Details

analyze42.0ms (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)

sample106.0ms (0.9%)

Algorithm

1×

intervals

Results

65.0ms	65×	body	1024	valid
15.0ms	143×	body	128	valid
8.0ms	26×	body	512	valid
4.0ms	22×	body	256	valid

Compiler

Compiled 26 to 22 computations (15.4% saved)

simplify25.0ms (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

17.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	17.9b	(-.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 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))
✓	3.4b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

series100.0ms (0.9%)

Counts

4 → 8

Calls

4 calls:

33.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
29.0ms	(/.f64 1 (sqrt.f64 x))
20.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
17.0ms	(sqrt.f64 (+.f64 x 1))

rewrite462.0ms (4.1%)

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:

93.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
44.0ms	(sqrt.f64 (+.f64 x 1))
10.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
6.0ms	(/.f64 1 (sqrt.f64 x))

simplify975.0ms (8.7%)

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

prune2.2s (19.5%)

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

17.3b

Counts

642 → 22

Alt Table

Status	Error	Program
	28.7b	(+.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)))))))
	19.3b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	28.0b	(+.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)))))))
	18.5b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
	30.0b	(/.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)))))))
	28.8b	(+.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)))))))
	61.2b	(+.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)))))))
▶	17.9b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
	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)))))))
	28.6b	(+.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)))))))
	28.1b	(+.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))))))))
	28.4b	(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))))
	29.2b	(+.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 (.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)))))))
	61.3b	(+.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)))))))
	28.4b	(+.f64 (fma.f64 (/.f64 1 (sqrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)))) (/.f64 1 (sqrt.f64 (cbrt.f64 x))) (neg.f64 (.f64 (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)))))))
	30.0b	(cbrt.f64 (.f64 (.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))) (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))) (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))))
	28.7b	(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))))
	28.1b	(fma.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
	18.1b	(*.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))))))
	61.2b	(+.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)))))))
	28.6b	(+.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 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)))))))
	27.9b	(+.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))))))))

Compiler

Compiled 32259 to 26067 computations (19.2% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 1 x))
✓	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)))
✓	3.4b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

series135.0ms (1.2%)

Counts

4 → 9

Calls

4 calls:

70.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
29.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
19.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
16.0ms	(sqrt.f64 (+.f64 1 x))

rewrite95.0ms (0.8%)

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:

32.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
16.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
14.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
5.0ms	(sqrt.f64 (+.f64 1 x))

simplify228.0ms (2%)

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 → 200

Iterations

Useful iterations: 3 (0.0ms)

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

prune423.0ms (3.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	224	4	228
Fresh	20	1	21
Picked	1	0	1
Done	0	0	0
Total	245	5	250

Error

0.1b

Counts

250 → 5

Alt Table

Status	Error	Program
	19.3b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	17.9b	(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
	17.9b	(/.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))))
▶	0.3b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
	18.0b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (.f64 (.f64 (sqrt.f64 x) (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 (sqrt.f64 (+.f64 1 x))))) (cbrt.f64 (sqrt.f64 (+.f64 1 x)))))

Compiler

Compiled 5720 to 3439 computations (39.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
✓	0.1b	(/.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))))
	0.2b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

series67.0ms (0.6%)

Counts

3 → 2

Calls

3 calls:

39.0ms

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

16.0ms

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

12.0ms

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

rewrite50.0ms (0.4%)

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:

17.0ms

(/.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)))

7.0ms

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

simplify213.0ms (1.9%)

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

prune652.0ms (5.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	211	6	217
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	215	7	222

Error

Counts

222 → 7

Alt Table

Status	Error	Program
	19.3b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	1.2b	(.f64 (.f64 (cbrt.f64 (/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))) (cbrt.f64 (/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))))) (cbrt.f64 (/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))))
	4.3b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (fma.f64 x x x)))
	0.4b	(/.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))))))
	0.6b	(/.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))))
▶	0.3b	(/.f64 (/.f64 1 (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) x)) (sqrt.f64 (+.f64 1 x)))
	4.3b	(.f64 (/.f64 (/.f64 1 (+.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) 3) (pow.f64 (sqrt.f64 x) 3))) (sqrt.f64 x)) (/.f64 (+.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)))) (sqrt.f64 (+.f64 1 x))))

Compiler

Compiled 5918 to 4051 computations (31.5% 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 (/.f64 1 (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) x)) (sqrt.f64 (+.f64 1 x)))
✓	0.2b	(/.f64 1 (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) x))

series196.0ms (1.7%)

Counts

3 → 4

Calls

3 calls:

104.0ms	(/.f64 (/.f64 1 (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) x)) (sqrt.f64 (+.f64 1 x)))
69.0ms	(/.f64 1 (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) x))
23.0ms	(fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) x)

rewrite60.0ms (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:

15.0ms	(/.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)

simplify444.0ms (3.9%)

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

prune601.0ms (5.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	233	1	234
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	234	7	241

Error

Counts

241 → 7

Alt Table

Status	Error	Program
	4.3b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (fma.f64 x x x)))
	0.4b	(/.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))))))
	0.4b	(*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (/.f64 (/.f64 1 (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) x)) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))))
	19.3b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	0.6b	(/.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))))
✓	0.3b	(/.f64 (/.f64 1 (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) x)) (sqrt.f64 (+.f64 1 x)))
	4.3b	(.f64 (/.f64 (/.f64 1 (+.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) 3) (pow.f64 (sqrt.f64 x) 3))) (sqrt.f64 x)) (/.f64 (+.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)))) (sqrt.f64 (+.f64 1 x))))

Compiler

Compiled 6487 to 4603 computations (29% saved)

regimes2.4s (21.1%)

Accuracy

Total 0.3b remaining (85.9%)

Threshold costs 0.3b (85.9%)

Counts

466 → 1

Compiler

Compiled 32997 to 26722 computations (19% saved)

simplify4.0ms (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)

sample1.7s (15.5%)

Algorithm

1×

intervals

Results

622.0ms	2242×	body	1024	valid
410.0ms	4232×	body	128	valid
236.0ms	1025×	body	512	valid
117.0ms	501×	body	256	valid

Compiler

Compiled 195 to 146 computations (25.1% 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

analyze42.0ms (0.4%)

sample106.0ms (0.9%)

simplify25.0ms (0.2%)

prune4.0ms (0%)

localize15.0ms (0.1%)

series100.0ms (0.9%)

rewrite462.0ms (4.1%)

simplify975.0ms (8.7%)

prune2.2s (19.5%)

localize15.0ms (0.1%)

series135.0ms (1.2%)

rewrite95.0ms (0.8%)

simplify228.0ms (2%)

prune423.0ms (3.8%)

localize9.0ms (0.1%)

series67.0ms (0.6%)

rewrite50.0ms (0.4%)

simplify213.0ms (1.9%)

prune652.0ms (5.8%)

localize15.0ms (0.1%)

series196.0ms (1.7%)

rewrite60.0ms (0.5%)

simplify444.0ms (3.9%)

prune601.0ms (5.3%)

regimes2.4s (21.1%)

simplify4.0ms (0%)

end1.0ms (0%)

sample1.7s (15.5%)

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