Details

analyze46.0ms (0.4%)

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)

sample70.0ms (0.6%)

Algorithm

1×

intervals

Results

29.0ms	74×	body	1024	valid
14.0ms	129×	body	128	valid
13.0ms	41×	body	512	valid
2.0ms	12×	body	256	valid

Compiler

Compiled 26 to 22 computations (15.4% saved)

simplify38.0ms (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

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

20.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	20.0b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 47 to 38 computations (19.1% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 x 1))
✓	0.2b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
✓	0.3b	(/.f64 1 (sqrt.f64 x))
✓	2.2b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite326.0ms (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:

84.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
9.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
7.0ms	(/.f64 1 (sqrt.f64 x))
5.0ms	(sqrt.f64 (+.f64 x 1))

series72.0ms (0.6%)

Counts

4 → 8

Calls

4 calls:

26.0ms	(/.f64 1 (sqrt.f64 x))
22.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
13.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
10.0ms	(sqrt.f64 (+.f64 x 1))

simplify1.8s (15.2%)

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 → 1617

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

prune2.7s (22.8%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	1596	21	1617
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	1597	21	1618

Error

19.4b

Counts

1618 → 21

Alt Table

Status	Error	Program
	31.2b	(+.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))))))))
	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)))))))
	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))))))))
	62.0b	(+.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)))))))
▶	20.0b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
	31.5b	(+.f64 (fma.f64 (/.f64 1 (sqrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)))) (/.f64 1 (sqrt.f64 (cbrt.f64 x))) (neg.f64 (.f64 (/.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)))))))
	61.8b	(+.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	(fma.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
	61.8b	(+.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)))))))
	23.2b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	31.7b	(+.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)))))))
	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))))))))
	31.0b	(+.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)))))))
	20.0b	(/.f64 (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (.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)))))
	31.1b	(+.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))))))))
	31.7b	(+.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)))))))
	31.7b	(+.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 (/.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)))))))
	31.5b	(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 (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)))))))
	31.7b	(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))))
	31.6b	(/.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)))))))

Compiler

Compiled 32348 to 26161 computations (19.1% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 1 x))
✓	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)))
✓	2.2b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite83.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

91×	`sqrt-prod_binary64`
81×	`*-un-lft-identity_binary64`
80×	`add-sqr-sqrt_binary64`
42×	`prod-diff_binary64`
41×	`add-cube-cbrt_binary64`

Counts

4 → 174

Calls

4 calls:

28.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
15.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
14.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
5.0ms	(sqrt.f64 (+.f64 1 x))

series112.0ms (0.9%)

Counts

4 → 9

Calls

4 calls:

59.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
22.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
17.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
12.0ms	(sqrt.f64 (+.f64 1 x))

simplify255.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

732×	`fma-def_binary64`
671×	`associate-/l*_binary64`
297×	`fma-neg_binary64`
210×	`distribute-rgt-in_binary64`
179×	`distribute-lft-in_binary64`

Counts

183 → 320

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	188	4435
1	417	3049
2	1600	2820
3	4995	2819
4	4966	2819

prune380.0ms (3.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	319	1	320
Fresh	19	1	20
Picked	0	1	1
Done	0	0	0
Total	338	3	341

Error

0.2b

Counts

341 → 3

Alt Table

Status	Error	Program
✓	20.0b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
▶	0.4b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
	23.2b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 5023 to 2979 computations (40.7% saved)

localize16.0ms (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)))

rewrite80.0ms (0.7%)

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:

29.0ms

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

17.0ms

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

11.0ms

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

series93.0ms (0.8%)

Counts

3 → 2

Calls

3 calls:

56.0ms

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

22.0ms

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

14.0ms

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

simplify243.0ms (2%)

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 → 255

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

prune534.0ms (4.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	318	7	325
Fresh	0	1	1
Picked	0	1	1
Done	1	0	1
Total	319	9	328

Error

0.0b

Counts

328 → 9

Alt Table

Status	Error	Program
	0.7b	(/.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)))))
✓	0.4b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
	23.2b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	0.5b	(/.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (/.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.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)))
	0.5b	(/.f64 (/.f64 1 (+.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 (/.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 1 (fma.f64 x (sqrt.f64 (+.f64 1 x)) (*.f64 (+.f64 1 x) (sqrt.f64 x))))
	1.0b	(/.f64 (/.f64 1 (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))

Compiler

Compiled 5906 to 4053 computations (31.4% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite51.0ms (0.4%)

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:

16.0ms	(/.f64 (/.f64 1 (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) x)) (sqrt.f64 (+.f64 1 x)))
4.0ms	(/.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)

series170.0ms (1.4%)

Counts

3 → 4

Calls

3 calls:

94.0ms	(/.f64 (/.f64 1 (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) x)) (sqrt.f64 (+.f64 1 x)))
57.0ms	(/.f64 1 (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) x))
19.0ms	(fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) x)

simplify761.0ms (6.3%)

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 → 305

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

prune548.0ms (4.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	335	5	340
Fresh	5	2	7
Picked	1	0	1
Done	0	1	1
Total	341	8	349

Error

Counts

349 → 8

Alt Table

Status	Error	Program
	0.3b	(/.f64 (/.f64 1 (+.f64 (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) x)) (sqrt.f64 (+.f64 1 x)))
	0.5b	(/.f64 (/.f64 1 (sqrt.f64 (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) x))) (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) x))))
	0.5b	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) x))) (/.f64 (sqrt.f64 (/.f64 1 (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) x))) (sqrt.f64 (+.f64 1 x))))
✓	0.4b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
	23.2b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	0.7b	(/.f64 1 (fma.f64 x (sqrt.f64 (+.f64 1 x)) (*.f64 (+.f64 1 x) (sqrt.f64 x))))
	1.2b	(.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) x)) (cbrt.f64 (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) x)))) (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 (sqrt.f64 (+.f64 1 x))))) (/.f64 (/.f64 1 (cbrt.f64 (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) x))) (cbrt.f64 (sqrt.f64 (+.f64 1 x)))))
	0.3b	(/.f64 (/.f64 1 (fma.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x) x)) (sqrt.f64 (+.f64 1 x)))

Compiler

Compiled 5932 to 4217 computations (28.9% saved)

regimes2.3s (19.2%)

Accuracy

Total 0.3b remaining (91.1%)

Threshold costs 0.3b (91.1%)

Compiler

Compiled 35131 to 28835 computations (17.9% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	14	23
2	13	23

end1.0ms (0%)

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

sample1.2s (10.1%)

Algorithm

1×

intervals

Results

440.0ms	2218×	body	1024	valid
234.0ms	4267×	body	128	valid
156.0ms	1010×	body	512	valid
49.0ms	505×	body	256	valid

Compiler

Compiled 222 to 166 computations (25.2% 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

analyze46.0ms (0.4%)

sample70.0ms (0.6%)

simplify38.0ms (0.3%)

prune4.0ms (0%)

localize14.0ms (0.1%)

rewrite326.0ms (2.7%)

series72.0ms (0.6%)

simplify1.8s (15.2%)

prune2.7s (22.8%)

localize13.0ms (0.1%)

rewrite83.0ms (0.7%)

series112.0ms (0.9%)

simplify255.0ms (2.1%)

prune380.0ms (3.2%)

localize16.0ms (0.1%)

rewrite80.0ms (0.7%)

series93.0ms (0.8%)

simplify243.0ms (2%)

prune534.0ms (4.5%)

localize15.0ms (0.1%)

rewrite51.0ms (0.4%)

series170.0ms (1.4%)

simplify761.0ms (6.3%)

prune548.0ms (4.6%)

regimes2.3s (19.2%)

simplify4.0ms (0%)

end1.0ms (0%)

sample1.2s (10.1%)

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