Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	0%	50%	2

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample54.0ms (0.5%)

Algorithm

1×

intervals

Results

16.0ms	79×	body	1024	valid
7.0ms	137×	body	128	valid
4.0ms	27×	body	512	valid
1.0ms	13×	body	256	valid

Compiler

Compiled 26 to 22 computations (15.4% saved)

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	14	17
2	20	17
3	28	17
4	36	17
5	54	17
6	79	17
7	96	17
8	113	17
9	123	17
10	127	17
11	129	17
12	115	17

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

18.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	18.3b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 47 to 38 computations (19.1% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 x 1))
✓	0.1b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
✓	0.2b	(/.f64 1 (sqrt.f64 x))
✓	2.5b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

series47.0ms (0.5%)

Counts

4 → 8

Calls

4 calls:

16.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
13.0ms	(/.f64 1 (sqrt.f64 x))
10.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
8.0ms	(sqrt.f64 (+.f64 x 1))

rewrite206.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

1084×	`times-frac_binary64`
922×	`*-un-lft-identity_binary64`
802×	`add-sqr-sqrt_binary64`
728×	`add-cube-cbrt_binary64`
594×	`prod-diff_binary64`

Counts

4 → 815

Calls

4 calls:

39.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
5.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
3.0ms	(/.f64 1 (sqrt.f64 x))
2.0ms	(sqrt.f64 (+.f64 x 1))

simplify785.0ms (7.7%)

Algorithm

1×	egg-herbie

Rules

814×	`fma-neg_binary64`
623×	`fma-def_binary64`
489×	`cancel-sign-sub-inv_binary64`
358×	`associate-r_binary64`
241×	`times-frac_binary64`

Counts

823 → 641

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	242	36505
1	501	25671
2	1210	18755
3	3412	17853
4	4423	17803
5	4884	17803
6	4730	17803

prune1.3s (12.2%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	620	21	641
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	621	21	642

Error

17.7b

Counts

642 → 21

Alt Table

Status	Error	Program
	30.4b	(+.f64 (fma.f64 1 (/.f64 1 (sqrt.f64 x)) (neg.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1)))) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 1 3))))))) (fma.f64 (neg.f64 (sqrt.f64 (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1))))) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 1 3)))) (.f64 (sqrt.f64 (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (*.f64 x 1)))) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 1 3)))))))
	20.1b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	29.6b	(+.f64 (fma.f64 1 (/.f64 1 (sqrt.f64 x)) (neg.f64 (.f64 (/.f64 1 (cbrt.f64 (sqrt.f64 (+.f64 x 1)))) (/.f64 1 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 (sqrt.f64 (+.f64 x 1)))))))) (fma.f64 (neg.f64 (/.f64 1 (cbrt.f64 (sqrt.f64 (+.f64 x 1))))) (/.f64 1 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 (sqrt.f64 (+.f64 x 1))))) (.f64 (/.f64 1 (cbrt.f64 (sqrt.f64 (+.f64 x 1)))) (/.f64 1 (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 (sqrt.f64 (+.f64 x 1))))))))
	29.8b	(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (neg.f64 (.f64 (/.f64 1 (cbrt.f64 (sqrt.f64 (+.f64 x 1)))) (/.f64 1 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 (sqrt.f64 (+.f64 x 1)))))))) (fma.f64 (neg.f64 (/.f64 1 (cbrt.f64 (sqrt.f64 (+.f64 x 1))))) (/.f64 1 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 (sqrt.f64 (+.f64 x 1))))) (.f64 (/.f64 1 (cbrt.f64 (sqrt.f64 (+.f64 x 1)))) (/.f64 1 (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 (sqrt.f64 (+.f64 x 1))))))))
	31.1b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 x))) (cbrt.f64 (/.f64 1 (sqrt.f64 x)))) (cbrt.f64 (/.f64 1 (sqrt.f64 x))) (neg.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1)))) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 1 3))))))) (fma.f64 (neg.f64 (sqrt.f64 (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1))))) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 1 3)))) (.f64 (sqrt.f64 (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1)))) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 1 3)))))))
	61.8b	(+.f64 (fma.f64 (/.f64 1 (.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x)))) (/.f64 1 (cbrt.f64 (sqrt.f64 x))) (neg.f64 (.f64 (sqrt.f64 (-.f64 x 1)) (/.f64 1 (sqrt.f64 (-.f64 (.f64 x x) (.f64 1 1))))))) (fma.f64 (neg.f64 (sqrt.f64 (-.f64 x 1))) (/.f64 1 (sqrt.f64 (-.f64 (.f64 x x) (.f64 1 1)))) (.f64 (sqrt.f64 (-.f64 x 1)) (/.f64 1 (sqrt.f64 (-.f64 (.f64 x x) (*.f64 1 1)))))))
	30.8b	(+.f64 (fma.f64 (/.f64 1 (sqrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)))) (/.f64 1 (sqrt.f64 (cbrt.f64 x))) (neg.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1)))) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 1 3))))))) (fma.f64 (neg.f64 (sqrt.f64 (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1))))) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 1 3)))) (.f64 (sqrt.f64 (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1)))) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 1 3)))))))
	30.3b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 x))) (cbrt.f64 (/.f64 1 (sqrt.f64 x)))) (cbrt.f64 (/.f64 1 (sqrt.f64 x))) (neg.f64 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))))))) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))) (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))))))
	29.9b	(fma.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
	18.8b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 x))) (cbrt.f64 (/.f64 1 (sqrt.f64 x)))) (cbrt.f64 (/.f64 1 (sqrt.f64 x))) (neg.f64 (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))) (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))) (cbrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))))) (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))) (cbrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))))) (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))) (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))) (cbrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))))))))
▶	18.3b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
	61.7b	(+.f64 (fma.f64 1 (/.f64 1 (sqrt.f64 x)) (neg.f64 (.f64 (sqrt.f64 (-.f64 x 1)) (/.f64 1 (sqrt.f64 (-.f64 (.f64 x x) (.f64 1 1))))))) (fma.f64 (neg.f64 (sqrt.f64 (-.f64 x 1))) (/.f64 1 (sqrt.f64 (-.f64 (.f64 x x) (.f64 1 1)))) (.f64 (sqrt.f64 (-.f64 x 1)) (/.f64 1 (sqrt.f64 (-.f64 (.f64 x x) (.f64 1 1)))))))
	30.6b	(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (neg.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1)))) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 1 3))))))) (fma.f64 (neg.f64 (sqrt.f64 (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1))))) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 1 3)))) (.f64 (sqrt.f64 (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (*.f64 x 1)))) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 1 3)))))))
	30.0b	(+.f64 (fma.f64 (/.f64 1 (sqrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)))) (/.f64 1 (sqrt.f64 (cbrt.f64 x))) (neg.f64 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))))))) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))) (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))))))
	61.8b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 x))) (cbrt.f64 (/.f64 1 (sqrt.f64 x)))) (cbrt.f64 (/.f64 1 (sqrt.f64 x))) (neg.f64 (.f64 (sqrt.f64 (-.f64 x 1)) (/.f64 1 (sqrt.f64 (-.f64 (.f64 x x) (.f64 1 1))))))) (fma.f64 (neg.f64 (sqrt.f64 (-.f64 x 1))) (/.f64 1 (sqrt.f64 (-.f64 (.f64 x x) (.f64 1 1)))) (.f64 (sqrt.f64 (-.f64 x 1)) (/.f64 1 (sqrt.f64 (-.f64 (.f64 x x) (*.f64 1 1)))))))
	29.6b	(+.f64 (fma.f64 1 (/.f64 1 (sqrt.f64 x)) (neg.f64 (.f64 (/.f64 1 (sqrt.f64 (cbrt.f64 (+.f64 x 1)))) (/.f64 1 (sqrt.f64 (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))))))) (fma.f64 (neg.f64 (/.f64 1 (sqrt.f64 (cbrt.f64 (+.f64 x 1))))) (/.f64 1 (sqrt.f64 (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))))) (.f64 (/.f64 1 (sqrt.f64 (cbrt.f64 (+.f64 x 1)))) (/.f64 1 (sqrt.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))))))))
	61.7b	(+.f64 (fma.f64 (/.f64 1 (sqrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)))) (/.f64 1 (sqrt.f64 (cbrt.f64 x))) (neg.f64 (.f64 (sqrt.f64 (-.f64 x 1)) (/.f64 1 (sqrt.f64 (-.f64 (.f64 x x) (.f64 1 1))))))) (fma.f64 (neg.f64 (sqrt.f64 (-.f64 x 1))) (/.f64 1 (sqrt.f64 (-.f64 (.f64 x x) (.f64 1 1)))) (.f64 (sqrt.f64 (-.f64 x 1)) (/.f64 1 (sqrt.f64 (-.f64 (.f64 x x) (*.f64 1 1)))))))
	29.7b	(+.f64 (fma.f64 1 (/.f64 1 (sqrt.f64 x)) (neg.f64 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))))))) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))) (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))))))
	29.6b	(+.f64 (fma.f64 1 (/.f64 1 (sqrt.f64 x)) (neg.f64 (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))) (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))) (cbrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))))) (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))) (cbrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))))) (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))) (*.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1)))) (cbrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))))))))
	29.3b	(/.f64 (+.f64 (/.f64 1 (pow.f64 x 3/2)) (/.f64 -1 (pow.f64 (sqrt.f64 (+.f64 1 x)) 3))) (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 1 (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))))))
	61.7b	(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (neg.f64 (.f64 (sqrt.f64 (-.f64 x 1)) (/.f64 1 (sqrt.f64 (-.f64 (.f64 x x) (.f64 1 1))))))) (fma.f64 (neg.f64 (sqrt.f64 (-.f64 x 1))) (/.f64 1 (sqrt.f64 (-.f64 (.f64 x x) (.f64 1 1)))) (.f64 (sqrt.f64 (-.f64 x 1)) (/.f64 1 (sqrt.f64 (-.f64 (.f64 x x) (.f64 1 1)))))))

Compiler

Compiled 32675 to 26431 computations (19.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
	0.2b	(/.f64 1 (sqrt.f64 x))
✓	0.3b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
✓	2.4b	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

series48.0ms (0.5%)

Counts

3 → 16

Calls

3 calls:

36.0ms	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
9.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
3.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

rewrite270.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

1631×	`*-un-lft-identity_binary64`
1558×	`times-frac_binary64`
946×	`add-sqr-sqrt_binary64`
514×	`add-cube-cbrt_binary64`
468×	`distribute-lft-out_binary64`

Counts

3 → 762

Calls

3 calls:

57.0ms	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
20.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))
9.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))

simplify716.0ms (7%)

Algorithm

1×	egg-herbie

Rules

789×	`fma-def_binary64`
594×	`times-frac_binary64`
422×	`div-sub_binary64`
388×	`fma-neg_binary64`
296×	`distribute-rgt-in_binary64`

Counts

778 → 568

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	302	32070
1	682	27791
2	1939	25611
3	4269	25601
4	4605	25601
5	4819	25601

prune780.0ms (7.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	615	2	617
Fresh	19	1	20
Picked	1	0	1
Done	0	0	0
Total	635	3	638

Error

6.0b

Counts

638 → 3

Alt Table

Status	Error	Program
	20.1b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
▶	6.2b	(/.f64 (/.f64 1 (fma.f64 x x x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
	17.6b	(/.f64 (/.f64 (-.f64 (.f64 1 (+.f64 1 x)) (.f64 x 1)) (*.f64 x (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))

Compiler

Compiled 27812 to 22144 computations (20.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
	0.2b	(/.f64 1 (sqrt.f64 x))
✓	0.6b	(/.f64 1 (fma.f64 x x x))
✓	5.5b	(/.f64 (/.f64 1 (fma.f64 x x x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))

series58.0ms (0.6%)

Counts

2 → 12

Calls

2 calls:

55.0ms	(/.f64 (/.f64 1 (fma.f64 x x x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
3.0ms	(/.f64 1 (fma.f64 x x x))

rewrite96.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

622×	`times-frac_binary64`
577×	`*-un-lft-identity_binary64`
227×	`add-sqr-sqrt_binary64`
227×	`add-cube-cbrt_binary64`
224×	`distribute-lft-out_binary64`

Counts

2 → 292

Calls

2 calls:

32.0ms	(/.f64 (/.f64 1 (fma.f64 x x x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
2.0ms	(/.f64 1 (fma.f64 x x x))

simplify236.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

722×	`distribute-rgt-in_binary64`
669×	`distribute-lft-in_binary64`
620×	`fma-def_binary64`
155×	`associate-/r*_binary64`
146×	`times-frac_binary64`

Counts

304 → 227

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	135	10736
1	324	10483
2	802	10360
3	2047	10355
4	5225	10355

prune482.0ms (4.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	333	9	342
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	335	10	345

Error

0.0b

Counts

345 → 10

Alt Table

Status	Error	Program
	1.1b	(.f64 (/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (.f64 (cbrt.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))) (cbrt.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))) (/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (cbrt.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))))
	23.9b	(cbrt.f64 (.f64 (.f64 (/.f64 (/.f64 1 (fma.f64 x x x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))) (/.f64 (/.f64 1 (fma.f64 x x x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))) (/.f64 (/.f64 1 (fma.f64 x x x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))))
	6.2b	(/.f64 (/.f64 1 (fma.f64 x x x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (*.f64 1 (sqrt.f64 (/.f64 1 (+.f64 1 x))))))
	6.8b	(/.f64 (/.f64 (/.f64 1 (fma.f64 x x x)) (*.f64 (cbrt.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))) (cbrt.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))) (cbrt.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))
	20.1b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	5.5b	(/.f64 (*.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 1 (hypot.f64 x (sqrt.f64 x)))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
▶	0.3b	(*.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))
	6.8b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))) (/.f64 (/.f64 1 (cbrt.f64 (fma.f64 x x x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))
	6.1b	(/.f64 (/.f64 1 (sqrt.f64 (fma.f64 x x x))) (*.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))) (hypot.f64 x (sqrt.f64 x))))
	6.2b	(/.f64 1 (/.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))) (/.f64 1 (fma.f64 x x x))))

Compiler

Compiled 10799 to 7009 computations (35.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (hypot.f64 x (sqrt.f64 x)))
	0.1b	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
	0.2b	(/.f64 1 (sqrt.f64 x))
✓	0.3b	(/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))

series606.0ms (5.9%)

Counts

2 → 2

Calls

2 calls:

579.0ms	(/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
27.0ms	(/.f64 1 (hypot.f64 x (sqrt.f64 x)))

rewrite97.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

622×	`times-frac_binary64`
577×	`*-un-lft-identity_binary64`
227×	`add-sqr-sqrt_binary64`
227×	`add-cube-cbrt_binary64`
224×	`distribute-lft-out_binary64`

Counts

2 → 292

Calls

2 calls:

31.0ms	(/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
2.0ms	(/.f64 1 (hypot.f64 x (sqrt.f64 x)))

simplify419.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

582×	`div-sub_binary64`
303×	`associate-/l*_binary64`
300×	`fma-def_binary64`
287×	`associate-+l+_binary64`
287×	`associate-/l/_binary64`

Counts

294 → 211

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	115	11045
1	267	10784
2	591	10767
3	1264	10767
4	2685	10767
5	3195	10767
6	4802	10767
7	4970	10767

prune753.0ms (7.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	359	5	364
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	365	9	374

Error

0.0b

Counts

374 → 9

Alt Table

Status	Error	Program
	0.5b	(.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (.f64 (/.f64 1 (sqrt.f64 (hypot.f64 x (sqrt.f64 x)))) (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 x (sqrt.f64 x)))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))))
	0.5b	(.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (+.f64 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 x)))) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))
	20.1b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	0.4b	(*.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 x (sqrt.f64 x)))) (sqrt.f64 (hypot.f64 x (sqrt.f64 x)))) (/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))
	0.3b	(.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (.f64 1 (sqrt.f64 (/.f64 1 (+.f64 1 x)))))))
	1.1b	(.f64 (/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (.f64 (cbrt.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))) (cbrt.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))) (/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (cbrt.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))))
	6.2b	(/.f64 (/.f64 1 (fma.f64 x x x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (*.f64 1 (sqrt.f64 (/.f64 1 (+.f64 1 x))))))
	21.9b	(.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (.f64 (/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (+.f64 (/.f64 (/.f64 1 x) (sqrt.f64 x)) (pow.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) 3))) (+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 1 (sqrt.f64 (+.f64 1 x)))) (*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))))
	6.2b	(/.f64 1 (/.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))) (/.f64 1 (fma.f64 x x x))))

Compiler

Compiled 13485 to 8090 computations (40% saved)

regimes2.1s (20.5%)

Accuracy

Total 0.3b remaining (92.8%)

Threshold costs 0.3b (92.8%)

Counts

696 → 1

Compiler

Compiled 54761 to 44132 computations (19.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	39
1	20	39
2	19	39

end1.0ms (0%)

Compiler: Compiled 26 to 17 computations (34.6% saved)

sample1.2s (11.5%)

Algorithm

1×

intervals

Results

432.0ms	2273×	body	1024	valid
222.0ms	4223×	body	128	valid
147.0ms	1000×	body	512	valid
46.0ms	504×	body	256	valid

Compiler

Compiled 341 to 236 computations (30.8% saved)

Iter	Nodes	Cost
0	9	17
1	14	17
2	20	17
3	28	17
4	36	17
5	54	17
6	79	17
7	96	17
8	113	17
9	123	17
10	127	17
11	129	17
12	115	17

Iter	Nodes	Cost
0	9	17
1	14	17
2	20	17
3	28	17
4	36	17
5	54	17
6	79	17
7	96	17
8	113	17
9	123	17
10	127	17
11	129	17
12	115	17

Details

analyze1.0ms (0%)

sample54.0ms (0.5%)

simplify12.0ms (0.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series47.0ms (0.5%)

rewrite206.0ms (2%)

simplify785.0ms (7.7%)

prune1.3s (12.2%)

localize11.0ms (0.1%)

series48.0ms (0.5%)

rewrite270.0ms (2.6%)

simplify716.0ms (7%)

prune780.0ms (7.6%)

localize10.0ms (0.1%)

series58.0ms (0.6%)

rewrite96.0ms (0.9%)

simplify236.0ms (2.3%)

prune482.0ms (4.7%)

localize12.0ms (0.1%)

series606.0ms (5.9%)

rewrite97.0ms (0.9%)

simplify419.0ms (4.1%)

prune753.0ms (7.3%)

regimes2.1s (20.5%)

simplify2.0ms (0%)

end1.0ms (0%)

sample1.2s (11.5%)

Profiling

Iter	Nodes	Cost
0	9	17
1	14	17
2	20	17
3	28	17
4	36	17
5	54	17
6	79	17
7	96	17
8	113	17
9	123	17
10	127	17
11	129	17
12	115	17