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)

sample1.9s (14.6%)

Results

959.0ms	2250×	body	1024	valid
458.0ms	4417×	body	128	valid
310.0ms	1054×	body	512	valid
97.0ms	535×	body	256	valid

Compiler

Compiled 38 to 32 computations (15.8% 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

21.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	21.5b	(-.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)))
✓	0.2b	(/.f64 1 (sqrt.f64 x))
✓	5.1b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

series88.0ms (0.7%)

Counts

4 → 8

Calls

4 calls:

51.0ms	(sqrt.f64 (+.f64 x 1))
16.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
12.0ms	(/.f64 1 (sqrt.f64 x))
8.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))

rewrite202.0ms (1.6%)

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:

37.0ms	(-.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))

simplify821.0ms (6.4%)

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 (10.6%)

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

20.6b

Counts

642 → 22

Alt Table

Status	Error	Program
	23.5b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
▶	21.5b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
	31.2b	(+.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))))))))
	31.1b	(+.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)))))))
	31.2b	(+.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))))))))
	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)))))))
	61.7b	(+.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)))))))
	32.0b	(/.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)))))))
	61.5b	(+.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)))))))
	61.5b	(+.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)))))))
	31.7b	(+.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)))))))
	31.0b	(+.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 (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))))))))
	31.0b	(+.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))))))))
	31.0b	(+.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))))))))
	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)))))))
	31.6b	(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))))
	32.0b	(+.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 (/.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)))))))
	31.9b	(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))))
	32.2b	(+.f64 (fma.f64 (/.f64 1 (sqrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)))) (/.f64 1 (sqrt.f64 (cbrt.f64 x))) (neg.f64 (.f64 (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)))))))
	32.0b	(/.f64 (-.f64 (pow.f64 (/.f64 1 (sqrt.f64 x)) 3) (pow.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))) 3)) (+.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (+.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))) (/.f64 1 (sqrt.f64 (+.f64 x 1)))) (*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))))))
	31.2b	(fma.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))

Compiler

Compiled 32553 to 26327 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)))))
✓	5.0b	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

series45.0ms (0.4%)

Counts

3 → 16

Calls

3 calls:

34.0ms	(/.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)))

rewrite267.0ms (2.1%)

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:

52.0ms	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
19.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))
6.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))

simplify844.0ms (6.6%)

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

prune831.0ms (6.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	616	1	617
Fresh	19	2	21
Picked	1	0	1
Done	0	0	0
Total	636	3	639

Error

3.7b

Counts

639 → 3

Alt Table

Status	Error	Program
	23.5b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	31.1b	(+.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)))))))
▶	3.9b	(/.f64 (/.f64 1 (fma.f64 x x x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))

Compiler

Compiled 27866 to 22196 computations (20.3% 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))
✓	0.4b	(/.f64 1 (fma.f64 x x x))
✓	3.4b	(/.f64 (/.f64 1 (fma.f64 x x x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))

series52.0ms (0.4%)

Counts

2 → 12

Calls

2 calls:

49.0ms	(/.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))

rewrite99.0ms (0.8%)

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)))))
3.0ms	(/.f64 1 (fma.f64 x x x))

simplify237.0ms (1.9%)

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

prune463.0ms (3.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	333	9	342
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	336	9	345

Error

0.0b

Counts

345 → 9

Alt Table

Status	Error	Program
▶	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))))))
	3.9b	(/.f64 (/.f64 1 (fma.f64 x x x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) 3))))
	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)))))))
	3.9b	(/.f64 (/.f64 1 (fma.f64 x x x)) (+.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
	0.6b	(*.f64 (/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (sqrt.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))) (/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (sqrt.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))))
	23.8b	(.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)))))))
	3.9b	(/.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))))
	4.1b	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))) (/.f64 (/.f64 1 (fma.f64 x x x)) (sqrt.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))))
	4.7b	(/.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))) (cbrt.f64 (fma.f64 x x x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))

Compiler

Compiled 10775 to 7001 computations (35% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.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))))))
✓	0.1b	(/.f64 1 (hypot.f64 x (sqrt.f64 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)))))

series757.0ms (5.9%)

Counts

3 → 2

Calls

3 calls:

533.0ms

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

196.0ms

(*.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))))))

27.0ms

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

rewrite331.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

1240×	`times-frac_binary64`
1121×	`*-un-lft-identity_binary64`
479×	`add-sqr-sqrt_binary64`
439×	`add-cube-cbrt_binary64`
432×	`distribute-lft-out_binary64`

Counts

3 → 572

Calls

3 calls:

84.0ms

(*.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))))))

32.0ms

(/.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)))

simplify594.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

380×	`distribute-rgt-in_binary64`
352×	`distribute-lft-in_binary64`
335×	`fma-def_binary64`
325×	`associate-l_binary64`
292×	`associate-/r*_binary64`

Counts

574 → 476

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	176	19874
1	467	18526
2	1273	18372
3	2380	18315
4	4187	18277
5	4716	18277
6	5120	18277

prune891.0ms (7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	557	6	563
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	564	8	572

Error

Counts

572 → 8

Alt Table

Status	Error	Program
	0.4b	(*.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (+.f64 (pow.f64 (sqrt.f64 x) -1) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))
	3.9b	(/.f64 (/.f64 1 (fma.f64 x x x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 1 (+.f64 1 x))) 3))))
	0.4b	(.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (.f64 (sqrt.f64 (/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))) (sqrt.f64 (/.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 (/.f64 1 (hypot.f64 x (sqrt.f64 x)))) (.f64 (hypot.f64 x (sqrt.f64 x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))
	3.9b	(/.f64 (/.f64 1 (fma.f64 x x x)) (+.f64 (pow.f64 x -1/2) (/.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 1 (sqrt.f64 (hypot.f64 x (sqrt.f64 x)))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))))
	0.6b	(*.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (+.f64 (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))
	0.3b	(/.f64 (/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))) (hypot.f64 x (sqrt.f64 x)))

Compiler

Compiled 22664 to 13432 computations (40.7% saved)

regimes2.8s (22.1%)

Accuracy

Total 0.3b remaining (93.8%)

Threshold costs 0.3b (93.8%)

Counts

880 → 1

Compiler

Compiled 66764 to 52290 computations (21.7% 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	36
1	20	36
2	19	36

end136.0ms (1.1%)

Compiler: Compiled 277 to 180 computations (35% 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%)

sample1.9s (14.6%)

simplify12.0ms (0.1%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series88.0ms (0.7%)

rewrite202.0ms (1.6%)

simplify821.0ms (6.4%)

prune1.4s (10.6%)

localize11.0ms (0.1%)

series45.0ms (0.4%)

rewrite267.0ms (2.1%)

simplify844.0ms (6.6%)

prune831.0ms (6.5%)

localize10.0ms (0.1%)

series52.0ms (0.4%)

rewrite99.0ms (0.8%)

simplify237.0ms (1.9%)

prune463.0ms (3.6%)

localize11.0ms (0.1%)

series757.0ms (5.9%)

rewrite331.0ms (2.6%)

simplify594.0ms (4.7%)

prune891.0ms (7%)

regimes2.8s (22.1%)

simplify2.0ms (0%)

end136.0ms (1.1%)

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