Details

analyze23.0ms (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 (27.4%)

Results

920.0ms	5900×	body	256	valid
475.0ms	1178×	body	1024	valid
296.0ms	1149×	body	512	valid
22.0ms	164×	body	256	invalid
15.0ms	29×	body	2048	valid

preprocess55.0ms (0.9%)

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)

simplify38.0ms (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

25.8b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	25.8b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 10 to 6 computations (40% saved)

localize17.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 (*.f64 x x) eps))
✓	4.2b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 26 to 6 computations (76.9% saved)

series17.0ms (0.3%)

Counts

2 → 32

Calls

12 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	(sqrt.f64 (-.f64 (*.f64 x x) eps))
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)))

rewrite132.0ms (2.1%)

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	21
1	162	21
2	2429	21

Stop Event

1×	node limit

Counts

2 → 57

Calls

Call 1

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

simplify93.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

704×	`unswap-sqr_binary64`
520×	`fma-def_binary64`
425×	`associate-/l/_binary64`
381×	`associate-/r/_binary64`
301×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	109	803
1	325	792
2	986	778
3	3940	764
4	6325	764

Stop Event

1×	node limit

Counts

89 → 105

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

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

eval62.0ms (1%)

Compiler: Compiled 1894 to 922 computations (51.3% saved)

prune19.0ms (0.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	99	6	105
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	99	7	106

Error

0.0b

Counts

106 → 7

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
▶	61.1b	(-.f64 x x)
	35.8b	(.f64 (/.f64 eps x) (+.f64 (.f64 (/.f64 eps (*.f64 x x)) 1/8) 1/2))
✓	25.8b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶	34.2b	(*.f64 1/2 (/.f64 eps x))
▶	61.8b	(*.f64 x 2)
▶	59.8b	(-.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x))

Compiler

Compiled 136 to 82 computations (39.7% saved)

localize45.0ms (0.7%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (-.f64 (*.f64 x x) eps))
✓	0.0b	(+.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 60 to 9 computations (85% saved)

series11.0ms (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))))
2.0ms	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	eps	@	0	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))

rewrite86.0ms (1.3%)

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)))))

simplify83.0ms (1.3%)

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))))))

localize3.0ms (0%)

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

localize3.0ms (0%)

Compiler: Compiled 6 to 3 computations (50% saved)

localize5.0ms (0.1%)

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

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)
✓	4.2b	(-.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x))

Compiler

Compiled 29 to 13 computations (55.2% saved)

series6.0ms (0.1%)

Counts

2 → 30

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(-.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x))
1.0ms	eps	@	inf	(-.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x))
1.0ms	x	@	0	(-.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x))
1.0ms	eps	@	0	(-.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x))
0.0ms	x	@	-inf	(-.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x))

rewrite79.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

490×	`log-prod_binary64`
468×	`fma-def_binary64`
313×	`pow-prod-down_binary64`
266×	`pow2_binary64`
218×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	191	19
2	2948	19

Stop Event

1×	node limit

Counts

2 → 164

Calls

Call 1

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

Outputs

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simplify13.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
4×	`associate-/l*_binary64`
2×	`associate-*r/_binary64`
2×	`associate-*l/_binary64`
2×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	192
1	14	192
2	21	192
3	29	192
4	31	192

Stop Event

1×

saturated

Counts

194 → 169

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

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

eval149.0ms (2.3%)

Compiler: Compiled 10088 to 3760 computations (62.7% saved)

prune75.0ms (1.2%)

Pruning

11 alts after pruning (5 fresh and 6 done)

	Pruned	Kept	Total
New	440	4	444
Fresh	0	1	1
Picked	0	1	1
Done	0	5	5
Total	440	11	451

Error

Counts

451 → 11

Alt Table

Click to see full alt table

Status	Error	Program
✓	61.8b	(*.f64 x 2)
▶	33.9b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x)))
✓	59.8b	(-.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x))
▶	60.7b	(-.f64 x (*.f64 eps (/.f64 -1/2 x)))
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	61.1b	(-.f64 x x)
▶	35.8b	(.f64 (/.f64 eps x) (+.f64 (.f64 (/.f64 eps (*.f64 x x)) 1/8) 1/2))
✓	25.8b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶	34.3b	(/.f64 1/2 (/.f64 x eps))
✓	34.2b	(*.f64 1/2 (/.f64 eps x))
▶	37.4b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) x))))

Compiler

Compiled 224 to 136 computations (39.3% saved)

localize19.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 67 to 21 computations (68.7% saved)

series7.0ms (0.1%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	eps	@	-inf	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x)))
1.0ms	x	@	0	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x)))
1.0ms	x	@	inf	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x)))
1.0ms	x	@	-inf	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x)))
0.0ms	eps	@	inf	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x)))

rewrite77.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

702×	`fma-def_binary64`
658×	`log-prod_binary64`
399×	`fma-neg_binary64`
233×	`log-div_binary64`
233×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	28
1	311	25
2	4869	25

Stop Event

1×	node limit

Counts

2 → 127

Calls

Call 1

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

Outputs

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

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

simplify87.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

766×	`associate-/l*_binary64`
603×	`associate-+l+_binary64`
566×	`fma-def_binary64`
454×	`associate-/r*_binary64`
335×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	51	804
1	133	804
2	369	804
3	1216	795
4	5726	795
5	6781	795
6	7244	795

Stop Event

1×	node limit

Counts

175 → 148

Calls

Call 1

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

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

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1/2 (/.f64 x eps))

Compiler

Compiled 13 to 6 computations (53.8% saved)

series2.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite48.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

699×	`pow1_binary64`
652×	`add-log-exp_binary64`
652×	`log1p-expm1-u_binary64`
652×	`expm1-log1p-u_binary64`
639×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	134	7
2	1770	7

Stop Event

1×	node limit

Counts

1 → 26

Calls

Call 1

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

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

simplify10.0ms (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

50 → 26

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))

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 20 to 12 computations (40% saved)

series6.0ms (0.1%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
3.0ms	eps	@	0	(-.f64 x (*.f64 eps (/.f64 -1/2 x)))
0.0ms	eps	@	0	(*.f64 eps (/.f64 -1/2 x))
0.0ms	x	@	-inf	(-.f64 x (*.f64 eps (/.f64 -1/2 x)))
0.0ms	eps	@	inf	(-.f64 x (*.f64 eps (/.f64 -1/2 x)))
0.0ms	x	@	0	(-.f64 x (*.f64 eps (/.f64 -1/2 x)))

rewrite68.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

902×	`pow1_binary64`
844×	`add-log-exp_binary64`
843×	`log1p-expm1-u_binary64`
843×	`expm1-log1p-u_binary64`
828×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	163	17
2	2290	17

Stop Event

1×	node limit

Counts

2 → 57

Calls

Call 1

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

simplify18.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
4×	`associate-/l*_binary64`
4×	`fma-def_binary64`
2×	`associate-*r/_binary64`
2×	`associate-*l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	336
1	17	336
2	25	336
3	33	336
4	36	336
5	37	336

Stop Event

1×

saturated

Counts

105 → 64

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

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

localize14.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (/.f64 eps x) (+.f64 (.f64 (/.f64 eps (*.f64 x x)) 1/8) 1/2))
✓	0.2b	(.f64 (/.f64 eps (.f64 x x)) 1/8)
✓	13.4b	(/.f64 eps (*.f64 x x))

Compiler

Compiled 46 to 18 computations (60.9% saved)

series25.0ms (0.4%)

Counts

3 → 72

Calls

18 calls:

Time	Variable		Point	Expression
11.0ms	eps	@	-inf	(.f64 (/.f64 eps x) (+.f64 (.f64 (/.f64 eps (*.f64 x x)) 1/8) 1/2))
4.0ms	eps	@	0	(.f64 (/.f64 eps x) (+.f64 (.f64 (/.f64 eps (*.f64 x x)) 1/8) 1/2))
1.0ms	eps	@	inf	(.f64 (/.f64 eps x) (+.f64 (.f64 (/.f64 eps (*.f64 x x)) 1/8) 1/2))
1.0ms	eps	@	0	(/.f64 eps (*.f64 x x))
1.0ms	eps	@	inf	(/.f64 eps (*.f64 x x))

rewrite80.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

647×	`log-prod_binary64`
442×	`prod-diff_binary64`
320×	`pow2_binary64`
226×	`pow1/3_binary64`
221×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	34
1	250	34
2	3601	34

Stop Event

1×	node limit

Counts

3 → 170

Calls

Call 1

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

Outputs

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

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(sqrt.f64 (/.f64 (*.f64 eps (*.f64 eps 1/8)) (pow.f64 x 3))) (sqrt.f64 (/.f64 (*.f64 eps (*.f64 eps 1/8)) (pow.f64 x 3))) (/.f64 (*.f64 1/2 eps) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 (*.f64 1/2 eps) x)) (sqrt.f64 (/.f64 (*.f64 1/2 eps) x)) (/.f64 (*.f64 eps (*.f64 eps 1/8)) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 (/.f64 eps x)) (/.f64 (sqrt.f64 (*.f64 eps 1/8)) x)) (*.f64 (sqrt.f64 (/.f64 eps x)) (/.f64 (sqrt.f64 (*.f64 eps 1/8)) x)) (/.f64 (*.f64 1/2 eps) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (/.f64 (sqrt.f64 (*.f64 eps 1/8)) x) (sqrt.f64 (/.f64 eps x))) (*.f64 (/.f64 (sqrt.f64 (*.f64 eps 1/8)) x) (sqrt.f64 (/.f64 eps x))) (/.f64 (*.f64 1/2 eps) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 eps (*.f64 (pow.f64 x -2) 1/8)) eps) (/.f64 1 x) (/.f64 (*.f64 1/2 eps) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/2 eps) (/.f64 1 x) (/.f64 (*.f64 eps (*.f64 eps 1/8)) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (/.f64 eps x) (*.f64 eps (pow.f64 x -2))) 1/8 (/.f64 (*.f64 1/2 eps) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (/.f64 eps x) 1/8) (*.f64 eps (pow.f64 x -2)) (/.f64 (*.f64 1/2 eps) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (/.f64 eps x) (pow.f64 (cbrt.f64 (*.f64 eps (*.f64 (pow.f64 x -2) 1/8))) 2)) (cbrt.f64 (*.f64 eps (*.f64 (pow.f64 x -2) 1/8))) (/.f64 (*.f64 1/2 eps) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (/.f64 eps x) (/.f64 (sqrt.f64 (*.f64 eps 1/8)) x)) (/.f64 (sqrt.f64 (*.f64 eps 1/8)) x) (/.f64 (*.f64 1/2 eps) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 eps (*.f64 (pow.f64 x -2) 1/8)) (pow.f64 (cbrt.f64 (/.f64 eps x)) 2)) (cbrt.f64 (/.f64 eps x)) (/.f64 (*.f64 1/2 eps) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 eps (*.f64 (pow.f64 x -2) 1/8)) (sqrt.f64 (/.f64 eps x))) (sqrt.f64 (/.f64 eps x)) (/.f64 (*.f64 1/2 eps) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/2 (pow.f64 (cbrt.f64 (/.f64 eps x)) 2)) (cbrt.f64 (/.f64 eps x)) (/.f64 (*.f64 eps (*.f64 eps 1/8)) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/2 (sqrt.f64 (/.f64 eps x))) (sqrt.f64 (/.f64 eps x)) (/.f64 (*.f64 eps (*.f64 eps 1/8)) (pow.f64 x 3)))))))

simplify155.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

1157×	`associate-/l/_binary64`
683×	`associate-/r/_binary64`
591×	`unswap-sqr_binary64`
407×	`sqr-pow_binary64`
313×	`times-frac_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	17	828
1	43	828
2	101	828
3	325	810
4	1981	774
5	2716	774
6	3664	774
7	3851	774
8	4080	774
9	4357	774
10	7233	774

Stop Event

1×	node limit

Counts

242 → 180

Calls

Call 1

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

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

localize45.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) x))
✓	0.0b	(+.f64 x (+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) x)))
✓	0.1b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) x))))
✓	25.5b	(/.f64 (pow.f64 eps 2) (pow.f64 x 3))

Compiler

Compiled 133 to 72 computations (45.9% saved)

series12.0ms (0.2%)

Counts

4 → 60

Calls

24 calls:

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

rewrite110.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

370×	`log1p-udef_binary64`
242×	`add-sqr-sqrt_binary64`
237×	`pow1_binary64`
234×	`*-un-lft-identity_binary64`
230×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	85
1	499	82
2	7333	82

Stop Event

1×	node limit

Counts

4 → 152

Calls

Call 1

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

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

simplify78.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

804×	`fma-neg_binary64`
729×	`associate-l_binary64`
610×	`associate-*l/_binary64`
417×	`associate-*r/_binary64`
327×	`fma-def_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	91	1239
1	254	1236
2	743	1230
3	2586	1206
4	7587	1203

Stop Event

1×	node limit

Counts

212 → 183

Calls

Call 1

Inputs
(*.f64 -8 (/.f64 (pow.f64 x 3) eps))
(+.f64 (.f64 -8 (/.f64 (pow.f64 x 3) eps)) (.f64 32 (/.f64 (pow.f64 x 5) (pow.f64 eps 2))))
(+.f64 (.f64 -8 (/.f64 (pow.f64 x 3) eps)) (+.f64 (.f64 32 (/.f64 (pow.f64 x 5) (pow.f64 eps 2))) (*.f64 -256 (/.f64 (pow.f64 x 7) (pow.f64 eps 3)))))
(+.f64 (.f64 -8 (/.f64 (pow.f64 x 3) eps)) (+.f64 (.f64 32 (/.f64 (pow.f64 x 5) (pow.f64 eps 2))) (+.f64 (.f64 1536 (/.f64 (pow.f64 x 9) (pow.f64 eps 4))) (.f64 -256 (/.f64 (pow.f64 x 7) (pow.f64 eps 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 (/.f64 (+.f64 (.f64 -1/128 (pow.f64 eps 4)) (.f64 -1/64 (pow.f64 eps 4))) (pow.f64 x 7))) (.f64 1/16 (/.f64 (pow.f64 eps 3) (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 1/2 (/.f64 eps x)) (+.f64 (.f64 1/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (*.f64 1/64 (/.f64 (pow.f64 eps 4) (pow.f64 x 7)))))))
(*.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 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (.f64 3/128 (/.f64 (pow.f64 eps 4) (pow.f64 x 7))))))
(*.f64 -8 (/.f64 (pow.f64 x 3) eps))
(+.f64 (.f64 -8 (/.f64 (pow.f64 x 3) eps)) (.f64 32 (/.f64 (pow.f64 x 5) (pow.f64 eps 2))))
(+.f64 (.f64 -8 (/.f64 (pow.f64 x 3) eps)) (+.f64 (.f64 32 (/.f64 (pow.f64 x 5) (pow.f64 eps 2))) (*.f64 -256 (/.f64 (pow.f64 x 7) (pow.f64 eps 3)))))
(+.f64 (.f64 -8 (/.f64 (pow.f64 x 3) eps)) (+.f64 (.f64 32 (/.f64 (pow.f64 x 5) (pow.f64 eps 2))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -1024 (pow.f64 x 9)) (.f64 -512 (pow.f64 x 9))) (pow.f64 eps 4))) (.f64 -256 (/.f64 (pow.f64 x 7) (pow.f64 eps 3))))))
(*.f64 -8 (/.f64 (pow.f64 x 3) eps))
(+.f64 (.f64 -8 (/.f64 (pow.f64 x 3) eps)) (.f64 32 (/.f64 (pow.f64 x 5) (pow.f64 eps 2))))
(+.f64 (.f64 -8 (/.f64 (pow.f64 x 3) eps)) (+.f64 (.f64 32 (/.f64 (pow.f64 x 5) (pow.f64 eps 2))) (*.f64 -256 (/.f64 (pow.f64 x 7) (pow.f64 eps 3)))))
(+.f64 (.f64 -8 (/.f64 (pow.f64 x 3) eps)) (+.f64 (.f64 32 (/.f64 (pow.f64 x 5) (pow.f64 eps 2))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -1024 (pow.f64 x 9)) (.f64 -512 (pow.f64 x 9))) (pow.f64 eps 4))) (.f64 -256 (/.f64 (pow.f64 x 7) (pow.f64 eps 3))))))
(*.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))
(+.f64 (.f64 -1/2 (/.f64 eps 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 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 2 x) (*.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(*.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 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(*.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 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
(*.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 -1/8 (/.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 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(+.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 -1/8 (/.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 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(+.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 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))))
x
(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)
(*.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3)))
(+.f64 (.f64 -1/2 (/.f64 eps x)) (.f64 -1/8 (/.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 -1/8 (/.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 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
x
(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)
x
(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)

Outputs
(*.f64 -8 (/.f64 (pow.f64 x 3) eps))
(+.f64 (.f64 -8 (/.f64 (pow.f64 x 3) eps)) (.f64 32 (/.f64 (pow.f64 x 5) (pow.f64 eps 2))))
(fma.f64 -8 (/.f64 (pow.f64 x 3) eps) (/.f64 (.f64 32 (pow.f64 x 5)) (.f64 eps eps)))
(fma.f64 -8 (/.f64 (pow.f64 x 3) eps) (.f64 32 (/.f64 (pow.f64 x 5) (.f64 eps eps))))
(fma.f64 -8 (/.f64 (pow.f64 x 3) eps) (*.f64 (/.f64 32 eps) (/.f64 (pow.f64 x 5) eps)))
(fma.f64 -8 (/.f64 (pow.f64 x 3) eps) (.f64 (pow.f64 x 5) (/.f64 32 (.f64 eps eps))))
(+.f64 (.f64 -8 (/.f64 (pow.f64 x 3) eps)) (+.f64 (.f64 32 (/.f64 (pow.f64 x 5) (pow.f64 eps 2))) (*.f64 -256 (/.f64 (pow.f64 x 7) (pow.f64 eps 3)))))
(fma.f64 -8 (/.f64 (pow.f64 x 3) eps) (fma.f64 32 (/.f64 (pow.f64 x 5) (.f64 eps eps)) (.f64 -256 (/.f64 (pow.f64 x 7) (pow.f64 eps 3)))))
(fma.f64 -8 (/.f64 (pow.f64 x 3) eps) (fma.f64 -256 (/.f64 (pow.f64 x 7) (pow.f64 eps 3)) (*.f64 (/.f64 32 eps) (/.f64 (pow.f64 x 5) eps))))
(fma.f64 -8 (/.f64 (pow.f64 x 3) eps) (fma.f64 -256 (/.f64 (pow.f64 x 7) (pow.f64 eps 3)) (.f64 (pow.f64 x 5) (/.f64 32 (.f64 eps eps)))))
(+.f64 (.f64 -8 (/.f64 (pow.f64 x 3) eps)) (+.f64 (.f64 32 (/.f64 (pow.f64 x 5) (pow.f64 eps 2))) (+.f64 (.f64 1536 (/.f64 (pow.f64 x 9) (pow.f64 eps 4))) (.f64 -256 (/.f64 (pow.f64 x 7) (pow.f64 eps 3))))))
(fma.f64 -8 (/.f64 (pow.f64 x 3) eps) (fma.f64 32 (/.f64 (pow.f64 x 5) (.f64 eps eps)) (fma.f64 1536 (/.f64 (pow.f64 x 9) (pow.f64 eps 4)) (.f64 -256 (/.f64 (pow.f64 x 7) (pow.f64 eps 3))))))
(fma.f64 -8 (/.f64 (pow.f64 x 3) eps) (fma.f64 32 (/.f64 (pow.f64 x 5) (.f64 eps eps)) (fma.f64 -256 (/.f64 (pow.f64 x 7) (pow.f64 eps 3)) (.f64 1536 (/.f64 (pow.f64 x 9) (pow.f64 eps 4))))))
(fma.f64 -8 (/.f64 (pow.f64 x 3) eps) (fma.f64 32 (/.f64 (pow.f64 x 5) (*.f64 eps eps)) (fma.f64 -256 (/.f64 (pow.f64 x 7) (pow.f64 eps 3)) (/.f64 (pow.f64 x 9) (/.f64 (pow.f64 eps 4) 1536)))))
(*.f64 1/2 (/.f64 eps x))
(*.f64 eps (/.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 1/8 (pow.f64 x 3)) (.f64 eps eps)))
(.f64 (/.f64 eps x) (+.f64 1/2 (.f64 1/8 (/.f64 eps (*.f64 x 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 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 1/8 (*.f64 (/.f64 eps (pow.f64 x 3)) eps) (fma.f64 1/2 (/.f64 eps x) (/.f64 (pow.f64 eps 3) (/.f64 (pow.f64 x 5) 1/16))))
(fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (.f64 (/.f64 eps x) (+.f64 1/2 (.f64 1/8 (/.f64 eps (*.f64 x x))))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 eps x)) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -1/128 (pow.f64 eps 4)) (.f64 -1/64 (pow.f64 eps 4))) (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 1/2 (/.f64 eps x) (fma.f64 -1 (/.f64 (.f64 (pow.f64 eps 4) -3/128) (pow.f64 x 7)) (*.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 (*.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5))) (/.f64 (pow.f64 eps 4) (/.f64 (pow.f64 x 7) -3/128)))))
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(fma.f64 1/2 (/.f64 eps x) (fma.f64 1/8 (/.f64 eps (/.f64 (pow.f64 x 3) eps)) (fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (*.f64 (pow.f64 eps 4) (/.f64 3/128 (pow.f64 x 7))))))
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(/.f64 -1/8 (/.f64 (pow.f64 x 3) (*.f64 eps 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 -1/2 (/.f64 eps x)) (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(fma.f64 -1/2 (/.f64 eps x) (/.f64 (.f64 -1/8 (.f64 eps eps)) (pow.f64 x 3)))
(fma.f64 (/.f64 eps x) -1/2 (/.f64 -1/8 (/.f64 (pow.f64 x 3) (*.f64 eps eps))))
(fma.f64 (/.f64 eps x) -1/2 (/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) -1/8)))
(.f64 (/.f64 eps x) (+.f64 (.f64 -1/8 (/.f64 eps (*.f64 x 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 -1/8 (.f64 eps eps)) (pow.f64 x 3))))
(fma.f64 (/.f64 eps x) -1/2 (fma.f64 x 2 (/.f64 -1/8 (/.f64 (pow.f64 x 3) (*.f64 eps eps)))))
(fma.f64 (/.f64 eps x) -1/2 (fma.f64 x 2 (/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) -1/8))))
(fma.f64 x 2 (.f64 (/.f64 eps x) (+.f64 (.f64 -1/8 (/.f64 eps (*.f64 x 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 -1/8 (.f64 eps eps)) (pow.f64 x 3))))
(fma.f64 (/.f64 eps x) -1/2 (fma.f64 x 2 (/.f64 -1/8 (/.f64 (pow.f64 x 3) (*.f64 eps eps)))))
(fma.f64 (/.f64 eps x) -1/2 (fma.f64 x 2 (/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) -1/8))))
(fma.f64 x 2 (.f64 (/.f64 eps x) (+.f64 (.f64 -1/8 (/.f64 eps (*.f64 x x))) -1/2)))
(*.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 (pow.f64 x 3) (*.f64 eps 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 -1/2 (/.f64 eps x)) (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(fma.f64 -1/2 (/.f64 eps x) (/.f64 (.f64 -1/8 (.f64 eps eps)) (pow.f64 x 3)))
(fma.f64 (/.f64 eps x) -1/2 (/.f64 -1/8 (/.f64 (pow.f64 x 3) (*.f64 eps eps))))
(fma.f64 (/.f64 eps x) -1/2 (/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) -1/8)))
(.f64 (/.f64 eps x) (+.f64 (.f64 -1/8 (/.f64 eps (*.f64 x 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 -1/8 (.f64 eps eps)) (pow.f64 x 3))))
(fma.f64 (/.f64 eps x) -1/2 (fma.f64 x 2 (/.f64 -1/8 (/.f64 (pow.f64 x 3) (*.f64 eps eps)))))
(fma.f64 (/.f64 eps x) -1/2 (fma.f64 x 2 (/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) -1/8))))
(fma.f64 x 2 (.f64 (/.f64 eps x) (+.f64 (.f64 -1/8 (/.f64 eps (*.f64 x 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 -1/8 (.f64 eps eps)) (pow.f64 x 3))))
(fma.f64 (/.f64 eps x) -1/2 (fma.f64 x 2 (/.f64 -1/8 (/.f64 (pow.f64 x 3) (*.f64 eps eps)))))
(fma.f64 (/.f64 eps x) -1/2 (fma.f64 x 2 (/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) -1/8))))
(fma.f64 x 2 (.f64 (/.f64 eps x) (+.f64 (.f64 -1/8 (/.f64 eps (*.f64 x x))) -1/2)))
x
(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)
(fma.f64 -1/2 (/.f64 eps x) x)
(fma.f64 (/.f64 eps x) -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 (pow.f64 x 3) (*.f64 eps 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 -1/2 (/.f64 eps x)) (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(fma.f64 -1/2 (/.f64 eps x) (/.f64 (.f64 -1/8 (.f64 eps eps)) (pow.f64 x 3)))
(fma.f64 (/.f64 eps x) -1/2 (/.f64 -1/8 (/.f64 (pow.f64 x 3) (*.f64 eps eps))))
(fma.f64 (/.f64 eps x) -1/2 (/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) -1/8)))
(.f64 (/.f64 eps x) (+.f64 (.f64 -1/8 (/.f64 eps (*.f64 x x))) -1/2))
(*.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 (pow.f64 x 3) (*.f64 eps 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 -1/2 (/.f64 eps x)) (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(fma.f64 -1/2 (/.f64 eps x) (/.f64 (.f64 -1/8 (.f64 eps eps)) (pow.f64 x 3)))
(fma.f64 (/.f64 eps x) -1/2 (/.f64 -1/8 (/.f64 (pow.f64 x 3) (*.f64 eps eps))))
(fma.f64 (/.f64 eps x) -1/2 (/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) -1/8)))
(.f64 (/.f64 eps x) (+.f64 (.f64 -1/8 (/.f64 eps (*.f64 x x))) -1/2))
(*.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 (pow.f64 x 3) (*.f64 eps 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 -1/2 (/.f64 eps x)) (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))))
(fma.f64 -1/2 (/.f64 eps x) (/.f64 (.f64 -1/8 (.f64 eps eps)) (pow.f64 x 3)))
(fma.f64 (/.f64 eps x) -1/2 (/.f64 -1/8 (/.f64 (pow.f64 x 3) (*.f64 eps eps))))
(fma.f64 (/.f64 eps x) -1/2 (/.f64 (*.f64 eps eps) (/.f64 (pow.f64 x 3) -1/8)))
(.f64 (/.f64 eps x) (+.f64 (.f64 -1/8 (/.f64 eps (*.f64 x x))) -1/2))
x
(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)
(fma.f64 -1/2 (/.f64 eps x) x)
(fma.f64 (/.f64 eps x) -1/2 x)
x
(+.f64 (*.f64 -1/2 (/.f64 eps x)) x)
(fma.f64 -1/2 (/.f64 eps x) x)
(fma.f64 (/.f64 eps x) -1/2 x)

eval436.0ms (6.8%)

Compiler: Compiled 15850 to 7891 computations (50.2% saved)

prune439.0ms (6.8%)

Pruning

19 alts after pruning (10 fresh and 9 done)

	Pruned	Kept	Total
New	657	10	667
Fresh	0	0	0
Picked	1	0	1
Done	1	9	10
Total	659	19	678

Error

Counts

678 → 19

Alt Table

Click to see full alt table

Status	Error	Program
✓	25.8b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶	34.3b	(*.f64 (/.f64 1/2 x) eps)
	60.7b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (*.f64 eps (/.f64 -1/2 x)))
▶	60.7b	(*.f64 -2 x)
▶	60.9b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 eps (neg.f64 (/.f64 -1/2 x))) (.f64 eps (neg.f64 (/.f64 -1/2 x))))) (-.f64 x (*.f64 eps (neg.f64 (/.f64 -1/2 x)))))
	60.7b	(-.f64 x (/.f64 1 (/.f64 x (*.f64 eps -1/2))))
	61.1b	(-.f64 x (-.f64 (+.f64 1 (*.f64 eps (/.f64 -1/2 x))) 1))
▶	60.4b	(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 eps x))) 1)
✓	59.8b	(-.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x))
✓	60.7b	(-.f64 x (*.f64 eps (/.f64 -1/2 x)))
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	61.1b	(-.f64 x x)
	34.6b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 -1/8 (.f64 (/.f64 eps (.f64 x x)) (/.f64 eps x))) x))))
✓	35.8b	(.f64 (/.f64 eps x) (+.f64 (.f64 (/.f64 eps (*.f64 x x)) 1/8) 1/2))
✓	34.3b	(/.f64 1/2 (/.f64 x eps))
✓	34.2b	(*.f64 1/2 (/.f64 eps x))
▶	60.7b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (*.f64 -1/2 (/.f64 eps x)))
✓	33.9b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x)))
	61.8b	x

Compiler

Compiled 392 to 242 computations (38.3% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (/.f64 1/2 x) eps)

Compiler

Compiled 13 to 8 computations (38.5% saved)

series2.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite48.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

617×	`pow1_binary64`
573×	`add-log-exp_binary64`
573×	`log1p-expm1-u_binary64`
573×	`expm1-log1p-u_binary64`
562×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	128	7
2	1560	7

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

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

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

simplify10.0ms (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

45 → 22

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%)

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

localize29.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (*.f64 1/2 (/.f64 eps x)))
✓	5.9b	(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 eps x))) 1)

Compiler

Compiled 30 to 17 computations (43.3% saved)

series3.0ms (0%)

Counts

2 → 30

Calls

12 calls:

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

rewrite207.0ms (3.2%)

Algorithm

1×	batch-egg-rewrite

Rules

650×	`unpow-prod-down_binary64`
490×	`prod-diff_binary64`
417×	`log-prod_binary64`
410×	`fma-def_binary64`
234×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	203	15
2	2844	15

Stop Event

1×	node limit

Counts

2 → 188

Calls

Call 1

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

Outputs

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

simplify13.0ms (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	7	192
1	12	192
2	16	192
3	20	192
4	21	192

Stop Event

1×

saturated

Counts

218 → 189

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

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

localize15.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (*.f64 -1/2 (/.f64 eps x)))

Compiler

Compiled 47 to 12 computations (74.5% saved)

series3.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite60.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

520×	`log-prod_binary64`
512×	`prod-diff_binary64`
263×	`fma-def_binary64`
255×	`pow2_binary64`
193×	`log-div_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	252	10
2	3765	10

Stop Event

1×	node limit

Counts

1 → 51

Calls

Call 1

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

Outputs

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

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	96
1	5	96

Stop Event

1×

saturated

Counts

75 → 52

Calls

Call 1

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

Outputs
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)
(*.f64 -2 x)

localize83.0ms (1.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (*.f64 eps (neg.f64 (/.f64 -1/2 x))))
✓	0.2b	(*.f64 eps (neg.f64 (/.f64 -1/2 x)))
✓	0.3b	(.f64 (.f64 eps (neg.f64 (/.f64 -1/2 x))) (*.f64 eps (neg.f64 (/.f64 -1/2 x))))
✓	5.7b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 eps (neg.f64 (/.f64 -1/2 x))) (.f64 eps (neg.f64 (/.f64 -1/2 x))))) (-.f64 x (*.f64 eps (neg.f64 (/.f64 -1/2 x)))))

Compiler

Compiled 85 to 53 computations (37.6% saved)

series10.0ms (0.2%)

Counts

4 → 96

Calls

24 calls:

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

rewrite136.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

683×	`log-prod_binary64`
609×	`fma-def_binary64`
260×	`fma-neg_binary64`
209×	`expm1-udef_binary64`
209×	`log1p-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	73
1	297	37
2	4981	33

Stop Event

1×	node limit

Counts

4 → 384

Calls

Call 1

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

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

simplify211.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

778×	`associate-/l*_binary64`
483×	`associate-/r*_binary64`
482×	`sqr-pow_binary64`
377×	`associate-/l/_binary64`
366×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	816
1	37	816
2	69	816
3	186	816
4	876	816
5	5354	816
6	6136	816
7	6376	816
8	6592	816
9	6840	816
10	7175	816
11	7611	816

Stop Event

1×	node limit

Counts

480 → 240

Calls

Call 1

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

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

eval398.0ms (6.2%)

Compiler: Compiled 11223 to 7121 computations (36.5% saved)

prune167.0ms (2.6%)

Pruning

23 alts after pruning (11 fresh and 12 done)

	Pruned	Kept	Total
New	548	7	555
Fresh	1	4	5
Picked	1	0	1
Done	1	12	13
Total	551	23	574

Error

Counts

574 → 23

Alt Table

Click to see full alt table

Status	Error	Program
	34.6b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 -1/8 (.f64 (/.f64 eps (.f64 x x)) (/.f64 eps x))) x))))
	60.9b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 eps (neg.f64 (/.f64 -1/2 x))) (.f64 eps (neg.f64 (/.f64 -1/2 x))))) (-.f64 x (/.f64 (*.f64 eps 1/2) x)))
✓	25.8b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	34.3b	(*.f64 (/.f64 1/2 x) eps)
✓	34.3b	(/.f64 1/2 (/.f64 x eps))
	60.7b	(*.f64 -2 (/.f64 eps (/.f64 eps x)))
	60.7b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (*.f64 eps (/.f64 -1/2 x)))
✓	60.7b	(*.f64 -2 x)
✓	33.9b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x)))
	60.7b	(.f64 (neg.f64 eps) (/.f64 1 (.f64 (/.f64 eps x) 1/2)))
	61.1b	(-.f64 x (-.f64 (+.f64 1 (*.f64 eps (/.f64 -1/2 x))) 1))
✓	60.4b	(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 eps x))) 1)
✓	59.8b	(-.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x))
✓	60.7b	(-.f64 x (*.f64 eps (/.f64 -1/2 x)))
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	61.1b	(-.f64 x x)
	61.8b	x
✓	35.8b	(.f64 (/.f64 eps x) (+.f64 (.f64 (/.f64 eps (*.f64 x x)) 1/8) 1/2))
✓	34.2b	(*.f64 1/2 (/.f64 eps x))
	60.7b	(*.f64 (/.f64 (/.f64 x eps) -1/2) eps)
	60.7b	(-.f64 x (/.f64 1 (/.f64 x (*.f64 eps -1/2))))
	61.6b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 eps (neg.f64 (/.f64 -1/2 x))) (.f64 eps (neg.f64 (/.f64 -1/2 x))))) (/.f64 (*.f64 eps -1/2) x))
	61.2b	(/.f64 (-.f64 (.f64 x x) (/.f64 (/.f64 (.f64 eps eps) x) (/.f64 x 1/4))) (-.f64 x (*.f64 eps (neg.f64 (/.f64 -1/2 x)))))

Compiler

Compiled 311 to 196 computations (37% saved)

regimes70.0ms (1.1%)

Counts

28 → 1

Calls

Call 1

Inputs
x
x
(*.f64 -2 x)
(-.f64 x x)
(*.f64 x 2)
(*.f64 (/.f64 1/2 x) eps)
(/.f64 1/2 (/.f64 x eps))
(*.f64 1/2 (/.f64 eps x))
(*.f64 -2 (/.f64 eps (/.f64 eps x)))
(*.f64 (/.f64 (/.f64 x eps) -1/2) eps)
(-.f64 x (*.f64 eps (/.f64 -1/2 x)))
(-.f64 x (/.f64 1 (/.f64 x (*.f64 eps -1/2))))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 eps x))) 1)
(-.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x))
(.f64 (neg.f64 eps) (/.f64 1 (.f64 (/.f64 eps x) 1/2)))
(-.f64 x (-.f64 (+.f64 1 (*.f64 eps (/.f64 -1/2 x))) 1))
(.f64 (/.f64 eps x) (+.f64 (.f64 (/.f64 eps (*.f64 x x)) 1/8) 1/2))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (*.f64 eps (/.f64 -1/2 x)))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (*.f64 -1/2 (/.f64 eps x)))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x)))
(/.f64 (-.f64 (.f64 x x) (/.f64 (/.f64 (.f64 eps eps) x) (/.f64 x 1/4))) (-.f64 x (*.f64 eps (neg.f64 (/.f64 -1/2 x)))))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 eps (neg.f64 (/.f64 -1/2 x))) (.f64 eps (neg.f64 (/.f64 -1/2 x))))) (/.f64 (*.f64 eps -1/2) x))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 eps (neg.f64 (/.f64 -1/2 x))) (.f64 eps (neg.f64 (/.f64 -1/2 x))))) (-.f64 x (/.f64 (*.f64 eps 1/2) x)))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 eps (neg.f64 (/.f64 -1/2 x))) (.f64 eps (neg.f64 (/.f64 -1/2 x))))) (-.f64 x (*.f64 eps (neg.f64 (/.f64 -1/2 x)))))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 -1/8 (.f64 (/.f64 eps (.f64 x x)) (/.f64 eps x))) x))))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) x))))

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

Calls

3 calls:

27.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
18.0ms	eps
16.0ms	x

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 357 to 171 computations (52.1% saved)

regimes196.0ms (3.1%)

Counts

26 → 2

Calls

Call 1

Inputs
x
x
(*.f64 -2 x)
(-.f64 x x)
(*.f64 x 2)
(*.f64 (/.f64 1/2 x) eps)
(/.f64 1/2 (/.f64 x eps))
(*.f64 1/2 (/.f64 eps x))
(*.f64 -2 (/.f64 eps (/.f64 eps x)))
(*.f64 (/.f64 (/.f64 x eps) -1/2) eps)
(-.f64 x (*.f64 eps (/.f64 -1/2 x)))
(-.f64 x (/.f64 1 (/.f64 x (*.f64 eps -1/2))))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 eps x))) 1)
(-.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x))
(.f64 (neg.f64 eps) (/.f64 1 (.f64 (/.f64 eps x) 1/2)))
(-.f64 x (-.f64 (+.f64 1 (*.f64 eps (/.f64 -1/2 x))) 1))
(.f64 (/.f64 eps x) (+.f64 (.f64 (/.f64 eps (*.f64 x x)) 1/8) 1/2))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (*.f64 eps (/.f64 -1/2 x)))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (*.f64 -1/2 (/.f64 eps x)))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x)))
(/.f64 (-.f64 (.f64 x x) (/.f64 (/.f64 (.f64 eps eps) x) (/.f64 x 1/4))) (-.f64 x (*.f64 eps (neg.f64 (/.f64 -1/2 x)))))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 eps (neg.f64 (/.f64 -1/2 x))) (.f64 eps (neg.f64 (/.f64 -1/2 x))))) (/.f64 (*.f64 eps -1/2) x))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 eps (neg.f64 (/.f64 -1/2 x))) (.f64 eps (neg.f64 (/.f64 -1/2 x))))) (-.f64 x (/.f64 (*.f64 eps 1/2) x)))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 eps (neg.f64 (/.f64 -1/2 x))) (.f64 eps (neg.f64 (/.f64 -1/2 x))))) (-.f64 x (*.f64 eps (neg.f64 (/.f64 -1/2 x)))))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 -1/8 (.f64 (/.f64 eps (.f64 x x)) (/.f64 eps x))) x))))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Outputs

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

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

Calls

3 calls:

121.0ms	eps
38.0ms	x
27.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

Error	Segments	Branch
7.1b	2	`x`
10.7b	4	`eps`
0.5b	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 310 to 156 computations (49.7% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.4716209599056253e-153	0.0

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes40.0ms (0.6%)

Counts

25 → 1

Calls

Call 1

Inputs
x
x
(*.f64 -2 x)
(-.f64 x x)
(*.f64 x 2)
(*.f64 (/.f64 1/2 x) eps)
(/.f64 1/2 (/.f64 x eps))
(*.f64 1/2 (/.f64 eps x))
(*.f64 -2 (/.f64 eps (/.f64 eps x)))
(*.f64 (/.f64 (/.f64 x eps) -1/2) eps)
(-.f64 x (*.f64 eps (/.f64 -1/2 x)))
(-.f64 x (/.f64 1 (/.f64 x (*.f64 eps -1/2))))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 eps x))) 1)
(-.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x))
(.f64 (neg.f64 eps) (/.f64 1 (.f64 (/.f64 eps x) 1/2)))
(-.f64 x (-.f64 (+.f64 1 (*.f64 eps (/.f64 -1/2 x))) 1))
(.f64 (/.f64 eps x) (+.f64 (.f64 (/.f64 eps (*.f64 x x)) 1/8) 1/2))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (*.f64 eps (/.f64 -1/2 x)))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (*.f64 -1/2 (/.f64 eps x)))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x)))
(/.f64 (-.f64 (.f64 x x) (/.f64 (/.f64 (.f64 eps eps) x) (/.f64 x 1/4))) (-.f64 x (*.f64 eps (neg.f64 (/.f64 -1/2 x)))))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 eps (neg.f64 (/.f64 -1/2 x))) (.f64 eps (neg.f64 (/.f64 -1/2 x))))) (/.f64 (*.f64 eps -1/2) x))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 eps (neg.f64 (/.f64 -1/2 x))) (.f64 eps (neg.f64 (/.f64 -1/2 x))))) (-.f64 x (/.f64 (*.f64 eps 1/2) x)))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 eps (neg.f64 (/.f64 -1/2 x))) (.f64 eps (neg.f64 (/.f64 -1/2 x))))) (-.f64 x (*.f64 eps (neg.f64 (/.f64 -1/2 x)))))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 -1/8 (.f64 (/.f64 eps (.f64 x x)) (/.f64 eps x))) x))))

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

Calls

2 calls:

16.0ms	x
16.0ms	eps

Results

Error	Segments	Branch
33.9b	1	`x`
33.9b	1	`eps`

Compiler

Compiled 292 to 147 computations (49.7% saved)

regimes31.0ms (0.5%)

Counts

19 → 1

Calls

Call 1

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

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

Calls

2 calls:

14.0ms	x
10.0ms	eps

Results

Error	Segments	Branch
34.2b	1	`x`
34.2b	1	`eps`

Compiler

Compiled 146 to 76 computations (47.9% saved)

regimes15.0ms (0.2%)

Counts

7 → 1

Calls

Call 1

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

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

Calls

2 calls:

7.0ms	x
5.0ms	eps

Results

Error	Segments	Branch
34.3b	1	`x`
34.3b	1	`eps`

Compiler

Compiled 29 to 17 computations (41.4% saved)

regimes14.0ms (0.2%)

Counts

6 → 1

Calls

Call 1

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

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

Calls

2 calls:

7.0ms	x
5.0ms	eps

Results

Error	Segments	Branch
34.3b	1	`x`
34.3b	1	`eps`

Compiler

Compiled 24 to 14 computations (41.7% saved)

regimes15.0ms (0.2%)

Counts

5 → 1

Calls

Call 1

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

Outputs
(*.f64 -2 x)

Calls

2 calls:

5.0ms	x
5.0ms	eps

Results

Error	Segments	Branch
60.7b	1	`x`
60.7b	1	`eps`

Compiler

Compiled 19 to 11 computations (42.1% saved)

regimes8.0ms (0.1%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0.0b (-0%)

Counts

2 → 1

Calls

Call 1

Inputs
x
x

Outputs
x

Calls

2 calls:

3.0ms	eps
3.0ms	x

Results

Error	Segments	Branch
61.8b	1	`x`
61.8b	1	`eps`

Compiler

Compiled 10 to 6 computations (40% saved)

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

14×	`+-commutative_binary64`
10×	`*-commutative_binary64`
7×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	156
1	59	156
2	73	156
3	81	156
4	85	156

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))) -7547924849643083/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 -1/8 (.f64 (/.f64 eps (.f64 x x)) (/.f64 eps x))) x)))))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x)))
(*.f64 1/2 (/.f64 eps x))
(/.f64 1/2 (/.f64 x eps))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 -2 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))) -7547924849643083/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 (.f64 -1/8 (.f64 (/.f64 eps (.f64 x x)) (/.f64 eps x))) x)))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) -7547924849643083/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (.f64 -1/2 (/.f64 eps x)) (+.f64 x (.f64 -1/8 (.f64 (/.f64 eps x) (/.f64 eps (.f64 x x)))))))))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 (*.f64 -1/2 (/.f64 eps x)) x)))
(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (+.f64 x (*.f64 -1/2 (/.f64 eps x)))))
(*.f64 1/2 (/.f64 eps x))
(*.f64 (/.f64 eps x) 1/2)
(/.f64 1/2 (/.f64 x eps))
(*.f64 (/.f64 1/2 x) eps)
(*.f64 eps (/.f64 1/2 x))
(*.f64 -2 x)
(*.f64 x -2)
x

Compiler

Compiled 122 to 63 computations (48.4% saved)

soundness0.0ms (0%)

end63.0ms (1%)

Compiler: Compiled 108 to 39 computations (63.9% 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	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

Details

analyze23.0ms (0.4%)

sample1.8s (27.4%)

preprocess55.0ms (0.9%)

simplify38.0ms (0.6%)

eval1.0ms (0%)

prune1.0ms (0%)

localize17.0ms (0.3%)

series17.0ms (0.3%)

rewrite132.0ms (2.1%)

simplify93.0ms (1.4%)

eval62.0ms (1%)

prune19.0ms (0.3%)

localize45.0ms (0.7%)

series11.0ms (0.2%)

rewrite86.0ms (1.3%)

simplify83.0ms (1.3%)

localize3.0ms (0%)

localize3.0ms (0%)

localize5.0ms (0.1%)

localize11.0ms (0.2%)

series6.0ms (0.1%)

rewrite79.0ms (1.2%)

simplify13.0ms (0.2%)

eval149.0ms (2.3%)

prune75.0ms (1.2%)

localize19.0ms (0.3%)

series7.0ms (0.1%)

rewrite77.0ms (1.2%)

simplify87.0ms (1.4%)

localize6.0ms (0.1%)

series2.0ms (0%)

rewrite48.0ms (0.7%)

simplify10.0ms (0.2%)

localize8.0ms (0.1%)

series6.0ms (0.1%)

rewrite68.0ms (1.1%)

simplify18.0ms (0.3%)

localize14.0ms (0.2%)

series25.0ms (0.4%)

rewrite80.0ms (1.2%)

simplify155.0ms (2.4%)

localize45.0ms (0.7%)

series12.0ms (0.2%)

rewrite110.0ms (1.7%)

simplify78.0ms (1.2%)

eval436.0ms (6.8%)

prune439.0ms (6.8%)

localize6.0ms (0.1%)

series2.0ms (0%)

rewrite48.0ms (0.8%)

simplify10.0ms (0.2%)

localize3.0ms (0%)

localize29.0ms (0.4%)

series3.0ms (0%)

rewrite207.0ms (3.2%)

simplify13.0ms (0.2%)

localize15.0ms (0.2%)

series3.0ms (0%)

rewrite60.0ms (0.9%)

simplify9.0ms (0.1%)

localize83.0ms (1.3%)

series10.0ms (0.2%)

rewrite136.0ms (2.1%)

simplify211.0ms (3.3%)

eval398.0ms (6.2%)

prune167.0ms (2.6%)

regimes70.0ms (1.1%)

regimes196.0ms (3.1%)

bsearch0.0ms (0%)

regimes40.0ms (0.6%)

regimes31.0ms (0.5%)

regimes15.0ms (0.2%)

regimes14.0ms (0.2%)

regimes15.0ms (0.2%)

regimes8.0ms (0.1%)

simplify12.0ms (0.2%)

soundness0.0ms (0%)

end63.0ms (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