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 (23.6%)

Results

896.0ms	2334×	body	1024	valid
520.0ms	4406×	body	128	valid
279.0ms	1025×	body	512	valid
153.0ms	491×	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

17.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	17.0b	(-.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 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
✓	0.3b	(/.f64 1 (sqrt.f64 x))
✓	2.6b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

series37.0ms (0.5%)

Counts

3 → 4

Calls

3 calls:

15.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
14.0ms	(/.f64 1 (sqrt.f64 x))
8.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))

rewrite204.0ms (2.6%)

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:

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))

simplify808.0ms (10.2%)

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 → 606

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

prune1.6s (19.6%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	586	20	606
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	587	20	607

Error

16.4b

Counts

607 → 20

Alt Table

Status	Error	Program
	27.3b	(fma.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
	27.9b	(+.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)))))))
	28.4b	(+.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)))))))
	29.5b	(/.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)))))))
	27.8b	(+.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 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)))))))
	62.0b	(+.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)))))))
	19.9b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	27.8b	(+.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)))))))
	27.7b	(+.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)))))))
	61.9b	(+.f64 (fma.f64 (/.f64 1 (sqrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)))) (/.f64 1 (sqrt.f64 (cbrt.f64 x))) (neg.f64 (.f64 (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)))))))
	27.0b	(+.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)))))))
	28.0b	(+.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 (.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)))))))
	27.0b	(+.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))))))))
	27.4b	(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))))
	27.4b	(+.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))))))))
▶	17.0b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
	26.9b	(+.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))))))))
	27.4b	(+.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)))))))
	27.2b	(+.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))))))))
	17.2b	(*.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))))))

Compiler

Compiled 31754 to 25718 computations (19% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
✓	0.2b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
✓	2.6b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

series65.0ms (0.8%)

Counts

3 → 5

Calls

3 calls:

37.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
17.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
11.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

rewrite46.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

87×	`sqrt-prod_binary64`
76×	`*-un-lft-identity_binary64`
73×	`add-sqr-sqrt_binary64`
42×	`prod-diff_binary64`
39×	`add-cube-cbrt_binary64`

Counts

3 → 153

Calls

3 calls:

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

simplify164.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

665×	`associate-/l*_binary64`
573×	`fma-def_binary64`
208×	`distribute-rgt-in_binary64`
177×	`distribute-lft-in_binary64`
165×	`associate-/l/_binary64`

Counts

158 → 172

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	171	4222
1	374	2844
2	1455	2621
3	4565	2619
4	4824	2619

prune176.0ms (2.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	169	3	172
Fresh	18	1	19
Picked	1	0	1
Done	0	0	0
Total	188	4	192

Error

0.2b

Counts

192 → 4

Alt Table

Status	Error	Program
	16.7b	(/.f64 (-.f64 (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (.f64 (sqrt.f64 x) (sqrt.f64 x))) (.f64 (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
	17.0b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (.f64 (.f64 (sqrt.f64 x) (fabs.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))))
	19.9b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
▶	0.4b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))

Compiler

Compiled 4533 to 2668 computations (41.1% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series88.0ms (1.1%)

Counts

3 → 2

Calls

3 calls:

65.0ms

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

14.0ms

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

9.0ms

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

rewrite47.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

115×	`*-un-lft-identity_binary64`
78×	`times-frac_binary64`
48×	`sqrt-prod_binary64`
45×	`distribute-lft-out_binary64`
36×	`add-sqr-sqrt_binary64`

Counts

3 → 146

Calls

3 calls:

18.0ms

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

9.0ms

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

6.0ms

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

simplify128.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

991×	`fma-def_binary64`
817×	`times-frac_binary64`
368×	`associate-/l*_binary64`
348×	`associate-l_binary64`
313×	`associate-/r*_binary64`

Counts

148 → 160

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	125	3751
1	292	3116
2	822	2988
3	3758	2982
4	4667	2982
5	4990	2982

prune340.0ms (4.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	210	7	217
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	213	8	221

Error

0.0b

Counts

221 → 8

Alt Table

Status	Error	Program
	19.9b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
▶	0.3b	(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) (+.f64 1 x))))
	17.3b	(.f64 (/.f64 1 (.f64 (hypot.f64 1 (pow.f64 x 3/2)) (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) x))) (sqrt.f64 (+.f64 (.f64 1 1) (-.f64 (.f64 x x) (*.f64 1 x)))))
	0.7b	(/.f64 (/.f64 1 (/.f64 (+.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) 3) (pow.f64 (sqrt.f64 x) 3)) (+.f64 (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (-.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
	0.6b	(/.f64 1 (fma.f64 x (sqrt.f64 (+.f64 1 x)) (*.f64 (+.f64 1 x) (sqrt.f64 x))))
	0.6b	(/.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (.f64 (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	1.2b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (cbrt.f64 (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (cbrt.f64 (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	0.6b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (sqrt.f64 x)) (/.f64 (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 1 x))))

Compiler

Compiled 5994 to 4107 computations (31.5% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) (+.f64 1 x)))
✓	0.0b	(fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) (+.f64 1 x))
✓	0.1b	(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) (+.f64 1 x))))
	0.3b	(/.f64 1 (sqrt.f64 x))

series57.0ms (0.7%)

Counts

3 → 6

Calls

3 calls:

30.0ms

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

17.0ms

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

10.0ms

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

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64`
58×	`times-frac_binary64`
47×	`add-exp-log_binary64`
42×	`*-un-lft-identity_binary64`
31×	`add-cube-cbrt_binary64`

Counts

3 → 130

Calls

3 calls:

12.0ms

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

4.0ms

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

0.0ms

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

simplify173.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

642×	`associate-+l+_binary64`
383×	`associate-/l/_binary64`
361×	`distribute-rgt-in_binary64`
350×	`*-commutative_binary64`
340×	`distribute-lft-in_binary64`

Counts

136 → 188

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	102	3941
1	204	3511
2	467	3494
3	984	3393
4	2277	3393
5	3703	3393
6	4876	3393
7	4878	3393

prune364.0ms (4.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	234	3	237
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	238	7	245

Error

Counts

245 → 7

Alt Table

Status	Error	Program
	19.9b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	0.8b	(.f64 (.f64 (/.f64 1 (fabs.f64 (cbrt.f64 x))) (/.f64 1 (sqrt.f64 (cbrt.f64 x)))) (/.f64 1 (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) (+.f64 1 x))))
	8.8b	(*.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (/.f64 1 (fma.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)) (+.f64 1 x))) 3)))
	0.6b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (sqrt.f64 x)) (/.f64 (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 1 x))))
	17.3b	(.f64 (/.f64 1 (.f64 (hypot.f64 1 (pow.f64 x 3/2)) (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) x))) (sqrt.f64 (+.f64 (.f64 1 1) (-.f64 (.f64 x x) (*.f64 1 x)))))
	0.6b	(/.f64 1 (fma.f64 x (sqrt.f64 (+.f64 1 x)) (*.f64 (+.f64 1 x) (sqrt.f64 x))))
	0.1b	(*.f64 (pow.f64 x -1/2) (/.f64 1 (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) (+.f64 1 x))))

Compiler

Compiled 6284 to 4190 computations (33.3% saved)

regimes1.6s (20.3%)

Accuracy

Total 0.1b remaining (82.3%)

Threshold costs 0.1b (82.3%)

Counts

526 → 1

Compiler

Compiled 37971 to 30462 computations (19.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	15	24
2	14	24

end125.0ms (1.6%)

Compiler: Compiled 194 to 147 computations (24.2% 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 (23.6%)

simplify12.0ms (0.1%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series37.0ms (0.5%)

rewrite204.0ms (2.6%)

simplify808.0ms (10.2%)

prune1.6s (19.6%)

localize7.0ms (0.1%)

series65.0ms (0.8%)

rewrite46.0ms (0.6%)

simplify164.0ms (2.1%)

prune176.0ms (2.2%)

localize7.0ms (0.1%)

series88.0ms (1.1%)

rewrite47.0ms (0.6%)

simplify128.0ms (1.6%)

prune340.0ms (4.3%)

localize9.0ms (0.1%)

series57.0ms (0.7%)

rewrite28.0ms (0.4%)

simplify173.0ms (2.2%)

prune364.0ms (4.6%)

regimes1.6s (20.3%)

simplify2.0ms (0%)

end125.0ms (1.6%)

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