Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
28.1%	28.1%	43.8%	2
56.2%	0%	43.8%	3

Compiler

Compiled 22 to 16 computations (27.3% saved)

sample1.9s (34.6%)

Results

782.0ms	6148×	body	128	valid
478.0ms	1024×	body	1024	valid
198.0ms	659×	body	512	valid
75.0ms	328×	body	256	valid
44.0ms	97×	body	2048	valid

Compiler

Compiled 59 to 43 computations (27.1% saved)

simplify210.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

890×	`sub-neg_binary64`
434×	`cancel-sign-sub-inv_binary64`
422×	`associate-/l*_binary64`
388×	`distribute-rgt-neg-in_binary64`
379×	`neg-mul-1_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	23	19
2	39	19
3	64	19
4	108	19
5	215	17
6	353	17
7	603	17
8	1141	17
9	2484	17
10	3195	17
11	3981	17
12	4235	17
13	4399	17
14	4503	17
15	4531	17
16	4533	17
17	4768	17
18	4708	17
19	4930	17
20	4826	17

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

15.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	15.9b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

Compiler

Compiled 55 to 39 computations (29.1% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
✓	2.8b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

series48.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

33.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
14.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
18×	`distribute-lft-out_binary64`
14×	`add-cube-cbrt_binary64`

Counts

2 → 64

Calls

2 calls:

10.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
0.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

simplify96.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

960×	`times-frac_binary64`
218×	`+-commutative_binary64`
206×	`fma-def_binary64`
194×	`fma-neg_binary64`
193×	`associate-+r+_binary64`

Counts

112 → 142

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	313	3790
1	962	3664
2	3486	3620
3	4984	3620

prune164.0ms (3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	138	4	142
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	139	4	143

Error

0.1b

Counts

143 → 4

Alt Table

Status	Error	Program
	46.5b	(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (.f64 5 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
	45.5b	(/.f64 (+.f64 beta 1) alpha)
▶	15.9b	(fma.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))) -1/2 1/2)
	42.2b	(fma.f64 (*.f64 (+.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (/.f64 (-.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2)

Compiler

Compiled 4387 to 2697 computations (38.5% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))
✓	0.1b	(/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta)))
✓	2.8b	(fma.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))) -1/2 1/2)

series62.0ms (1.1%)

Counts

3 → 72

Calls

3 calls:

26.0ms

(fma.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))) -1/2 1/2)

20.0ms

(/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta)))

15.0ms

(/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))

rewrite53.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

273×	`*-un-lft-identity_binary64`
218×	`times-frac_binary64`
143×	`add-sqr-sqrt_binary64`
91×	`add-cube-cbrt_binary64`
78×	`distribute-lft-out_binary64`

Counts

3 → 213

Calls

3 calls:

16.0ms

(/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta)))

8.0ms

(/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))

0.0ms

(fma.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))) -1/2 1/2)

simplify196.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

351×	`associate-+r+_binary64`
322×	`fma-def_binary64`
312×	`+-commutative_binary64`
277×	`associate-+l+_binary64`
239×	`fma-neg_binary64`

Counts

285 → 312

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	429	8554
1	1278	7974
2	4784	7972
3	4975	7972

prune248.0ms (4.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	312	0	312
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	312	4	316

Error

0.1b

Counts

316 → 4

Alt Table

Status	Error	Program
	46.5b	(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (.f64 5 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
	45.5b	(/.f64 (+.f64 beta 1) alpha)
✓	15.9b	(fma.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))) -1/2 1/2)
▶	42.2b	(fma.f64 (*.f64 (+.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (/.f64 (-.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2)

Compiler

Compiled 9353 to 5678 computations (39.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (sqrt.f64 alpha) (sqrt.f64 beta))
✓	0.1b	(/.f64 (-.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (+.f64 beta (+.f64 2 alpha)))
✓	0.2b	(*.f64 (+.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (/.f64 (-.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (+.f64 beta (+.f64 2 alpha))))
✓	6.4b	(fma.f64 (*.f64 (+.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (/.f64 (-.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2)

series197.0ms (3.6%)

Counts

4 → 16

Calls

4 calls:

81.0ms	(*.f64 (+.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (/.f64 (-.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (+.f64 beta (+.f64 2 alpha))))
56.0ms	(/.f64 (-.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (+.f64 beta (+.f64 2 alpha)))
51.0ms	(fma.f64 (*.f64 (+.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (/.f64 (-.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2)
8.0ms	(+.f64 (sqrt.f64 alpha) (sqrt.f64 beta))

rewrite66.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

185×	`*-un-lft-identity_binary64`
131×	`add-sqr-sqrt_binary64`
91×	`times-frac_binary64`
73×	`sqrt-prod_binary64`
61×	`distribute-lft-out_binary64`

Counts

4 → 187

Calls

4 calls:

25.0ms	(*.f64 (+.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (/.f64 (-.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (+.f64 beta (+.f64 2 alpha))))
11.0ms	(/.f64 (-.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (+.f64 beta (+.f64 2 alpha)))
5.0ms	(+.f64 (sqrt.f64 alpha) (sqrt.f64 beta))
0.0ms	(fma.f64 (*.f64 (+.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (/.f64 (-.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2)

simplify115.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

936×	`distribute-rgt-in_binary64`
921×	`distribute-lft-in_binary64`
492×	`fma-def_binary64`
271×	`times-frac_binary64`
107×	`associate-l_binary64`

Counts

203 → 200

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	187	4849
1	507	4624
2	1829	4611
3	5753	4611

prune128.0ms (2.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	199	1	200
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	199	5	204

Error

0.1b

Counts

204 → 5

Alt Table

Status	Error	Program
▶	42.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 (+.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (/.f64 (-.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2)) (cbrt.f64 (fma.f64 (.f64 (+.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (/.f64 (-.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2))) (cbrt.f64 (fma.f64 (*.f64 (+.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (/.f64 (-.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2)))
✓	42.2b	(fma.f64 (*.f64 (+.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (/.f64 (-.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2)
	46.5b	(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (.f64 5 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
	45.5b	(/.f64 (+.f64 beta 1) alpha)
✓	15.9b	(fma.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))) -1/2 1/2)

Compiler

Compiled 5983 to 2695 computations (55% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(/.f64 (-.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (+.f64 beta (+.f64 2 alpha)))
	0.2b	(*.f64 (+.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (/.f64 (-.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (+.f64 beta (+.f64 2 alpha))))
✓	0.2b	(.f64 (cbrt.f64 (fma.f64 (.f64 (+.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (/.f64 (-.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2)) (cbrt.f64 (fma.f64 (*.f64 (+.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (/.f64 (-.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2)))
	6.4b	(fma.f64 (*.f64 (+.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (/.f64 (-.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2)

series209.0ms (3.9%)

Counts

1 → 8

Calls

1 calls:

209.0ms

(*.f64 (cbrt.f64 (fma.f64 (*.f64 (+.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (/.f64 (-.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2)) (cbrt.f64 (fma.f64 (*.f64 (+.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (/.f64 (-.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2)))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
16×	`cbrt-prod_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`
8×	`pow1_binary64`

Counts

1 → 42

Calls

1 calls:

5.0ms

(*.f64 (cbrt.f64 (fma.f64 (*.f64 (+.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (/.f64 (-.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2)) (cbrt.f64 (fma.f64 (*.f64 (+.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (/.f64 (-.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2)))

simplify96.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

860×	`fma-def_binary64`
401×	`associate-l_binary64`
392×	`associate-r_binary64`
284×	`fma-neg_binary64`
237×	`times-frac_binary64`

Counts

50 → 67

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	103	3360
1	253	3000
2	805	2352
3	3947	2315
4	4973	2315

prune646.0ms (11.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	570	1	571
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	571	5	576

Error

0.1b

Counts

576 → 5

Alt Table

Status	Error	Program
	42.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 (+.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (/.f64 (-.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2)) (cbrt.f64 (fma.f64 (.f64 (+.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (/.f64 (-.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2))) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)))))
	46.5b	(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (.f64 5 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
	45.5b	(/.f64 (+.f64 beta 1) alpha)
✓	15.9b	(fma.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))) -1/2 1/2)
✓	42.2b	(fma.f64 (*.f64 (+.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (/.f64 (-.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2)

Compiler

Compiled 42597 to 19691 computations (53.8% saved)

regimes782.0ms (14.5%)

Accuracy

Total 0.0b remaining (33.6%)

Threshold costs 0.0b (33.6%)

Counts

83 → 2

Compiler

Compiled 10139 to 6980 computations (31.2% saved)

bsearch5.0ms (0.1%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`+-commutative_binary64`
8×	`sub-neg_binary64`
5×	`*-commutative_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	79
1	42	79
2	56	79
3	71	79
4	78	79
5	80	79
6	78	79

end130.0ms (2.4%)

Compiler: Compiled 304 to 184 computations (39.5% saved)

Details

analyze2.0ms (0%)

sample1.9s (34.6%)

simplify210.0ms (3.9%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series48.0ms (0.9%)

rewrite15.0ms (0.3%)

simplify96.0ms (1.8%)

prune164.0ms (3%)

localize9.0ms (0.2%)

series62.0ms (1.1%)

rewrite53.0ms (1%)

simplify196.0ms (3.6%)

prune248.0ms (4.6%)

localize12.0ms (0.2%)

series197.0ms (3.6%)

rewrite66.0ms (1.2%)

simplify115.0ms (2.1%)

prune128.0ms (2.4%)

localize19.0ms (0.3%)

series209.0ms (3.9%)

rewrite12.0ms (0.2%)

simplify96.0ms (1.8%)

prune646.0ms (11.9%)

regimes782.0ms (14.5%)

bsearch5.0ms (0.1%)

simplify4.0ms (0.1%)

end130.0ms (2.4%)

Profiling