Details

analyze2.0ms (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)

sample56.0ms (0.7%)

Algorithm

1×

intervals

Results

15.0ms	74×	body	1024	valid
9.0ms	130×	body	128	valid
6.0ms	39×	body	512	valid
1.0ms	13×	body	256	valid

Compiler

Compiled 26 to 22 computations (15.4% saved)

simplify10.0ms (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

20.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	20.6b	(-.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))
✓	0.1b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
✓	0.3b	(/.f64 1 (sqrt.f64 x))
✓	2.4b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

series47.0ms (0.6%)

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))
11.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
7.0ms	(sqrt.f64 (+.f64 x 1))

rewrite209.0ms (2.7%)

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:

40.0ms	(-.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))

simplify820.0ms (10.5%)

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

prune1.5s (18.7%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	619	22	641
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	620	22	642

Error

19.9b

Counts

642 → 22

Alt Table

Status	Error	Program
	31.5b	(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))))
	32.1b	(+.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)))))))
	31.0b	(+.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))))))))
	22.4b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	61.5b	(+.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)))))))
	61.6b	(+.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)))))))
	31.6b	(+.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)))))))
	31.8b	(+.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)))))))
	30.9b	(+.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))))))))
	31.2b	(+.f64 (fma.f64 (/.f64 1 (sqrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)))) (/.f64 1 (sqrt.f64 (cbrt.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)))))))
	31.7b	(/.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)))))))
	30.8b	(+.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)))))))
	31.5b	(fma.f64 (/.f64 1 (*.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x)))) (/.f64 1 (cbrt.f64 (sqrt.f64 x))) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
	31.1b	(+.f64 (fma.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 x))) (/.f64 1 (sqrt.f64 (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))))))))
	31.7b	(+.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)))))))
	31.2b	(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))))
	32.2b	(+.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 (.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)))))))
	31.0b	(fma.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
▶	20.6b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
	61.6b	(+.f64 (fma.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 x))) (/.f64 1 (sqrt.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)))))))
	61.6b	(+.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)))))))
	31.0b	(+.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))))))))

Compiler

Compiled 32547 to 26297 computations (19.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series51.0ms (0.7%)

Counts

3 → 16

Calls

3 calls:

39.0ms	(/.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)))

rewrite325.0ms (4.2%)

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:

64.0ms	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
22.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))
5.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))

simplify728.0ms (9.3%)

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

prune747.0ms (9.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	615	2	617
Fresh	20	1	21
Picked	1	0	1
Done	0	0	0
Total	636	3	639

Error

6.1b

Counts

639 → 3

Alt Table

Status	Error	Program
▶	19.9b	(/.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)))))
	22.4b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	36.6b	(/.f64 (-.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))) (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))

Compiler

Compiled 27832 to 22162 computations (20.4% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.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)))))
	0.3b	(/.f64 1 (sqrt.f64 x))
✓	1.7b	(-.f64 (.f64 1 (+.f64 1 x)) (.f64 x 1))
✓	5.9b	(*.f64 (fma.f64 x x x) (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x))))

series71.0ms (0.9%)

Counts

3 → 12

Calls

3 calls:

57.0ms

(/.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)))))

13.0ms

(*.f64 (fma.f64 x x x) (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x))))

1.0ms

(-.f64 (*.f64 1 (+.f64 1 x)) (*.f64 x 1))

rewrite63.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`

Counts

3 → 74

Calls

3 calls:

28.0ms

(/.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)))))

26.0ms

(*.f64 (fma.f64 x x x) (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x))))

5.0ms

(-.f64 (*.f64 1 (+.f64 1 x)) (*.f64 x 1))

simplify57.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

811×	`distribute-rgt-in_binary64`
787×	`distribute-lft-in_binary64`
645×	`times-frac_binary64`
345×	`fma-def_binary64`
93×	`associate-l_binary64`

Counts

86 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	128	2223
1	363	1643
2	1294	1637
3	5318	1637

prune195.0ms (2.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	153	5	158
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	154	7	161

Error

6.0b

Counts

161 → 7

Alt Table

Status	Error	Program
	22.4b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	6.3b	(/.f64 1 (*.f64 (fma.f64 x x x) (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x)))))
	36.6b	(/.f64 (-.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))) (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
	26.9b	(.f64 (/.f64 1 (.f64 (fma.f64 x x x) (+.f64 (pow.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) 3) (pow.f64 (/.f64 1 (sqrt.f64 x)) 3)))) (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (sqrt.f64 (/.f64 1 (+.f64 1 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (*.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x))))))
▶	6.3b	(*.f64 (/.f64 1 (fma.f64 x x x)) (/.f64 1 (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x)))))
	6.5b	(.f64 (sqrt.f64 (/.f64 1 (.f64 (fma.f64 x x x) (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x)))))) (sqrt.f64 (/.f64 1 (*.f64 (fma.f64 x x x) (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x)))))))
	7.0b	(.f64 (.f64 (cbrt.f64 (/.f64 1 (.f64 (fma.f64 x x x) (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x)))))) (cbrt.f64 (/.f64 1 (.f64 (fma.f64 x x x) (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x))))))) (cbrt.f64 (/.f64 1 (*.f64 (fma.f64 x x x) (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x)))))))

Compiler

Compiled 5882 to 3937 computations (33.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (fma.f64 x x x))
	0.3b	(/.f64 1 (sqrt.f64 x))
✓	0.3b	(/.f64 1 (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x))))
✓	6.0b	(*.f64 (/.f64 1 (fma.f64 x x x)) (/.f64 1 (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x)))))

series94.0ms (1.2%)

Counts

3 → 12

Calls

3 calls:

59.0ms

(*.f64 (/.f64 1 (fma.f64 x x x)) (/.f64 1 (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x)))))

32.0ms

(/.f64 1 (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x))))

3.0ms

(/.f64 1 (fma.f64 x x x))

rewrite70.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`*-un-lft-identity_binary64`
61×	`add-sqr-sqrt_binary64`
60×	`times-frac_binary64`
51×	`add-exp-log_binary64`
37×	`add-cube-cbrt_binary64`

Counts

3 → 158

Calls

3 calls:

31.0ms

(*.f64 (/.f64 1 (fma.f64 x x x)) (/.f64 1 (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x)))))

24.0ms

(/.f64 1 (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x))))

2.0ms

(/.f64 1 (fma.f64 x x x))

simplify138.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

641×	`associate-/l/_binary64`
544×	`fma-def_binary64`
382×	`distribute-rgt-in_binary64`
343×	`distribute-lft-in_binary64`
321×	`associate-/r/_binary64`

Counts

170 → 206

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	143	4518
1	343	4069
2	818	4016
3	1903	3878
4	4499	3878
5	5034	3878

prune260.0ms (3.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	251	4	255
Fresh	5	1	6
Picked	0	1	1
Done	0	0	0
Total	256	6	262

Error

0.0b

Counts

262 → 6

Alt Table

Status	Error	Program
	2.4b	(expm1.f64 (log1p.f64 (/.f64 (/.f64 1 (+.f64 1 x)) (fma.f64 x (sqrt.f64 (/.f64 1 (+.f64 1 x))) (sqrt.f64 x)))))
✓	6.3b	(*.f64 (/.f64 1 (fma.f64 x x x)) (/.f64 1 (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x)))))
	22.4b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	0.6b	(*.f64 (/.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x))))) (hypot.f64 x (sqrt.f64 x))) (/.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x))))) (hypot.f64 x (sqrt.f64 x))))
	9.2b	(.f64 (/.f64 (/.f64 1 (fma.f64 x x x)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	0.7b	(pow.f64 (*.f64 (+.f64 1 x) (fma.f64 x (sqrt.f64 (/.f64 1 (+.f64 1 x))) (sqrt.f64 x))) -1)

Compiler

Compiled 7684 to 5173 computations (32.7% saved)

regimes1.2s (15.5%)

Accuracy

Total 0.5b remaining (96%)

Threshold costs 0.5b (96%)

Counts

441 → 1

Compiler

Compiled 33192 to 27501 computations (17.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	54
1	14	54
2	13	54

end1.0ms (0%)

Compiler: Compiled 36 to 27 computations (25% saved)

sample1.1s (14.5%)

Algorithm

1×

intervals

Results

446.0ms	2225×	body	1024	valid
224.0ms	4317×	body	128	valid
145.0ms	985×	body	512	valid
49.0ms	473×	body	256	valid

Compiler

Compiled 181 to 135 computations (25.4% 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

analyze2.0ms (0%)

sample56.0ms (0.7%)

simplify10.0ms (0.1%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series47.0ms (0.6%)

rewrite209.0ms (2.7%)

simplify820.0ms (10.5%)

prune1.5s (18.7%)

localize12.0ms (0.2%)

series51.0ms (0.7%)

rewrite325.0ms (4.2%)

simplify728.0ms (9.3%)

prune747.0ms (9.6%)

localize16.0ms (0.2%)

series71.0ms (0.9%)

rewrite63.0ms (0.8%)

simplify57.0ms (0.7%)

prune195.0ms (2.5%)

localize12.0ms (0.2%)

series94.0ms (1.2%)

rewrite70.0ms (0.9%)

simplify138.0ms (1.8%)

prune260.0ms (3.3%)

regimes1.2s (15.5%)

simplify2.0ms (0%)

end1.0ms (0%)

sample1.1s (14.5%)

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