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)

sample1.7s (16%)

Results

817.0ms	2226×	body	1024	valid
476.0ms	4487×	body	128	valid
273.0ms	1030×	body	512	valid
98.0ms	513×	body	256	valid

Compiler

Compiled 38 to 32 computations (15.8% saved)

simplify11.0ms (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

20.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	20.3b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 47 to 38 computations (19.1% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 x 1))
✓	0.2b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
✓	0.3b	(/.f64 1 (sqrt.f64 x))
✓	2.7b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

series46.0ms (0.4%)

Counts

4 → 8

Calls

4 calls:

14.0ms	(/.f64 1 (sqrt.f64 x))
14.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
8.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
8.0ms	(sqrt.f64 (+.f64 x 1))

rewrite214.0ms (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:

38.0ms	(-.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))
3.0ms	(sqrt.f64 (+.f64 x 1))

simplify831.0ms (7.9%)

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

prune1.4s (13.6%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	618	23	641
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	619	23	642

Error

19.5b

Counts

642 → 23

Alt Table

Status	Error	Program
	30.4b	(fma.f64 (*.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 x))) (cbrt.f64 (/.f64 1 (sqrt.f64 x)))) (cbrt.f64 (/.f64 1 (sqrt.f64 x))) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
	29.9b	(+.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))))))))
	30.5b	(+.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 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 x 1)))) (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 x 1))))))) (fma.f64 (neg.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 x 1))))) (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 x 1)))) (*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 x 1)))) (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 x 1)))))))
	23.7b	(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 x 1) -1/2))
	20.2b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
	29.8b	(+.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)))))))
	60.3b	(+.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)))))))
	30.7b	(+.f64 (fma.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 x))) (/.f64 1 (sqrt.f64 (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)))))))
	20.4b	(*.f64 (+.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))))) (-.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))))))
	30.0b	(+.f64 (fma.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 x))) (/.f64 1 (sqrt.f64 (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))))))))
▶	20.2b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
	30.0b	(fma.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
	30.0b	(+.f64 (fma.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 x))) (/.f64 1 (sqrt.f64 (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))))))))
	31.0b	(+.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)))))))
	30.6b	(+.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 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)))))))
	31.4b	(/.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)))))))
	30.3b	(fma.f64 (/.f64 1 (sqrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))) (/.f64 1 (sqrt.f64 (cbrt.f64 x))) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
	60.3b	(+.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)))))))
	30.5b	(+.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)))))))
	60.3b	(+.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)))))))
	29.8b	(+.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))))))))
	29.8b	(+.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))))))))
	23.5b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 32429 to 26233 computations (19.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (sqrt.f64 (+.f64 1 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)))))
	0.3b	(/.f64 1 (sqrt.f64 x))
✓	2.7b	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

series44.0ms (0.4%)

Counts

3 → 16

Calls

3 calls:

33.0ms	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
8.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
3.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

rewrite324.0ms (3.1%)

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:

53.0ms	(/.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)))
5.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))

simplify789.0ms (7.5%)

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

prune812.0ms (7.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	614	3	617
Fresh	20	2	22
Picked	1	0	1
Done	0	0	0
Total	635	5	640

Error

5.5b

Counts

640 → 5

Alt Table

Status	Error	Program
	31.4b	(/.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)))))))
▶	5.8b	(/.f64 (/.f64 1 (fma.f64 x x x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
	23.5b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	19.3b	(/.f64 (-.f64 (.f64 1 (+.f64 1 x)) (.f64 x 1)) (*.f64 (fma.f64 x x x) (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x)))))
	36.5b	(/.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (fma.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 -1 x) 1) (/.f64 -1 (pow.f64 x 5)))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))

Compiler

Compiled 27950 to 22254 computations (20.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
	0.3b	(/.f64 1 (sqrt.f64 x))
✓	0.5b	(/.f64 1 (fma.f64 x x x))
✓	5.2b	(/.f64 (/.f64 1 (fma.f64 x x x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))

series55.0ms (0.5%)

Counts

2 → 12

Calls

2 calls:

52.0ms	(/.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))

rewrite98.0ms (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 (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))

simplify238.0ms (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

prune418.0ms (4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	337	5	342
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	340	7	347

Error

0.0b

Counts

347 → 7

Alt Table

Status	Error	Program
✓	5.8b	(/.f64 (/.f64 1 (fma.f64 x x x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
	1.2b	(.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)))))))
▶	0.4b	(*.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))))))
	25.6b	(.f64 (/.f64 (/.f64 1 (fma.f64 x x x)) (+.f64 (/.f64 1 (pow.f64 x 3/2)) (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)))))))
	8.4b	(.f64 (/.f64 (/.f64 1 (fma.f64 x x x)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
	5.8b	(/.f64 1 (/.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))) (/.f64 1 (fma.f64 x x x))))
	23.5b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 10560 to 6857 computations (35.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series563.0ms (5.3%)

Counts

2 → 2

Calls

2 calls:

534.0ms	(/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
29.0ms	(/.f64 1 (hypot.f64 x (sqrt.f64 x)))

rewrite102.0ms (1%)

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:

33.0ms	(/.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)))

simplify398.0ms (3.8%)

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

prune515.0ms (4.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	362	2	364
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	364	7	371

Error

0.0b

Counts

371 → 7

Alt Table

Status	Error	Program
	0.5b	(*.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))))))
✓	0.4b	(*.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))))))
	0.5b	(.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 x (sqrt.f64 x)))) (.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 (hypot.f64 x (sqrt.f64 x))))))
	25.6b	(.f64 (/.f64 (/.f64 1 (fma.f64 x x x)) (+.f64 (/.f64 1 (pow.f64 x 3/2)) (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)))))))
	8.4b	(.f64 (/.f64 (/.f64 1 (fma.f64 x x x)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
✓	5.8b	(/.f64 (/.f64 1 (fma.f64 x x x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
	23.5b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 13387 to 8021 computations (40.1% saved)

regimes1.8s (17%)

Accuracy

Total 0.3b remaining (91.2%)

Threshold costs 0.3b (91.2%)

Counts

548 → 1

Compiler

Compiled 43414 to 33845 computations (22% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	54
1	20	54
2	19	54

end137.0ms (1.3%)

Compiler: Compiled 273 to 188 computations (31.1% 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%)

sample1.7s (16%)

simplify11.0ms (0.1%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series46.0ms (0.4%)

rewrite214.0ms (2%)

simplify831.0ms (7.9%)

prune1.4s (13.6%)

localize12.0ms (0.1%)

series44.0ms (0.4%)

rewrite324.0ms (3.1%)

simplify789.0ms (7.5%)

prune812.0ms (7.7%)

localize10.0ms (0.1%)

series55.0ms (0.5%)

rewrite98.0ms (0.9%)

simplify238.0ms (2.3%)

prune418.0ms (4%)

localize11.0ms (0.1%)

series563.0ms (5.3%)

rewrite102.0ms (1%)

simplify398.0ms (3.8%)

prune515.0ms (4.9%)

regimes1.8s (17%)

simplify2.0ms (0%)

end137.0ms (1.3%)

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