Details

analyze51.0ms (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)

sample60.0ms (0.7%)

Algorithm

1×

intervals

Results

16.0ms	67×	body	1024	valid
9.0ms	140×	body	128	valid
7.0ms	37×	body	512	valid
2.0ms	12×	body	256	valid

Compiler

Compiled 26 to 22 computations (15.4% saved)

simplify20.0ms (0.3%)

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

20.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	20.7b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 47 to 38 computations (19.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
✓	0.2b	(/.f64 1 (sqrt.f64 x))
✓	2.9b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

series134.0ms (1.7%)

Counts

3 → 4

Calls

3 calls:

44.0ms	(/.f64 1 (sqrt.f64 x))
34.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
29.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite202.0ms (2.5%)

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:

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))

simplify986.0ms (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 → 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

prune1.7s (20.7%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	584	22	606
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	585	22	607

Error

20.1b

Counts

607 → 22

Alt Table

Status	Error	Program
	29.4b	(+.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))))))))
	30.2b	(+.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)))))))
	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)))))))
	29.5b	(+.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)))))))
	29.7b	(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))))
	29.6b	(+.f64 (fma.f64 (/.f64 1 (sqrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)))) (/.f64 1 (sqrt.f64 (cbrt.f64 x))) (neg.f64 (.f64 (/.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)))))))
▶	20.7b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
	29.6b	(+.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 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)))))))
	22.1b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	29.5b	(fma.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
	30.2b	(+.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)))))))
	23.1b	(exp.f64 (log.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))))
	61.4b	(+.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)))))))
	29.7b	(+.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))))))))
	20.8b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
	61.4b	(+.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)))))))
	29.7b	(+.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))))))))
	30.0b	(+.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)))))))
	61.5b	(+.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)))))))
	61.4b	(+.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)))))))
	29.6b	(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))))
	29.6b	(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (sqrt.f64 (/.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))))))))

Compiler

Compiled 31788 to 25732 computations (19.1% saved)

localize21.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
✓	0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
✓	3.2b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

series91.0ms (1.1%)

Counts

3 → 5

Calls

3 calls:

40.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
38.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
12.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

rewrite42.0ms (0.5%)

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:

14.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
9.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
7.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

simplify137.0ms (1.7%)

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

prune208.0ms (2.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	170	2	172
Fresh	19	2	21
Picked	1	0	1
Done	0	0	0
Total	190	4	194

Error

0.3b

Counts

194 → 4

Alt Table

Status	Error	Program
	20.4b	(/.f64 (-.f64 (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (.f64 (sqrt.f64 x) (sqrt.f64 x))) (fma.f64 x (sqrt.f64 (+.f64 1 x)) (*.f64 (+.f64 1 x) (sqrt.f64 x))))
▶	0.4b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
	22.1b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	20.8b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))

Compiler

Compiled 4525 to 2666 computations (41.1% saved)

localize8.0ms (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 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
	0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

series55.0ms (0.7%)

Counts

3 → 2

Calls

3 calls:

33.0ms

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

12.0ms

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

9.0ms

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

rewrite42.0ms (0.5%)

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:

14.0ms

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

8.0ms

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

6.0ms

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

simplify169.0ms (2.1%)

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

prune347.0ms (4.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	209	8	217
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	212	9	221

Error

0.0b

Counts

221 → 9

Alt Table

Status	Error	Program
	0.5b	(/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
	0.5b	(/.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))))) (/.f64 (sqrt.f64 x) (/.f64 (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 1 x)))))
	22.1b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	0.9b	(.f64 (sqrt.f64 (/.f64 1 (fma.f64 x (sqrt.f64 (+.f64 1 x)) (.f64 (+.f64 1 x) (sqrt.f64 x))))) (sqrt.f64 (/.f64 1 (fma.f64 x (sqrt.f64 (+.f64 1 x)) (*.f64 (+.f64 1 x) (sqrt.f64 x))))))
	0.7b	(/.f64 1 (fma.f64 x (sqrt.f64 (+.f64 1 x)) (*.f64 (+.f64 1 x) (sqrt.f64 x))))
	1.1b	(.f64 (.f64 (cbrt.f64 (/.f64 1 (fma.f64 x (sqrt.f64 (+.f64 1 x)) (.f64 (+.f64 1 x) (sqrt.f64 x))))) (cbrt.f64 (/.f64 1 (fma.f64 x (sqrt.f64 (+.f64 1 x)) (.f64 (+.f64 1 x) (sqrt.f64 x)))))) (cbrt.f64 (/.f64 1 (fma.f64 x (sqrt.f64 (+.f64 1 x)) (*.f64 (+.f64 1 x) (sqrt.f64 x))))))
	0.5b	(.f64 (/.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))))) (sqrt.f64 x)) (/.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 1 x))))
	18.2b	(.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)))))
▶	0.3b	(/.f64 (/.f64 1 (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) x)) (sqrt.f64 (+.f64 1 x)))

Compiler

Compiled 6048 to 4151 computations (31.4% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series117.0ms (1.5%)

Counts

3 → 4

Calls

3 calls:

52.0ms	(/.f64 (/.f64 1 (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) x)) (sqrt.f64 (+.f64 1 x)))
43.0ms	(/.f64 1 (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) x))
11.0ms	(fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) x)

rewrite38.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

172×	`times-frac_binary64`
123×	`*-un-lft-identity_binary64`
95×	`add-sqr-sqrt_binary64`
95×	`add-cube-cbrt_binary64`
56×	`sqrt-prod_binary64`

Counts

3 → 175

Calls

3 calls:

12.0ms	(/.f64 (/.f64 1 (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) x)) (sqrt.f64 (+.f64 1 x)))
3.0ms	(/.f64 1 (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) x))
1.0ms	(fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) x)

simplify306.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

979×	`fma-neg_binary64`
710×	`fma-def_binary64`
427×	`times-frac_binary64`
402×	`+-commutative_binary64`
307×	`associate-+r+_binary64`

Counts

179 → 178

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	127	6480
1	255	6206
2	585	6206
3	1255	6130
4	2512	6130
5	3628	6130
6	4476	6130
7	5214	6130

prune361.0ms (4.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	176	2	178
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	177	10	187

Error

Counts

187 → 10

Alt Table

Status	Error	Program
	0.5b	(/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
	0.5b	(/.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))))) (/.f64 (sqrt.f64 x) (/.f64 (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 1 x)))))
	22.1b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	0.9b	(.f64 (sqrt.f64 (/.f64 1 (fma.f64 x (sqrt.f64 (+.f64 1 x)) (.f64 (+.f64 1 x) (sqrt.f64 x))))) (sqrt.f64 (/.f64 1 (fma.f64 x (sqrt.f64 (+.f64 1 x)) (*.f64 (+.f64 1 x) (sqrt.f64 x))))))
	18.2b	(.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)))))
	0.3b	(*.f64 (/.f64 1 (fabs.f64 (cbrt.f64 (+.f64 1 x)))) (/.f64 (/.f64 1 (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) x)) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))))
	0.5b	(.f64 (/.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))))) (sqrt.f64 x)) (/.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 1 x))))
	0.3b	(/.f64 (/.f64 1 (+.f64 (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) x)) (sqrt.f64 (+.f64 1 x)))
	0.7b	(/.f64 1 (fma.f64 x (sqrt.f64 (+.f64 1 x)) (*.f64 (+.f64 1 x) (sqrt.f64 x))))
✓	0.3b	(/.f64 (/.f64 1 (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) x)) (sqrt.f64 (+.f64 1 x)))

Compiler

Compiled 5436 to 3876 computations (28.7% saved)

regimes1.6s (20.6%)

Accuracy

Total 0.3b remaining (94.6%)

Threshold costs 0.3b (94.6%)

Counts

507 → 1

Compiler

Compiled 39018 to 31479 computations (19.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	12	23
2	11	23

end1.0ms (0%)

Compiler: Compiled 16 to 12 computations (25% saved)

sample1.3s (15.8%)

Algorithm

1×

intervals

Results

448.0ms	2225×	body	1024	valid
225.0ms	4244×	body	128	valid
155.0ms	1049×	body	512	valid
48.0ms	482×	body	256	valid

Compiler

Compiled 286 to 215 computations (24.8% 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

analyze51.0ms (0.6%)

sample60.0ms (0.7%)

simplify20.0ms (0.3%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series134.0ms (1.7%)

rewrite202.0ms (2.5%)

simplify986.0ms (12.4%)

prune1.7s (20.7%)

localize21.0ms (0.3%)

series91.0ms (1.1%)

rewrite42.0ms (0.5%)

simplify137.0ms (1.7%)

prune208.0ms (2.6%)

localize8.0ms (0.1%)

series55.0ms (0.7%)

rewrite42.0ms (0.5%)

simplify169.0ms (2.1%)

prune347.0ms (4.4%)

localize8.0ms (0.1%)

series117.0ms (1.5%)

rewrite38.0ms (0.5%)

simplify306.0ms (3.8%)

prune361.0ms (4.5%)

regimes1.6s (20.6%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.3s (15.8%)

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