Details

analyze92.0ms (0.6%)

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)

sample66.0ms (0.4%)

Algorithm

1×

intervals

Results

28.0ms	69×	body	1024	valid
13.0ms	135×	body	128	valid
11.0ms	33×	body	512	valid
4.0ms	19×	body	256	valid

Compiler

Compiled 26 to 22 computations (15.4% saved)

simplify26.0ms (0.2%)

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

prune4.0ms (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

19.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	19.7b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 47 to 38 computations (19.1% saved)

localize15.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
✓	0.2b	(/.f64 1 (sqrt.f64 x))
✓	3.4b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite331.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

1084×	`times-frac_binary64`
917×	`*-un-lft-identity_binary64`
796×	`add-sqr-sqrt_binary64`
726×	`add-cube-cbrt_binary64`
594×	`prod-diff_binary64`

Counts

3 → 795

Calls

3 calls:

75.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
10.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
5.0ms	(/.f64 1 (sqrt.f64 x))

series61.0ms (0.4%)

Counts

3 → 4

Calls

3 calls:

25.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
21.0ms	(/.f64 1 (sqrt.f64 x))
14.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))

simplify1.9s (12.4%)

Algorithm

1×	egg-herbie

Rules

824×	`fma-neg_binary64`
536×	`fma-def_binary64`
507×	`cancel-sign-sub-inv_binary64`
328×	`associate-l_binary64`
257×	`associate-r_binary64`

Counts

799 → 1576

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	230	36293
1	470	25468
2	1124	18558
3	3380	17657
4	4412	17607
5	4895	17607
6	4726	17607

prune2.9s (19.3%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	1555	21	1576
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	1556	21	1577

Error

19.0b

Counts

1577 → 21

Alt Table

Status	Error	Program
	61.6b	(+.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)))))))
	31.3b	(+.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 (*.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))))
▶	19.8b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
	30.5b	(+.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))))))))
	30.5b	(+.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))))))))
	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)))))))
	30.4b	(+.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)))))))
	30.7b	(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (sqrt.f64 (/.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))))))))
	30.3b	(/.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)))))))
	30.9b	(+.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)))))))
	23.0b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	30.7b	(fma.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
	31.4b	(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))))
	30.7b	(+.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))))))))
	61.6b	(+.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 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)))))))
	31.2b	(+.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)))))))
	30.4b	(+.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))))))))
	30.2b	(/.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)))))))
	30.7b	(+.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))))))))

Compiler

Compiled 31797 to 25752 computations (19% saved)

localize23.0ms (0.2%)

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)))))
✓	3.4b	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

rewrite499.0ms (3.3%)

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:

183.0ms	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
66.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))
11.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))

series80.0ms (0.5%)

Counts

3 → 16

Calls

3 calls:

61.0ms	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
14.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
5.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

simplify1.8s (12%)

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 → 1533

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

prune808.0ms (5.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	1608	3	1611
Fresh	19	1	20
Picked	1	0	1
Done	0	0	0
Total	1628	4	1632

Error

4.6b

Counts

1632 → 4

Alt Table

Status	Error	Program
	19.8b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
	19.1b	(/.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)))))
▶	4.8b	(/.f64 (/.f64 1 (fma.f64 x x x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
	23.0b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 27810 to 22142 computations (20.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (fma.f64 x x x))
	0.1b	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
	0.2b	(/.f64 1 (sqrt.f64 x))
✓	4.8b	(/.f64 (/.f64 1 (fma.f64 x x x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))

rewrite72.0ms (0.5%)

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:

34.0ms	(/.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))

series52.0ms (0.3%)

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))

simplify297.0ms (2%)

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 → 572

Iterations

Useful iterations: 3 (0.0ms)

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

prune528.0ms (3.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	823	8	831
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	826	9	835

Error

0.0b

Counts

835 → 9

Alt Table

Status	Error	Program
	22.9b	(cbrt.f64 (pow.f64 (/.f64 (/.f64 1 (fma.f64 x x x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.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)))))))
	4.8b	(/.f64 (/.f64 1 (fma.f64 x x x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 x) -1/2)))
	4.8b	(/.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)))))
	24.7b	(.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)))))))
	5.5b	(/.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)))))
▶	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))))))
	23.0b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	4.8b	(/.f64 1 (*.f64 (fma.f64 x x x) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))

Compiler

Compiled 10633 to 6904 computations (35.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite208.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

1231×	`times-frac_binary64`
1112×	`*-un-lft-identity_binary64`
470×	`add-sqr-sqrt_binary64`
432×	`distribute-lft-out_binary64`
430×	`add-cube-cbrt_binary64`

Counts

2 → 539

Calls

2 calls:

95.0ms

(*.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))))))

35.0ms

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

series622.0ms (4.2%)

Counts

2 → 0

Calls

2 calls:

458.0ms

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

164.0ms

(*.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))))))

simplify640.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

380×	`distribute-rgt-in_binary64`
352×	`distribute-lft-in_binary64`
331×	`fma-def_binary64`
326×	`associate-l_binary64`
305×	`associate-/r*_binary64`

Counts

539 → 1051

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	167	19412
1	459	18096
2	1256	17942
3	2370	17885
4	4166	17847
5	4689	17847
6	5026	17847

prune854.0ms (5.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	1564	5	1569
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	1571	7	1578

Error

Counts

1578 → 7

Alt Table

Status	Error	Program
	23.0b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	0.4b	(.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))))))
	0.3b	(*.f64 (/.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)))))) (hypot.f64 x (sqrt.f64 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))))))
	0.4b	(*.f64 (/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (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))))))
	0.4b	(*.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (+.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))
	4.8b	(/.f64 1 (*.f64 (fma.f64 x x x) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))

Compiler

Compiled 22235 to 13333 computations (40% saved)

regimes2.0s (13.3%)

Accuracy

Total 0.3b remaining (94.4%)

Threshold costs 0.3b (94.4%)

Compiler

Compiled 55580 to 42774 computations (23% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	36
1	17	36
2	16	36

end1.0ms (0%)

Compiler: Compiled 24 to 15 computations (37.5% saved)

sample1.1s (7.4%)

Algorithm

1×

intervals

Results

411.0ms	2229×	body	1024	valid
214.0ms	4280×	body	128	valid
140.0ms	992×	body	512	valid
48.0ms	499×	body	256	valid

Compiler

Compiled 230 to 151 computations (34.3% 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

analyze92.0ms (0.6%)

sample66.0ms (0.4%)

simplify26.0ms (0.2%)

prune4.0ms (0%)

localize15.0ms (0.1%)

rewrite331.0ms (2.2%)

series61.0ms (0.4%)

simplify1.9s (12.4%)

prune2.9s (19.3%)

localize23.0ms (0.2%)

rewrite499.0ms (3.3%)

series80.0ms (0.5%)

simplify1.8s (12%)

prune808.0ms (5.4%)

localize11.0ms (0.1%)

rewrite72.0ms (0.5%)

series52.0ms (0.3%)

simplify297.0ms (2%)

prune528.0ms (3.5%)

localize12.0ms (0.1%)

rewrite208.0ms (1.4%)

series622.0ms (4.2%)

simplify640.0ms (4.3%)

prune854.0ms (5.7%)

regimes2.0s (13.3%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.1s (7.4%)

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