2 x (fma.f64 -1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (/.f64 (.f64 (.f64 eps eps) -1/8) (pow.f64 x 3)))))
(fma.f64 (/.f64 eps x) -1/2 (fma.f64 x 2 (fma.f64 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) -1/8 (/.f64 -1/16 (/.f64 (pow.f64 x 5) (pow.f64 eps 3))))))
(fma.f64 (/.f64 eps x) -1/2 (fma.f64 x 2 (fma.f64 (*.f64 (/.f64 eps (pow.f64 x 3)) eps) -1/8 (/.f64 -1/16 (/.f64 (pow.f64 x 5) (pow.f64 eps 3))))))

localize6.0ms (0.1%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

localize10.0ms (0.2%)

Compiler: Compiled 13 to 6 computations (53.8% saved)

localize11.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (sqrt.f64 (neg.f64 eps)))

Compiler

Compiled 14 to 5 computations (64.3% saved)

series7.0ms (0.1%)

Counts

1 → 13

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	eps	@	0	(-.f64 x (sqrt.f64 (neg.f64 eps)))
1.0ms	eps	@	inf	(-.f64 x (sqrt.f64 (neg.f64 eps)))
1.0ms	x	@	0	(-.f64 x (sqrt.f64 (neg.f64 eps)))
1.0ms	eps	@	-inf	(-.f64 x (sqrt.f64 (neg.f64 eps)))
1.0ms	x	@	inf	(-.f64 x (sqrt.f64 (neg.f64 eps)))

rewrite93.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

625×	`pow1_binary64`
583×	`add-log-exp_binary64`
582×	`log1p-expm1-u_binary64`
582×	`expm1-log1p-u_binary64`
569×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	133	6
2	1911	6

Stop Event

1×	node limit

Counts

1 → 35

Calls

Call 1

Inputs
(-.f64 x (sqrt.f64 (neg.f64 eps)))

Outputs

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

simplify36.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

101×	`fma-def_binary64`
56×	`fma-neg_binary64`
27×	`cancel-sign-sub-inv_binary64`
17×	`sub-neg_binary64`
13×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	121
1	16	112
2	32	112
3	45	112
4	57	112
5	88	112
6	148	112
7	196	112
8	254	112
9	341	112
10	391	112
11	397	112

Stop Event

1×

saturated

Counts

48 → 40

Calls

Call 1

Inputs
(.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1)))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
x
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
x
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
x

Outputs
(.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1)))
(neg.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)))
(*.f64 (sqrt.f64 -1) (neg.f64 (sqrt.f64 eps)))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
(fma.f64 -1 (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
(fma.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 -1) x)
(fma.f64 (sqrt.f64 -1) (neg.f64 (sqrt.f64 eps)) x)
(-.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
(fma.f64 -1 (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
(fma.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 -1) x)
(fma.f64 (sqrt.f64 -1) (neg.f64 (sqrt.f64 eps)) x)
(-.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
(fma.f64 -1 (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
(fma.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 -1) x)
(fma.f64 (sqrt.f64 -1) (neg.f64 (sqrt.f64 eps)) x)
(-.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)))
x
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
(fma.f64 -1 (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
(fma.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 -1) x)
(fma.f64 (sqrt.f64 -1) (neg.f64 (sqrt.f64 eps)) x)
(-.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
(fma.f64 -1 (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
(fma.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 -1) x)
(fma.f64 (sqrt.f64 -1) (neg.f64 (sqrt.f64 eps)) x)
(-.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
(fma.f64 -1 (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
(fma.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 -1) x)
(fma.f64 (sqrt.f64 -1) (neg.f64 (sqrt.f64 eps)) x)
(-.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)))
x
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
(fma.f64 -1 (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
(fma.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 -1) x)
(fma.f64 (sqrt.f64 -1) (neg.f64 (sqrt.f64 eps)) x)
(-.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
(fma.f64 -1 (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
(fma.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 -1) x)
(fma.f64 (sqrt.f64 -1) (neg.f64 (sqrt.f64 eps)) x)
(-.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 eps) (sqrt.f64 -1))) x)
(fma.f64 -1 (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
(fma.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 -1) x)
(fma.f64 (sqrt.f64 -1) (neg.f64 (sqrt.f64 eps)) x)
(-.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)))
x

localize39.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1/2 x) (/.f64 1/8 (/.f64 (pow.f64 x 3) eps)))
✓	0.3b	(/.f64 1/8 (/.f64 (pow.f64 x 3) eps))
✓	7.4b	(*.f64 eps (+.f64 (/.f64 1/2 x) (/.f64 1/8 (/.f64 (pow.f64 x 3) eps))))
✓	7.5b	(/.f64 (pow.f64 x 3) eps)

Compiler

Compiled 49 to 34 computations (30.6% saved)

series29.0ms (0.5%)

Counts

4 → 72

Calls

24 calls:

Time	Variable		Point	Expression
6.0ms	eps	@	-inf	(/.f64 1/8 (/.f64 (pow.f64 x 3) eps))
2.0ms	eps	@	0	(*.f64 eps (+.f64 (/.f64 1/2 x) (/.f64 1/8 (/.f64 (pow.f64 x 3) eps))))
2.0ms	x	@	0	(*.f64 eps (+.f64 (/.f64 1/2 x) (/.f64 1/8 (/.f64 (pow.f64 x 3) eps))))
1.0ms	eps	@	0	(/.f64 (pow.f64 x 3) eps)
1.0ms	x	@	0	(/.f64 (pow.f64 x 3) eps)

rewrite145.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

691×	`log-prod_binary64`
407×	`fma-def_binary64`
264×	`log-div_binary64`
248×	`pow1/3_binary64`
243×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	52
1	288	48
2	4216	48

Stop Event

1×	node limit

Counts

4 → 223

Calls

Call 1

Inputs
(/.f64 (pow.f64 x 3) eps)
(*.f64 eps (+.f64 (/.f64 1/2 x) (/.f64 1/8 (/.f64 (pow.f64 x 3) eps))))
(/.f64 1/8 (/.f64 (pow.f64 x 3) eps))
(+.f64 (/.f64 1/2 x) (/.f64 1/8 (/.f64 (pow.f64 x 3) eps)))

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

simplify118.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

688×	`associate-/r*_binary64`
682×	`associate-/l/_binary64`
657×	`associate-*l/_binary64`
644×	`fma-def_binary64`
478×	`associate-l_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	21	954
1	49	954
2	114	954
3	324	936
4	1403	900
5	6369	900
6	7853	900

Stop Event

1×	node limit

Counts

295 → 231

Calls

Call 1

Inputs
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 x)
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 x)
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 x)
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))

Outputs
(*.f64 1/2 (/.f64 eps x))
(/.f64 eps (/.f64 x 1/2))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps)))
(.f64 (/.f64 eps x) (+.f64 1/2 (.f64 (/.f64 eps x) (/.f64 1/8 x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps)))
(.f64 (/.f64 eps x) (+.f64 1/2 (.f64 (/.f64 eps x) (/.f64 1/8 x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps)))
(.f64 (/.f64 eps x) (+.f64 1/2 (.f64 (/.f64 eps x) (/.f64 1/8 x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))
(/.f64 (.f64 1/8 (.f64 eps eps)) (pow.f64 x 3))
(*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)))
(.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps))
(.f64 1/8 (.f64 eps (/.f64 eps (pow.f64 x 3))))
(.f64 eps (.f64 eps (/.f64 1/8 (pow.f64 x 3))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps)))
(.f64 (/.f64 eps x) (+.f64 1/2 (.f64 (/.f64 eps x) (/.f64 1/8 x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps)))
(.f64 (/.f64 eps x) (+.f64 1/2 (.f64 (/.f64 eps x) (/.f64 1/8 x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps)))
(.f64 (/.f64 eps x) (+.f64 1/2 (.f64 (/.f64 eps x) (/.f64 1/8 x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))
(/.f64 (.f64 1/8 (.f64 eps eps)) (pow.f64 x 3))
(*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)))
(.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps))
(.f64 1/8 (.f64 eps (/.f64 eps (pow.f64 x 3))))
(.f64 eps (.f64 eps (/.f64 1/8 (pow.f64 x 3))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps)))
(.f64 (/.f64 eps x) (+.f64 1/2 (.f64 (/.f64 eps x) (/.f64 1/8 x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps)))
(.f64 (/.f64 eps x) (+.f64 1/2 (.f64 (/.f64 eps x) (/.f64 1/8 x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps)))
(.f64 (/.f64 eps x) (+.f64 1/2 (.f64 (/.f64 eps x) (/.f64 1/8 x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))
(/.f64 (.f64 1/8 (.f64 eps eps)) (pow.f64 x 3))
(*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)))
(.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps))
(.f64 1/8 (.f64 eps (/.f64 eps (pow.f64 x 3))))
(.f64 eps (.f64 eps (/.f64 1/8 (pow.f64 x 3))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps)))
(.f64 (/.f64 eps x) (+.f64 1/2 (.f64 (/.f64 eps x) (/.f64 1/8 x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps)))
(.f64 (/.f64 eps x) (+.f64 1/2 (.f64 (/.f64 eps x) (/.f64 1/8 x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps)))
(.f64 (/.f64 eps x) (+.f64 1/2 (.f64 (/.f64 eps x) (/.f64 1/8 x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(*.f64 1/2 (/.f64 eps x))
(/.f64 eps (/.f64 x 1/2))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps)))
(.f64 (/.f64 eps x) (+.f64 1/2 (.f64 (/.f64 eps x) (/.f64 1/8 x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps)))
(.f64 (/.f64 eps x) (+.f64 1/2 (.f64 (/.f64 eps x) (/.f64 1/8 x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps)))
(.f64 (/.f64 eps x) (+.f64 1/2 (.f64 (/.f64 eps x) (/.f64 1/8 x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(*.f64 1/2 (/.f64 eps x))
(/.f64 eps (/.f64 x 1/2))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps)))
(.f64 (/.f64 eps x) (+.f64 1/2 (.f64 (/.f64 eps x) (/.f64 1/8 x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps)))
(.f64 (/.f64 eps x) (+.f64 1/2 (.f64 (/.f64 eps x) (/.f64 1/8 x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (.f64 1/8 (.f64 (/.f64 eps (pow.f64 x 3)) eps)))
(.f64 (/.f64 eps x) (+.f64 1/2 (.f64 (/.f64 eps x) (/.f64 1/8 x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(/.f64 1/2 x)
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(/.f64 1/2 x)
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(/.f64 1/2 x)
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))

eval246.0ms (4.6%)

Compiler: Compiled 11725 to 5197 computations (55.7% saved)

prune79.0ms (1.5%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	543	4	547
Fresh	0	0	0
Picked	1	0	1
Done	1	4	5
Total	545	8	553

Error

Counts

553 → 8

Alt Table

Click to see full alt table

Status	Error	Program
▶	24.5b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (neg.f64 eps))))
✓	26.5b	(-.f64 x (sqrt.f64 (neg.f64 eps)))
▶	37.8b	(.f64 eps (+.f64 (/.f64 1/2 x) (/.f64 1/8 (.f64 (/.f64 (*.f64 x x) 1) (/.f64 x eps)))))
▶	36.1b	(*.f64 eps (/.f64 1/2 x))
✓	36.0b	(*.f64 1/2 (/.f64 eps x))
✓	24.0b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
	61.9b	x
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))

Compiler

Compiled 90 to 54 computations (40% saved)

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1/2 x) (/.f64 1/8 (.f64 (/.f64 (.f64 x x) 1) (/.f64 x eps))))
✓	0.3b	(/.f64 1/8 (.f64 (/.f64 (.f64 x x) 1) (/.f64 x eps)))
✓	2.1b	(.f64 (/.f64 (.f64 x x) 1) (/.f64 x eps))
✓	7.4b	(.f64 eps (+.f64 (/.f64 1/2 x) (/.f64 1/8 (.f64 (/.f64 (*.f64 x x) 1) (/.f64 x eps)))))

Compiler

Compiled 73 to 36 computations (50.7% saved)

series6.0ms (0.1%)

Counts

4 → 96

Calls

24 calls:

Time	Variable		Point	Expression
0.0ms	eps	@	0	(.f64 eps (+.f64 (/.f64 1/2 x) (/.f64 1/8 (.f64 (/.f64 (*.f64 x x) 1) (/.f64 x eps)))))
0.0ms	eps	@	inf	(.f64 eps (+.f64 (/.f64 1/2 x) (/.f64 1/8 (.f64 (/.f64 (*.f64 x x) 1) (/.f64 x eps)))))
0.0ms	x	@	-inf	(.f64 eps (+.f64 (/.f64 1/2 x) (/.f64 1/8 (.f64 (/.f64 (*.f64 x x) 1) (/.f64 x eps)))))
0.0ms	x	@	inf	(.f64 eps (+.f64 (/.f64 1/2 x) (/.f64 1/8 (.f64 (/.f64 (*.f64 x x) 1) (/.f64 x eps)))))
0.0ms	eps	@	-inf	(.f64 eps (+.f64 (/.f64 1/2 x) (/.f64 1/8 (.f64 (/.f64 (*.f64 x x) 1) (/.f64 x eps)))))

rewrite99.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

744×	`log-prod_binary64`
412×	`fma-def_binary64`
384×	`log-div_binary64`
258×	`expm1-udef_binary64`
258×	`log1p-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	64
1	327	52
2	4569	48

Stop Event

1×	node limit

Counts

4 → 229

Calls

Call 1

Inputs
(.f64 eps (+.f64 (/.f64 1/2 x) (/.f64 1/8 (.f64 (/.f64 (*.f64 x x) 1) (/.f64 x eps)))))
(.f64 (/.f64 (.f64 x x) 1) (/.f64 x eps))
(/.f64 1/8 (.f64 (/.f64 (.f64 x x) 1) (/.f64 x eps)))
(+.f64 (/.f64 1/2 x) (/.f64 1/8 (.f64 (/.f64 (.f64 x x) 1) (/.f64 x eps))))

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

simplify94.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

714×	`associate-/l/_binary64`
690×	`associate-/r*_binary64`
646×	`fma-def_binary64`
515×	`associate-l_binary64`
511×	`associate-*r/_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	22	1122
1	50	1122
2	117	1122
3	328	1104
4	1440	1068
5	6002	1068
6	7638	1068

Stop Event

1×	node limit

Counts

325 → 240

Calls

Call 1

Inputs
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 x)
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 x)
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 x)
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))

Outputs
(*.f64 1/2 (/.f64 eps x))
(/.f64 (*.f64 1/2 eps) x)
(/.f64 eps (/.f64 x 1/2))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) 1/8)))
(.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (*.f64 x x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) 1/8)))
(.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (*.f64 x x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) 1/8)))
(.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (*.f64 x x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))
(.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)))
(/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) 1/8))
(.f64 (.f64 eps eps) (/.f64 1/8 (pow.f64 x 3)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) 1/8)))
(.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (*.f64 x x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) 1/8)))
(.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (*.f64 x x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) 1/8)))
(.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (*.f64 x x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))
(.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)))
(/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) 1/8))
(.f64 (.f64 eps eps) (/.f64 1/8 (pow.f64 x 3)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) 1/8)))
(.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (*.f64 x x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) 1/8)))
(.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (*.f64 x x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) 1/8)))
(.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (*.f64 x x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))
(.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)))
(/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) 1/8))
(.f64 (.f64 eps eps) (/.f64 1/8 (pow.f64 x 3)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) 1/8)))
(.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (*.f64 x x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) 1/8)))
(.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (*.f64 x x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) 1/8)))
(.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (*.f64 x x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(*.f64 1/2 (/.f64 eps x))
(/.f64 (*.f64 1/2 eps) x)
(/.f64 eps (/.f64 x 1/2))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) 1/8)))
(.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (*.f64 x x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) 1/8)))
(.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (*.f64 x x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) 1/8)))
(.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (*.f64 x x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(*.f64 1/2 (/.f64 eps x))
(/.f64 (*.f64 1/2 eps) x)
(/.f64 eps (/.f64 x 1/2))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) 1/8)))
(.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (*.f64 x x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) 1/8)))
(.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (*.f64 x x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) 1/8)))
(.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (*.f64 x x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 (/.f64 1/8 (pow.f64 x 3)) eps)
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 (/.f64 1/8 (pow.f64 x 3)) eps)
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 (/.f64 1/8 (pow.f64 x 3)) eps)
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 (/.f64 1/8 (pow.f64 x 3)) eps)
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 (/.f64 1/8 (pow.f64 x 3)) eps)
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 (/.f64 1/8 (pow.f64 x 3)) eps)
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 (/.f64 1/8 (pow.f64 x 3)) eps)
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 (/.f64 1/8 (pow.f64 x 3)) eps)
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 (/.f64 1/8 (pow.f64 x 3)) eps)
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 (/.f64 1/8 (pow.f64 x 3)) eps)
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 (/.f64 1/8 (pow.f64 x 3)) eps)
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 (/.f64 1/8 (pow.f64 x 3)) eps)
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 (/.f64 1/8 (pow.f64 x 3)) eps)
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 (/.f64 1/8 (pow.f64 x 3)) eps)
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 (/.f64 1/8 (pow.f64 x 3)) eps)
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 (/.f64 1/8 (pow.f64 x 3)) eps)
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 (/.f64 1/8 (pow.f64 x 3)) eps)
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 (/.f64 1/8 (pow.f64 x 3)) eps)
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 (/.f64 1/8 (pow.f64 x 3)) eps)
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 (/.f64 1/8 (pow.f64 x 3)) eps)
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 (/.f64 1/8 (pow.f64 x 3)) eps)
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 (/.f64 1/8 (pow.f64 x 3)) eps)
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 (/.f64 1/8 (pow.f64 x 3)) eps)
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 (/.f64 1/8 (pow.f64 x 3)) eps)
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 (/.f64 1/8 (pow.f64 x 3)) eps)
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(/.f64 1/2 x)
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(/.f64 1/2 x)
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(/.f64 1/2 x)
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 (/.f64 1/8 (pow.f64 x 3)) eps)
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 (/.f64 1/8 (pow.f64 x 3)) eps)
(*.f64 eps (/.f64 1/8 (pow.f64 x 3)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 eps (/.f64 1/2 x))

Compiler

Compiled 13 to 8 computations (38.5% saved)

series4.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite50.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

616×	`pow1_binary64`
572×	`add-log-exp_binary64`
572×	`log1p-expm1-u_binary64`
572×	`expm1-log1p-u_binary64`
561×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	128	7
2	1557	7

Stop Event

1×	node limit

Counts

1 → 20

Calls

Call 1

Inputs
(*.f64 eps (/.f64 1/2 x))

Outputs

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

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
1×	`associate-*r/_binary64`
1×	`associate-*l/_binary64`
1×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	168
1	9	168
2	13	168
3	17	168
4	18	168

Stop Event

1×

saturated

Counts

44 → 21

Calls

Call 1

Inputs
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))

Outputs
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))

localize13.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (sqrt.f64 (neg.f64 eps)))
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (neg.f64 eps))))

Compiler

Compiled 48 to 9 computations (81.3% saved)

series20.0ms (0.4%)

Counts

2 → 26

Calls

12 calls:

Time	Variable		Point	Expression
12.0ms	eps	@	inf	(+.f64 x (sqrt.f64 (neg.f64 eps)))
2.0ms	eps	@	inf	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (neg.f64 eps))))
2.0ms	x	@	inf	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (neg.f64 eps))))
1.0ms	eps	@	-inf	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (neg.f64 eps))))
1.0ms	eps	@	0	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (neg.f64 eps))))

rewrite68.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

444×	`log-prod_binary64`
417×	`fma-def_binary64`
296×	`fma-neg_binary64`
287×	`pow-prod-down_binary64`
229×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	255	15
2	4012	15

Stop Event

1×	node limit

Counts

2 → 94

Calls

Call 1

Inputs
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (neg.f64 eps))))
(+.f64 x (sqrt.f64 (neg.f64 eps)))

Outputs

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

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

simplify62.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

634×	`fma-neg_binary64`
593×	`cancel-sign-sub-inv_binary64`
411×	`div-sub_binary64`
310×	`neg-sub0_binary64`
294×	`neg-mul-1_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	60	513
1	170	450
2	568	406
3	2491	387
4	6123	387

Stop Event

1×	node limit

Counts

120 → 114

Calls

Call 1

Inputs
(*.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps)) (.f64 -1 (/.f64 x (pow.f64 (sqrt.f64 -1) 2))))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps)) (+.f64 (.f64 -1 (/.f64 x (pow.f64 (sqrt.f64 -1) 2))) (*.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 -1) 3)))))
(+.f64 (.f64 -1 (/.f64 (pow.f64 x 3) (.f64 (pow.f64 (sqrt.f64 -1) 4) eps))) (+.f64 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps)) (+.f64 (.f64 -1 (/.f64 x (pow.f64 (sqrt.f64 -1) 2))) (*.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 -1) 3))))))
(/.f64 eps x)
(+.f64 (.f64 -1 (.f64 (sqrt.f64 (pow.f64 eps 3)) (/.f64 (sqrt.f64 -1) (pow.f64 x 2)))) (/.f64 eps x))
(+.f64 (/.f64 (.f64 (pow.f64 eps 2) (pow.f64 (sqrt.f64 -1) 2)) (pow.f64 x 3)) (+.f64 (.f64 -1 (*.f64 (sqrt.f64 (pow.f64 eps 3)) (/.f64 (sqrt.f64 -1) (pow.f64 x 2)))) (/.f64 eps x)))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 (pow.f64 eps 3)) (/.f64 (sqrt.f64 -1) (pow.f64 x 2)))) (+.f64 (/.f64 eps x) (+.f64 (/.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) (pow.f64 eps 2)) (pow.f64 x 3)) (.f64 -1 (*.f64 (/.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4)) (sqrt.f64 (pow.f64 eps 5)))))))
(/.f64 eps x)
(+.f64 (.f64 -1 (.f64 (sqrt.f64 (pow.f64 eps 3)) (/.f64 (sqrt.f64 -1) (pow.f64 x 2)))) (/.f64 eps x))
(+.f64 (/.f64 (.f64 (pow.f64 eps 2) (pow.f64 (sqrt.f64 -1) 2)) (pow.f64 x 3)) (+.f64 (.f64 -1 (*.f64 (sqrt.f64 (pow.f64 eps 3)) (/.f64 (sqrt.f64 -1) (pow.f64 x 2)))) (/.f64 eps x)))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 (pow.f64 eps 3)) (/.f64 (sqrt.f64 -1) (pow.f64 x 2)))) (+.f64 (/.f64 eps x) (+.f64 (/.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) (pow.f64 eps 2)) (pow.f64 x 3)) (.f64 -1 (*.f64 (sqrt.f64 (pow.f64 eps 5)) (/.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4)))))))
(/.f64 eps x)
(*.f64 (sqrt.f64 eps) (sqrt.f64 -1))
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
x
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
x
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
x

Outputs
(*.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps))
(/.f64 (sqrt.f64 eps) (sqrt.f64 -1))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps)) (.f64 -1 (/.f64 x (pow.f64 (sqrt.f64 -1) 2))))
(fma.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps) (neg.f64 (/.f64 x (pow.f64 (sqrt.f64 -1) 2))))
(-.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 -1)) (/.f64 x -1))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
(+.f64 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps)) (+.f64 (.f64 -1 (/.f64 x (pow.f64 (sqrt.f64 -1) 2))) (*.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 -1) 3)))))
(fma.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps) (fma.f64 -1 (/.f64 x (pow.f64 (sqrt.f64 -1) 2)) (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (.f64 x x) (pow.f64 (sqrt.f64 -1) 3)))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 -1)) (-.f64 (.f64 (sqrt.f64 (/.f64 1 eps)) (.f64 (/.f64 x -1) (/.f64 x (sqrt.f64 -1)))) (/.f64 x -1)))
(+.f64 x (fma.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 x (/.f64 (neg.f64 (sqrt.f64 -1)) x)) (/.f64 (sqrt.f64 eps) (sqrt.f64 -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 -1)) (fma.f64 (neg.f64 x) (*.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 x (sqrt.f64 -1))) x))
(+.f64 (.f64 -1 (/.f64 (pow.f64 x 3) (.f64 (pow.f64 (sqrt.f64 -1) 4) eps))) (+.f64 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps)) (+.f64 (.f64 -1 (/.f64 x (pow.f64 (sqrt.f64 -1) 2))) (*.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 -1) 3))))))
(fma.f64 -1 (/.f64 (pow.f64 x 3) (.f64 eps (pow.f64 (sqrt.f64 -1) 4))) (fma.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 eps) (fma.f64 -1 (/.f64 x (pow.f64 (sqrt.f64 -1) 2)) (.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 -1) 3))))))
(-.f64 (+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 -1)) (-.f64 (.f64 (sqrt.f64 (/.f64 1 eps)) (.f64 (/.f64 x -1) (/.f64 x (sqrt.f64 -1)))) (/.f64 x -1))) (/.f64 (pow.f64 x 3) (*.f64 1 eps)))
(+.f64 x (-.f64 (fma.f64 (sqrt.f64 (/.f64 1 eps)) (/.f64 x (/.f64 (neg.f64 (sqrt.f64 -1)) x)) (/.f64 (sqrt.f64 eps) (sqrt.f64 -1))) (/.f64 (pow.f64 x 3) eps)))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 -1)) (+.f64 x (.f64 (.f64 x x) (-.f64 (/.f64 (sqrt.f64 (/.f64 1 eps)) (neg.f64 (sqrt.f64 -1))) (/.f64 x eps)))))
(/.f64 eps x)
(+.f64 (.f64 -1 (.f64 (sqrt.f64 (pow.f64 eps 3)) (/.f64 (sqrt.f64 -1) (pow.f64 x 2)))) (/.f64 eps x))
(fma.f64 -1 (.f64 (sqrt.f64 (pow.f64 eps 3)) (/.f64 (sqrt.f64 -1) (.f64 x x))) (/.f64 eps x))
(-.f64 (/.f64 eps x) (.f64 (sqrt.f64 (pow.f64 eps 3)) (/.f64 (sqrt.f64 -1) (.f64 x x))))
(-.f64 (/.f64 eps x) (.f64 (/.f64 (pow.f64 eps 3/2) (.f64 x x)) (sqrt.f64 -1)))
(fma.f64 (/.f64 (sqrt.f64 -1) (*.f64 x x)) (neg.f64 (pow.f64 eps 3/2)) (/.f64 eps x))
(+.f64 (/.f64 (.f64 (pow.f64 eps 2) (pow.f64 (sqrt.f64 -1) 2)) (pow.f64 x 3)) (+.f64 (.f64 -1 (*.f64 (sqrt.f64 (pow.f64 eps 3)) (/.f64 (sqrt.f64 -1) (pow.f64 x 2)))) (/.f64 eps x)))
(+.f64 (fma.f64 -1 (.f64 (sqrt.f64 (pow.f64 eps 3)) (/.f64 (sqrt.f64 -1) (.f64 x x))) (/.f64 eps x)) (/.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) (.f64 eps eps)) (pow.f64 x 3)))
(+.f64 (/.f64 eps x) (-.f64 (.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1) (.f64 (sqrt.f64 (pow.f64 eps 3)) (/.f64 (sqrt.f64 -1) (.f64 x x)))))
(-.f64 (fma.f64 (/.f64 -1 (pow.f64 x 3)) (.f64 eps eps) (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 3/2) (*.f64 x x)) (sqrt.f64 -1)))
(-.f64 (/.f64 eps x) (fma.f64 (pow.f64 eps 3/2) (/.f64 (sqrt.f64 -1) (.f64 x x)) (/.f64 (.f64 eps eps) (pow.f64 x 3))))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 (pow.f64 eps 3)) (/.f64 (sqrt.f64 -1) (pow.f64 x 2)))) (+.f64 (/.f64 eps x) (+.f64 (/.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) (pow.f64 eps 2)) (pow.f64 x 3)) (.f64 -1 (*.f64 (/.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4)) (sqrt.f64 (pow.f64 eps 5)))))))
(+.f64 (fma.f64 -1 (.f64 (sqrt.f64 (pow.f64 eps 3)) (/.f64 (sqrt.f64 -1) (.f64 x x))) (/.f64 eps x)) (+.f64 (/.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) (.f64 eps eps)) (pow.f64 x 3)) (neg.f64 (*.f64 (/.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4)) (sqrt.f64 (pow.f64 eps 5))))))
(+.f64 (-.f64 (/.f64 eps x) (.f64 (sqrt.f64 (pow.f64 eps 3)) (/.f64 (sqrt.f64 -1) (.f64 x x)))) (-.f64 (.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1) (/.f64 (*.f64 (sqrt.f64 -1) (neg.f64 (fabs.f64 (pow.f64 eps 5/2)))) (pow.f64 x 4))))
(-.f64 (fma.f64 (pow.f64 eps 5/2) (/.f64 1 (/.f64 (pow.f64 x 4) (sqrt.f64 -1))) (fma.f64 (/.f64 -1 (pow.f64 x 3)) (.f64 eps eps) (/.f64 eps x))) (.f64 (/.f64 (pow.f64 eps 3/2) (*.f64 x x)) (sqrt.f64 -1)))
(-.f64 (fma.f64 (pow.f64 eps 5/2) (/.f64 (sqrt.f64 -1) (pow.f64 x 4)) (/.f64 eps x)) (fma.f64 (pow.f64 eps 3/2) (/.f64 (sqrt.f64 -1) (.f64 x x)) (/.f64 (.f64 eps eps) (pow.f64 x 3))))
(/.f64 eps x)
(+.f64 (.f64 -1 (.f64 (sqrt.f64 (pow.f64 eps 3)) (/.f64 (sqrt.f64 -1) (pow.f64 x 2)))) (/.f64 eps x))
(fma.f64 -1 (.f64 (sqrt.f64 (pow.f64 eps 3)) (/.f64 (sqrt.f64 -1) (.f64 x x))) (/.f64 eps x))
(-.f64 (/.f64 eps x) (.f64 (sqrt.f64 (pow.f64 eps 3)) (/.f64 (sqrt.f64 -1) (.f64 x x))))
(-.f64 (/.f64 eps x) (.f64 (/.f64 (pow.f64 eps 3/2) (.f64 x x)) (sqrt.f64 -1)))
(fma.f64 (/.f64 (sqrt.f64 -1) (*.f64 x x)) (neg.f64 (pow.f64 eps 3/2)) (/.f64 eps x))
(+.f64 (/.f64 (.f64 (pow.f64 eps 2) (pow.f64 (sqrt.f64 -1) 2)) (pow.f64 x 3)) (+.f64 (.f64 -1 (*.f64 (sqrt.f64 (pow.f64 eps 3)) (/.f64 (sqrt.f64 -1) (pow.f64 x 2)))) (/.f64 eps x)))
(+.f64 (fma.f64 -1 (.f64 (sqrt.f64 (pow.f64 eps 3)) (/.f64 (sqrt.f64 -1) (.f64 x x))) (/.f64 eps x)) (/.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) (.f64 eps eps)) (pow.f64 x 3)))
(+.f64 (/.f64 eps x) (-.f64 (.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1) (.f64 (sqrt.f64 (pow.f64 eps 3)) (/.f64 (sqrt.f64 -1) (.f64 x x)))))
(-.f64 (fma.f64 (/.f64 -1 (pow.f64 x 3)) (.f64 eps eps) (/.f64 eps x)) (.f64 (/.f64 (pow.f64 eps 3/2) (*.f64 x x)) (sqrt.f64 -1)))
(-.f64 (/.f64 eps x) (fma.f64 (pow.f64 eps 3/2) (/.f64 (sqrt.f64 -1) (.f64 x x)) (/.f64 (.f64 eps eps) (pow.f64 x 3))))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 (pow.f64 eps 3)) (/.f64 (sqrt.f64 -1) (pow.f64 x 2)))) (+.f64 (/.f64 eps x) (+.f64 (/.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) (pow.f64 eps 2)) (pow.f64 x 3)) (.f64 -1 (*.f64 (sqrt.f64 (pow.f64 eps 5)) (/.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4)))))))
(+.f64 (fma.f64 -1 (.f64 (sqrt.f64 (pow.f64 eps 3)) (/.f64 (sqrt.f64 -1) (.f64 x x))) (/.f64 eps x)) (+.f64 (/.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) (.f64 eps eps)) (pow.f64 x 3)) (neg.f64 (*.f64 (/.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4)) (sqrt.f64 (pow.f64 eps 5))))))
(+.f64 (-.f64 (/.f64 eps x) (.f64 (sqrt.f64 (pow.f64 eps 3)) (/.f64 (sqrt.f64 -1) (.f64 x x)))) (-.f64 (.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1) (/.f64 (*.f64 (sqrt.f64 -1) (neg.f64 (fabs.f64 (pow.f64 eps 5/2)))) (pow.f64 x 4))))
(-.f64 (fma.f64 (pow.f64 eps 5/2) (/.f64 1 (/.f64 (pow.f64 x 4) (sqrt.f64 -1))) (fma.f64 (/.f64 -1 (pow.f64 x 3)) (.f64 eps eps) (/.f64 eps x))) (.f64 (/.f64 (pow.f64 eps 3/2) (*.f64 x x)) (sqrt.f64 -1)))
(-.f64 (fma.f64 (pow.f64 eps 5/2) (/.f64 (sqrt.f64 -1) (pow.f64 x 4)) (/.f64 eps x)) (fma.f64 (pow.f64 eps 3/2) (/.f64 (sqrt.f64 -1) (.f64 x x)) (/.f64 (.f64 eps eps) (pow.f64 x 3))))
(/.f64 eps x)
(*.f64 (sqrt.f64 eps) (sqrt.f64 -1))
(*.f64 (sqrt.f64 -1) (sqrt.f64 eps))
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
(fma.f64 (sqrt.f64 eps) (sqrt.f64 -1) x)
(fma.f64 (sqrt.f64 -1) (sqrt.f64 eps) x)
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
(fma.f64 (sqrt.f64 eps) (sqrt.f64 -1) x)
(fma.f64 (sqrt.f64 -1) (sqrt.f64 eps) x)
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
(fma.f64 (sqrt.f64 eps) (sqrt.f64 -1) x)
(fma.f64 (sqrt.f64 -1) (sqrt.f64 eps) x)
x
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
(fma.f64 (sqrt.f64 eps) (sqrt.f64 -1) x)
(fma.f64 (sqrt.f64 -1) (sqrt.f64 eps) x)
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
(fma.f64 (sqrt.f64 eps) (sqrt.f64 -1) x)
(fma.f64 (sqrt.f64 -1) (sqrt.f64 eps) x)
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
(fma.f64 (sqrt.f64 eps) (sqrt.f64 -1) x)
(fma.f64 (sqrt.f64 -1) (sqrt.f64 eps) x)
x
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
(fma.f64 (sqrt.f64 eps) (sqrt.f64 -1) x)
(fma.f64 (sqrt.f64 -1) (sqrt.f64 eps) x)
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
(fma.f64 (sqrt.f64 eps) (sqrt.f64 -1) x)
(fma.f64 (sqrt.f64 -1) (sqrt.f64 eps) x)
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 -1)) x)
(fma.f64 (sqrt.f64 eps) (sqrt.f64 -1) x)
(fma.f64 (sqrt.f64 -1) (sqrt.f64 eps) x)
x

eval121.0ms (2.2%)

Compiler: Compiled 6737 to 3947 computations (41.4% saved)

prune59.0ms (1.1%)

Pruning

11 alts after pruning (5 fresh and 6 done)

	Pruned	Kept	Total
New	371	4	375
Fresh	0	1	1
Picked	0	1	1
Done	1	5	6
Total	372	11	383

Error

Counts

383 → 11

Alt Table

Click to see full alt table

Status	Error	Program
✓	24.5b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (neg.f64 eps))))
✓	26.5b	(-.f64 x (sqrt.f64 (neg.f64 eps)))
▶	36.1b	(/.f64 1 (/.f64 x (*.f64 eps 1/2)))
▶	37.8b	(.f64 eps (+.f64 (/.f64 1/2 x) (/.f64 1/8 (/.f64 (.f64 x x) (/.f64 eps x)))))
▶	56.8b	(/.f64 eps x)
✓	36.0b	(*.f64 1/2 (/.f64 eps x))
	61.9b	x
▶	60.8b	(-.f64 (+.f64 1 (*.f64 eps (/.f64 1/2 x))) 1)
✓	36.1b	(*.f64 eps (/.f64 1/2 x))
✓	24.0b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))

Compiler

Compiled 113 to 71 computations (37.2% saved)

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1/2 x) (/.f64 1/8 (/.f64 (*.f64 x x) (/.f64 eps x))))
✓	0.3b	(/.f64 1/8 (/.f64 (*.f64 x x) (/.f64 eps x)))
✓	2.1b	(/.f64 (*.f64 x x) (/.f64 eps x))
✓	7.4b	(.f64 eps (+.f64 (/.f64 1/2 x) (/.f64 1/8 (/.f64 (.f64 x x) (/.f64 eps x)))))

Compiler

Compiled 59 to 22 computations (62.7% saved)

series6.0ms (0.1%)

Counts

4 → 96

Calls

24 calls:

Time	Variable		Point	Expression
0.0ms	eps	@	0	(.f64 eps (+.f64 (/.f64 1/2 x) (/.f64 1/8 (/.f64 (.f64 x x) (/.f64 eps x)))))
0.0ms	x	@	-inf	(.f64 eps (+.f64 (/.f64 1/2 x) (/.f64 1/8 (/.f64 (.f64 x x) (/.f64 eps x)))))
0.0ms	eps	@	-inf	(.f64 eps (+.f64 (/.f64 1/2 x) (/.f64 1/8 (/.f64 (.f64 x x) (/.f64 eps x)))))
0.0ms	x	@	inf	(.f64 eps (+.f64 (/.f64 1/2 x) (/.f64 1/8 (/.f64 (.f64 x x) (/.f64 eps x)))))
0.0ms	x	@	0	(/.f64 1/8 (/.f64 (*.f64 x x) (/.f64 eps x)))

rewrite97.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

792×	`log-prod_binary64`
424×	`fma-def_binary64`
354×	`log-div_binary64`
254×	`expm1-udef_binary64`
254×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	64
1	288	48
2	4615	48

Stop Event

1×	node limit

Counts

4 → 226

Calls

Call 1

Inputs
(.f64 eps (+.f64 (/.f64 1/2 x) (/.f64 1/8 (/.f64 (.f64 x x) (/.f64 eps x)))))
(/.f64 (*.f64 x x) (/.f64 eps x))
(/.f64 1/8 (/.f64 (*.f64 x x) (/.f64 eps x)))
(+.f64 (/.f64 1/2 x) (/.f64 1/8 (/.f64 (*.f64 x x) (/.f64 eps x))))

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

simplify91.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

714×	`associate-/l/_binary64`
690×	`associate-/r*_binary64`
646×	`fma-def_binary64`
515×	`associate-l_binary64`
511×	`associate-*r/_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	22	1122
1	50	1122
2	117	1122
3	328	1104
4	1440	1068
5	6002	1068
6	7638	1068

Stop Event

1×	node limit

Counts

322 → 237

Calls

Call 1

Inputs
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(*.f64 1/2 (/.f64 eps x))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(/.f64 (pow.f64 x 3) eps)
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 x)
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 x)
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(/.f64 1/2 x)
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(*.f64 1/8 (/.f64 eps (pow.f64 x 3)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))

Outputs
(*.f64 1/2 (/.f64 eps x))
(/.f64 (*.f64 1/2 eps) x)
(/.f64 eps (/.f64 x 1/2))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) 1/8)))
(.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (*.f64 x x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) 1/8)))
(.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (*.f64 x x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) 1/8)))
(.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (*.f64 x x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(*.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))
(.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)))
(*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)))
(/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) 1/8))
(.f64 (.f64 eps eps) (/.f64 1/8 (pow.f64 x 3)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
(fma.f64 1/2 (/.f64 eps x) (/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) 1/8)))
(.f64 (/.f64 eps x) (+.f64 1/2 (/.f64 (.f64 eps 1/8) (*.f64 x x))))
(*.f64 eps (fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (.f64 1/2 (/.f64 eps x)))
(fma.f64 1/2 (/.f64 eps x) (*.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps))))
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(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
(+.f64 (.f64 1/8 (/.f64 eps (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(fma.f64 1/8 (/.f64 eps (pow.f64 x 3)) (/.f64 1/2 x))
(fma.f64 eps (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))

localize15.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.3b	(*.f64 eps (/.f64 1/2 x))
✓	4.2b	(-.f64 (+.f64 1 (*.f64 eps (/.f64 1/2 x))) 1)

Compiler

Compiled 30 to 21 computations (30% saved)

series2.0ms (0%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	eps	@	inf	(-.f64 (+.f64 1 (*.f64 eps (/.f64 1/2 x))) 1)
0.0ms	eps	@	0	(-.f64 (+.f64 1 (*.f64 eps (/.f64 1/2 x))) 1)
0.0ms	eps	@	-inf	(-.f64 (+.f64 1 (*.f64 eps (/.f64 1/2 x))) 1)
0.0ms	x	@	-inf	(-.f64 (+.f64 1 (*.f64 eps (/.f64 1/2 x))) 1)
0.0ms	x	@	0	(-.f64 (+.f64 1 (*.f64 eps (/.f64 1/2 x))) 1)

rewrite68.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

997×	`pow1_binary64`
932×	`add-log-exp_binary64`
932×	`log1p-expm1-u_binary64`
932×	`expm1-log1p-u_binary64`
104×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	204	7
2	2785	7

Stop Event

1×	node limit

Counts

1 → 62

Calls

Call 1

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

Outputs

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

simplify95.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
1×	`associate-*r/_binary64`
1×	`associate-*l/_binary64`
1×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	168
1	9	168
2	13	168
3	17	168
4	18	168

Stop Event

1×

saturated

Counts

86 → 63

Calls

Call 1

Inputs
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))

Outputs
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))

localize9.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (/.f64 x (*.f64 eps 1/2)))

Compiler

Compiled 21 to 14 computations (33.3% saved)

series2.0ms (0%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(/.f64 1 (/.f64 x (*.f64 eps 1/2)))
0.0ms	x	@	inf	(/.f64 1 (/.f64 x (*.f64 eps 1/2)))
0.0ms	eps	@	inf	(/.f64 1 (/.f64 x (*.f64 eps 1/2)))
0.0ms	x	@	-inf	(/.f64 1 (/.f64 x (*.f64 eps 1/2)))
0.0ms	eps	@	-inf	(/.f64 1 (/.f64 x (*.f64 eps 1/2)))

rewrite58.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

843×	`pow1_binary64`
784×	`add-log-exp_binary64`
784×	`log1p-expm1-u_binary64`
784×	`expm1-log1p-u_binary64`
767×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	168	7
2	2164	7

Stop Event

1×	node limit

Counts

1 → 45

Calls

Call 1

Inputs
(/.f64 1 (/.f64 x (*.f64 eps 1/2)))

Outputs

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

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
1×	`associate-*r/_binary64`
1×	`associate-*l/_binary64`
1×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	168
1	9	168
2	13	168
3	17	168
4	18	168

Stop Event

1×

saturated

Counts

69 → 45

Calls

Call 1

Inputs
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))

Outputs
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))
(*.f64 1/2 (/.f64 eps x))

localize3.0ms (0.1%)

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

eval389.0ms (7.2%)

Compiler: Compiled 6150 to 4199 computations (31.7% saved)

prune78.0ms (1.5%)

Pruning

12 alts after pruning (2 fresh and 10 done)

	Pruned	Kept	Total
New	365	1	366
Fresh	0	1	1
Picked	0	1	1
Done	0	9	9
Total	365	12	377

Error

Counts

377 → 12

Alt Table

Click to see full alt table

Status	Error	Program
✓	24.5b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (neg.f64 eps))))
✓	26.5b	(-.f64 x (sqrt.f64 (neg.f64 eps)))
✓	36.1b	(/.f64 1 (/.f64 x (*.f64 eps 1/2)))
✓	37.8b	(.f64 eps (+.f64 (/.f64 1/2 x) (/.f64 1/8 (/.f64 (.f64 x x) (/.f64 eps x)))))
✓	56.8b	(/.f64 eps x)
✓	36.0b	(*.f64 1/2 (/.f64 eps x))
	61.9b	x
✓	60.8b	(-.f64 (+.f64 1 (*.f64 eps (/.f64 1/2 x))) 1)
	36.2b	(.f64 -1 (/.f64 1 (.f64 (neg.f64 x) (/.f64 2 eps))))
✓	36.1b	(*.f64 eps (/.f64 1/2 x))
✓	24.0b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))

Compiler

Compiled 125 to 81 computations (35.2% saved)

regimes192.0ms (3.6%)

Counts

15 → 1

Calls

Call 1

Inputs
x
(/.f64 eps x)
(*.f64 x 2)
(*.f64 eps (/.f64 1/2 x))
(*.f64 1/2 (/.f64 eps x))
(/.f64 1 (/.f64 x (*.f64 eps 1/2)))
(-.f64 (+.f64 1 (*.f64 eps (/.f64 1/2 x))) 1)
(.f64 -1 (/.f64 1 (.f64 (neg.f64 x) (/.f64 2 eps))))
(.f64 eps (+.f64 (/.f64 1/2 x) (/.f64 1/8 (/.f64 (.f64 x x) (/.f64 eps x)))))
(.f64 eps (+.f64 (/.f64 1/2 x) (/.f64 1/8 (.f64 (/.f64 (*.f64 x x) 1) (/.f64 x eps)))))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(*.f64 eps (+.f64 (/.f64 1/2 x) (/.f64 1/8 (/.f64 (pow.f64 x 3) eps))))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (neg.f64 eps))))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))

Outputs
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))

Calls

3 calls:

170.0ms	x
9.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
8.0ms	eps

Results

Error	Segments	Branch
0.3b	1	`x`
0.3b	1	`eps`
0.3b	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 152 to 79 computations (48% saved)

regimes92.0ms (1.7%)

Counts

14 → 2

Calls

Call 1

Inputs
x
(/.f64 eps x)
(*.f64 x 2)
(*.f64 eps (/.f64 1/2 x))
(*.f64 1/2 (/.f64 eps x))
(/.f64 1 (/.f64 x (*.f64 eps 1/2)))
(-.f64 (+.f64 1 (*.f64 eps (/.f64 1/2 x))) 1)
(.f64 -1 (/.f64 1 (.f64 (neg.f64 x) (/.f64 2 eps))))
(.f64 eps (+.f64 (/.f64 1/2 x) (/.f64 1/8 (/.f64 (.f64 x x) (/.f64 eps x)))))
(.f64 eps (+.f64 (/.f64 1/2 x) (/.f64 1/8 (.f64 (/.f64 (*.f64 x x) 1) (/.f64 x eps)))))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(*.f64 eps (+.f64 (/.f64 1/2 x) (/.f64 1/8 (/.f64 (pow.f64 x 3) eps))))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (neg.f64 eps))))

Outputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(.f64 eps (+.f64 (/.f64 1/2 x) (/.f64 1/8 (/.f64 (.f64 x x) (/.f64 eps x)))))

Calls

3 calls:

40.0ms	x
31.0ms	eps
17.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

Error	Segments	Branch
6.6b	2	`x`
10.1b	4	`eps`
0.8b	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 134 to 77 computations (42.5% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-9.090668973682444e-152	0.0

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes47.0ms (0.9%)

Counts

11 → 2

Calls

Call 1

Inputs
x
(/.f64 eps x)
(*.f64 x 2)
(*.f64 eps (/.f64 1/2 x))
(*.f64 1/2 (/.f64 eps x))
(/.f64 1 (/.f64 x (*.f64 eps 1/2)))
(-.f64 (+.f64 1 (*.f64 eps (/.f64 1/2 x))) 1)
(.f64 -1 (/.f64 1 (.f64 (neg.f64 x) (/.f64 2 eps))))
(.f64 eps (+.f64 (/.f64 1/2 x) (/.f64 1/8 (/.f64 (.f64 x x) (/.f64 eps x)))))
(.f64 eps (+.f64 (/.f64 1/2 x) (/.f64 1/8 (.f64 (/.f64 (*.f64 x x) 1) (/.f64 x eps)))))
(-.f64 x (sqrt.f64 (neg.f64 eps)))

Outputs
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(*.f64 1/2 (/.f64 eps x))

Calls

2 calls:

24.0ms	eps
18.0ms	x

Results

Error	Segments	Branch
7.4b	2	`x`
10.9b	4	`eps`

Compiler

Compiled 88 to 55 computations (37.5% saved)

bsearch65.0ms (1.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
65.0ms	1.5001288424543555e-103	4.835302113324458e-103

Compiler

Compiled 95 to 70 computations (26.3% saved)

regimes16.0ms (0.3%)

Counts

10 → 1

Calls

Call 1

Inputs
x
(/.f64 eps x)
(*.f64 x 2)
(*.f64 eps (/.f64 1/2 x))
(*.f64 1/2 (/.f64 eps x))
(/.f64 1 (/.f64 x (*.f64 eps 1/2)))
(-.f64 (+.f64 1 (*.f64 eps (/.f64 1/2 x))) 1)
(.f64 -1 (/.f64 1 (.f64 (neg.f64 x) (/.f64 2 eps))))
(.f64 eps (+.f64 (/.f64 1/2 x) (/.f64 1/8 (/.f64 (.f64 x x) (/.f64 eps x)))))
(.f64 eps (+.f64 (/.f64 1/2 x) (/.f64 1/8 (.f64 (/.f64 (*.f64 x x) 1) (/.f64 x eps)))))

Outputs
(*.f64 1/2 (/.f64 eps x))

Calls

2 calls:

6.0ms	x
6.0ms	eps

Results

Error	Segments	Branch
36.0b	1	`x`
36.0b	1	`eps`

Compiler

Compiled 83 to 52 computations (37.3% saved)

regimes96.0ms (1.8%)

Counts

4 → 1

Calls

Call 1

Inputs
x
(/.f64 eps x)
(*.f64 x 2)
(*.f64 eps (/.f64 1/2 x))

Outputs
(*.f64 eps (/.f64 1/2 x))

Calls

2 calls:

4.0ms	eps
4.0ms	x

Results

Error	Segments	Branch
36.1b	1	`x`
36.1b	1	`eps`

Compiler

Compiled 20 to 12 computations (40% saved)

regimes8.0ms (0.2%)

Accuracy

Total -5.1b remaining (-8.9%)

Threshold costs -5.1b (-8.9%)

Counts

3 → 1

Calls

Call 1

Inputs
x
(/.f64 eps x)
(*.f64 x 2)

Outputs
(/.f64 eps x)

Calls

2 calls:

4.0ms	x
4.0ms	eps

Results

Error	Segments	Branch
56.8b	1	`x`
56.8b	1	`eps`

Compiler

Compiled 15 to 9 computations (40% saved)

simplify13.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
9×	`sub-neg_binary64`
8×	`*-commutative_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	118
1	51	118
2	66	118
3	75	118
4	79	118

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) -2948408144391829/58968162887836583628774290327941701420576894069006881693378223441337877537377325813845730080900918242835443359855685076558915384842574884883772410178635875682021801984) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (.f64 eps (+.f64 (/.f64 1/2 x) (/.f64 1/8 (/.f64 (.f64 x x) (/.f64 eps x))))))
(if (<=.f64 x 1563471605872933/10086913586276986678343434265636765134100413253239154346994763111486904773503285916522052161250538404046496765518544896) (-.f64 x (sqrt.f64 (neg.f64 eps))) (*.f64 1/2 (/.f64 eps x)))
(*.f64 1/2 (/.f64 eps x))
(*.f64 eps (/.f64 1/2 x))
(/.f64 eps x)
x

Outputs
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) -2948408144391829/58968162887836583628774290327941701420576894069006881693378223441337877537377325813845730080900918242835443359855685076558915384842574884883772410178635875682021801984) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (.f64 eps (+.f64 (/.f64 1/2 x) (/.f64 1/8 (/.f64 (.f64 x x) (/.f64 eps x))))))
(if (<=.f64 x 1563471605872933/10086913586276986678343434265636765134100413253239154346994763111486904773503285916522052161250538404046496765518544896) (-.f64 x (sqrt.f64 (neg.f64 eps))) (*.f64 1/2 (/.f64 eps x)))
(*.f64 1/2 (/.f64 eps x))
(*.f64 eps (/.f64 1/2 x))
(/.f64 eps x)
x

Compiler

Compiled 94 to 52 computations (44.7% saved)

soundness0.0ms (0%)

end60.0ms (1.1%)

Compiler: Compiled 82 to 34 computations (58.5% saved)

Iter	Nodes	Cost
0	11	24
1	21	24
2	35	24
3	63	24
4	102	24
5	210	24
6	353	24
7	506	24
8	608	24
9	660	24
10	670	24
0	2	2

Iter	Nodes	Cost
0	7	12
1	12	12
2	20	12
3	34	12
4	55	12
5	103	12
6	196	12
7	269	12
8	361	12
9	439	12
10	495	12
11	499	12

Iter	Nodes	Cost
0	9	121
1	16	112
2	32	112
3	45	112
4	57	112
5	88	112
6	148	112
7	196	112
8	254	112
9	341	112
10	391	112
11	397	112

Iter	Nodes	Cost
0	11	24
1	21	24
2	35	24
3	63	24
4	102	24
5	210	24
6	353	24
7	506	24
8	608	24
9	660	24
10	670	24
0	2	2

Iter	Nodes	Cost
0	7	12
1	12	12
2	20	12
3	34	12
4	55	12
5	103	12
6	196	12
7	269	12
8	361	12
9	439	12
10	495	12
11	499	12

Iter	Nodes	Cost
0	9	121
1	16	112
2	32	112
3	45	112
4	57	112
5	88	112
6	148	112
7	196	112
8	254	112
9	341	112
10	391	112
11	397	112

Details

analyze20.0ms (0.4%)

sample1.8s (33.6%)

preprocess62.0ms (1.2%)

simplify33.0ms (0.6%)

eval1.0ms (0%)

prune1.0ms (0%)

localize16.0ms (0.3%)

series14.0ms (0.3%)

rewrite70.0ms (1.3%)

simplify67.0ms (1.3%)

eval33.0ms (0.6%)

prune38.0ms (0.7%)

localize14.0ms (0.3%)

series10.0ms (0.2%)

rewrite113.0ms (2.1%)

simplify95.0ms (1.8%)

localize6.0ms (0.1%)

localize10.0ms (0.2%)

localize11.0ms (0.2%)

series7.0ms (0.1%)

rewrite93.0ms (1.7%)

simplify36.0ms (0.7%)

localize39.0ms (0.7%)

series29.0ms (0.5%)

rewrite145.0ms (2.7%)

simplify118.0ms (2.2%)

eval246.0ms (4.6%)

prune79.0ms (1.5%)

localize24.0ms (0.4%)

series6.0ms (0.1%)

rewrite99.0ms (1.8%)

simplify94.0ms (1.7%)

localize6.0ms (0.1%)

series4.0ms (0.1%)

rewrite50.0ms (0.9%)

simplify11.0ms (0.2%)

localize13.0ms (0.2%)

series20.0ms (0.4%)

rewrite68.0ms (1.3%)

simplify62.0ms (1.2%)

eval121.0ms (2.2%)

prune59.0ms (1.1%)

localize20.0ms (0.4%)

series6.0ms (0.1%)

rewrite97.0ms (1.8%)

simplify91.0ms (1.7%)

localize15.0ms (0.3%)

series2.0ms (0%)

rewrite68.0ms (1.3%)

simplify95.0ms (1.8%)

localize9.0ms (0.2%)

series2.0ms (0%)

rewrite58.0ms (1.1%)

simplify12.0ms (0.2%)

localize3.0ms (0.1%)

eval389.0ms (7.2%)

prune78.0ms (1.5%)

regimes192.0ms (3.6%)

regimes92.0ms (1.7%)

bsearch0.0ms (0%)

regimes47.0ms (0.9%)

bsearch65.0ms (1.2%)

regimes16.0ms (0.3%)

regimes96.0ms (1.8%)

regimes8.0ms (0.2%)

simplify13.0ms (0.2%)

soundness0.0ms (0%)

end60.0ms (1.1%)

Profiling

Iter	Nodes	Cost
0	11	24
1	21	24
2	35	24
3	63	24
4	102	24
5	210	24
6	353	24
7	506	24
8	608	24
9	660	24
10	670	24
0	2	2

Iter	Nodes	Cost
0	7	12
1	12	12
2	20	12
3	34	12
4	55	12
5	103	12
6	196	12
7	269	12
8	361	12
9	439	12
10	495	12
11	499	12

Iter	Nodes	Cost
0	9	121
1	16	112
2	32	112
3	45	112
4	57	112
5	88	112
6	148	112
7	196	112
8	254	112
9	341	112
10	391	112
11	397	112