Details

analyze317.0ms (4%)

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)

sample32.0ms (0.4%)

Algorithm

1×

intervals

Results

6.0ms	185×	body	128	valid
5.0ms	37×	body	1024	valid
4.0ms	256×	pre	128	true
2.0ms	22×	body	512	valid
1.0ms	9×	body	256	valid
0.0ms	3×	body	2048	valid

Compiler

Compiled 39 to 29 computations (25.6% saved)

simplify260.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

1179×	`div-sub_binary64`
672×	`sub-neg_binary64`
434×	`cancel-sign-sub-inv_binary64`
422×	`associate-/l*_binary64`
385×	`distribute-rgt-neg-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	23	19
2	39	19
3	63	19
4	104	19
5	204	19
6	320	19
7	513	19
8	943	19
9	2087	19
10	2930	19
11	3705	19
12	3906	19
13	4077	19
14	4165	19
15	4198	19
16	4200	19
17	4320	19
18	4594	19
19	4698	19
20	4698	19
21	5018	19

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

18.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	18.5b	(/.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1) 2)

Compiler

Compiled 45 to 33 computations (26.7% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
3.0b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite106.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

17.6b

Rules

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

Counts

2 → 65

Calls

2 calls:

18.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
10.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 1149 to 611 computations (46.8% saved)

series150.0ms (1.9%)

Error

0.0b

Counts

2 → 36

Calls

2 calls:

70.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
50.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 2600 to 2053 computations (21% saved)

simplify117.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

423×	`distribute-rgt-in_binary64`
362×	`distribute-lft-in_binary64`
356×	`times-frac_binary64`
336×	`associate-/l*_binary64`
321×	`cancel-sign-sub-inv_binary64`

Counts

101 → 88

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	219	2679
1	599	2632
2	1879	2536
3	4728	2536
4	5096	2536

prune67.0ms (0.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	84	4	88
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	84	5	89

Error

0.0b

Counts

89 → 5

Alt Table

Status	Error	Program
	44.3b	(/.f64 (-.f64 2 (+.f64 (/.f64 2 beta) (*.f64 2 (/.f64 alpha beta)))) 2)
▶	43.2b	(/.f64 (/.f64 (+.f64 2 (*.f64 2 beta)) alpha) 2)
✓	18.5b	(/.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1) 2)
	43.8b	(/.f64 (+.f64 (.f64 2 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (/.f64 beta alpha))) (-.f64 (+.f64 (/.f64 2 alpha) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (+.f64 (.f64 16 (/.f64 beta (pow.f64 alpha 3))) (.f64 10 (.f64 (/.f64 beta (pow.f64 alpha 3)) beta))))) (+.f64 (.f64 6 (/.f64 beta (.f64 alpha alpha))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (.f64 2 (*.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))) 2)
	44.1b	(/.f64 (+.f64 (-.f64 (+.f64 (/.f64 2 alpha) (.f64 (/.f64 beta alpha) (-.f64 2 (/.f64 6 alpha)))) (/.f64 4 (.f64 alpha alpha))) (.f64 (.f64 (/.f64 beta alpha) (/.f64 beta alpha)) -2)) 2)

Compiler

Compiled 1802 to 1126 computations (37.5% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(/.f64 (+.f64 2 (*.f64 2 beta)) alpha)

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

9×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `times-frac_binary64` `*-un-lft-identity_binary64`
3×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l_binary64` `associate-/r_binary64`
2×	`associate-/l/_binary64`
1×	`pow1_binary64` `div-exp_binary64` `add-log-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `clear-num_binary64` `div-inv_binary64` `flip3-+_binary64` `flip-+_binary64`

Counts

1 → 29

Calls

1 calls:

5.0ms

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

Compiler

Compiled 518 to 398 computations (23.2% saved)

series25.0ms (0.3%)

Error

0.0b

Counts

1 → 9

Calls

1 calls:

21.0ms

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

Compiler

Compiled 217 to 173 computations (20.3% saved)

simplify80.0ms (1%)

Algorithm

1×	egg-herbie

Rules

578×	`distribute-rgt-out_binary64`
472×	`times-frac_binary64`
457×	`div-sub_binary64`
353×	`associate-l_binary64`
347×	`associate-/l*_binary64`

Counts

38 → 19

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	67	639
1	156	592
2	364	592
3	874	592
4	3161	571
5	4426	571
6	5341	571

prune19.0ms (0.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	19	0	19
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	19	5	24

Error

0.0b

Counts

24 → 5

Alt Table

Status	Error	Program
	44.3b	(/.f64 (-.f64 2 (+.f64 (/.f64 2 beta) (*.f64 2 (/.f64 alpha beta)))) 2)
✓	43.2b	(/.f64 (/.f64 (+.f64 2 (*.f64 2 beta)) alpha) 2)
✓	18.5b	(/.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1) 2)
▶	43.8b	(/.f64 (+.f64 (.f64 2 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (/.f64 beta alpha))) (-.f64 (+.f64 (/.f64 2 alpha) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (+.f64 (.f64 16 (/.f64 beta (pow.f64 alpha 3))) (.f64 10 (.f64 (/.f64 beta (pow.f64 alpha 3)) beta))))) (+.f64 (.f64 6 (/.f64 beta (.f64 alpha alpha))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (.f64 2 (*.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))) 2)
	44.1b	(/.f64 (+.f64 (-.f64 (+.f64 (/.f64 2 alpha) (.f64 (/.f64 beta alpha) (-.f64 2 (/.f64 6 alpha)))) (/.f64 4 (.f64 alpha alpha))) (.f64 (.f64 (/.f64 beta alpha) (/.f64 beta alpha)) -2)) 2)

Compiler

Compiled 442 to 323 computations (26.9% saved)

localize35.0ms (0.4%)

Local error

Found 4 expressions with local error:

5.3b	(*.f64 (/.f64 beta (pow.f64 alpha 3)) beta)
5.5b	(+.f64 (/.f64 8 (pow.f64 alpha 3)) (+.f64 (.f64 16 (/.f64 beta (pow.f64 alpha 3))) (.f64 10 (*.f64 (/.f64 beta (pow.f64 alpha 3)) beta))))
7.9b	(/.f64 beta (*.f64 alpha alpha))
10.2b	(-.f64 (+.f64 (/.f64 2 alpha) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (+.f64 (.f64 16 (/.f64 beta (pow.f64 alpha 3))) (.f64 10 (.f64 (/.f64 beta (pow.f64 alpha 3)) beta))))) (+.f64 (.f64 6 (/.f64 beta (.f64 alpha alpha))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (.f64 2 (.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))

rewrite694.0ms (8.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

123×	`frac-add_binary64`
79×	`associate-*r/_binary64`
63×	`add-log-exp_binary64`
49×	`frac-sub_binary64`
45×	`add-sqr-sqrt_binary64`

Counts

4 → 182

Calls

4 calls:

56.0ms	(-.f64 (+.f64 (/.f64 2 alpha) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (+.f64 (.f64 16 (/.f64 beta (pow.f64 alpha 3))) (.f64 10 (.f64 (/.f64 beta (pow.f64 alpha 3)) beta))))) (+.f64 (.f64 6 (/.f64 beta (.f64 alpha alpha))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (.f64 2 (.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))
26.0ms	(+.f64 (/.f64 8 (pow.f64 alpha 3)) (+.f64 (.f64 16 (/.f64 beta (pow.f64 alpha 3))) (.f64 10 (*.f64 (/.f64 beta (pow.f64 alpha 3)) beta))))
21.0ms	(*.f64 (/.f64 beta (pow.f64 alpha 3)) beta)
5.0ms	(/.f64 beta (*.f64 alpha alpha))

Compiler

Compiled 22945 to 13501 computations (41.2% saved)

series274.0ms (3.5%)

Error

0.0b

Counts

4 → 36

Calls

4 calls:

118.0ms	(-.f64 (+.f64 (/.f64 2 alpha) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (+.f64 (.f64 16 (/.f64 beta (pow.f64 alpha 3))) (.f64 10 (.f64 (/.f64 beta (pow.f64 alpha 3)) beta))))) (+.f64 (.f64 6 (/.f64 beta (.f64 alpha alpha))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (.f64 2 (.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))
68.0ms	(+.f64 (/.f64 8 (pow.f64 alpha 3)) (+.f64 (.f64 16 (/.f64 beta (pow.f64 alpha 3))) (.f64 10 (*.f64 (/.f64 beta (pow.f64 alpha 3)) beta))))
33.0ms	(*.f64 (/.f64 beta (pow.f64 alpha 3)) beta)
28.0ms	(/.f64 beta (*.f64 alpha alpha))

Compiler

Compiled 4391 to 2998 computations (31.7% saved)

simplify344.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

900×	`distribute-rgt-in_binary64`
249×	`*-commutative_binary64`
218×	`cancel-sign-sub-inv_binary64`
186×	`distribute-rgt-neg-in_binary64`
182×	`times-frac_binary64`

Counts

218 → 191

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	558	22284
1	2094	20966
2	5210	20966

prune487.0ms (6.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	190	1	191
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	191	5	196

Error

0.0b

Counts

196 → 5

Alt Table

Status	Error	Program
	62.9b	(/.f64 (+.f64 (.f64 2 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (/.f64 beta alpha))) (/.f64 (-.f64 (.f64 (pow.f64 alpha 6) (+.f64 (.f64 2 (pow.f64 (pow.f64 alpha 3) 3)) (.f64 alpha (+.f64 (.f64 8 (pow.f64 alpha 6)) (.f64 (pow.f64 alpha 3) (.f64 (pow.f64 alpha 3) (.f64 beta (+.f64 (.f64 10 beta) 16)))))))) (.f64 (.f64 alpha (pow.f64 (pow.f64 alpha 3) 3)) (+.f64 (.f64 (pow.f64 alpha 4) (.f64 beta 6)) (.f64 (.f64 alpha alpha) (.f64 (.f64 alpha alpha) (+.f64 4 (.f64 2 (.f64 beta beta)))))))) (.f64 (pow.f64 alpha 6) (*.f64 alpha (pow.f64 (pow.f64 alpha 3) 3))))) 2)
	44.3b	(/.f64 (-.f64 2 (+.f64 (/.f64 2 beta) (*.f64 2 (/.f64 alpha beta)))) 2)
✓	43.2b	(/.f64 (/.f64 (+.f64 2 (*.f64 2 beta)) alpha) 2)
✓	18.5b	(/.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1) 2)
▶	44.1b	(/.f64 (+.f64 (-.f64 (+.f64 (/.f64 2 alpha) (.f64 (/.f64 beta alpha) (-.f64 2 (/.f64 6 alpha)))) (/.f64 4 (.f64 alpha alpha))) (.f64 (.f64 (/.f64 beta alpha) (/.f64 beta alpha)) -2)) 2)

Compiler

Compiled 16211 to 9676 computations (40.3% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (/.f64 beta alpha) (-.f64 2 (/.f64 6 alpha)))
0.2b	(*.f64 (/.f64 beta alpha) (/.f64 beta alpha))
0.3b	(/.f64 4 (*.f64 alpha alpha))
4.0b	(-.f64 (+.f64 (/.f64 2 alpha) (.f64 (/.f64 beta alpha) (-.f64 2 (/.f64 6 alpha)))) (/.f64 4 (.f64 alpha alpha)))

rewrite260.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

84×	`add-sqr-sqrt_binary64`
76×	`times-frac_binary64`
62×	`*-un-lft-identity_binary64`
58×	`add-cube-cbrt_binary64`
33×	`cancel-sign-sub-inv_binary64`

Counts

4 → 186

Calls

4 calls:

15.0ms	(*.f64 (/.f64 beta alpha) (/.f64 beta alpha))
14.0ms	(*.f64 (/.f64 beta alpha) (-.f64 2 (/.f64 6 alpha)))
13.0ms	(-.f64 (+.f64 (/.f64 2 alpha) (.f64 (/.f64 beta alpha) (-.f64 2 (/.f64 6 alpha)))) (/.f64 4 (.f64 alpha alpha)))
4.0ms	(/.f64 4 (*.f64 alpha alpha))

Compiler

Compiled 7487 to 3991 computations (46.7% saved)

series145.0ms (1.8%)

Error

0.0b

Counts

4 → 30

Calls

4 calls:

63.0ms	(-.f64 (+.f64 (/.f64 2 alpha) (.f64 (/.f64 beta alpha) (-.f64 2 (/.f64 6 alpha)))) (/.f64 4 (.f64 alpha alpha)))
34.0ms	(*.f64 (/.f64 beta alpha) (-.f64 2 (/.f64 6 alpha)))
24.0ms	(*.f64 (/.f64 beta alpha) (/.f64 beta alpha))
10.0ms	(/.f64 4 (*.f64 alpha alpha))

Compiler

Compiled 2111 to 1447 computations (31.5% saved)

simplify181.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

410×	`associate-l_binary64`
386×	`associate-r_binary64`
322×	`associate-*l/_binary64`
316×	`*-commutative_binary64`
309×	`associate-*r/_binary64`

Counts

216 → 178

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	404	4689
1	1249	4282
2	4381	4010
3	4767	3968
4	5008	3968

prune111.0ms (1.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	178	0	178
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	178	5	183

Error

0.0b

Counts

183 → 5

Alt Table

Status	Error	Program
	62.9b	(/.f64 (+.f64 (.f64 2 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (/.f64 beta alpha))) (/.f64 (-.f64 (.f64 (pow.f64 alpha 6) (+.f64 (.f64 2 (pow.f64 (pow.f64 alpha 3) 3)) (.f64 alpha (+.f64 (.f64 8 (pow.f64 alpha 6)) (.f64 (pow.f64 alpha 3) (.f64 (pow.f64 alpha 3) (.f64 beta (+.f64 (.f64 10 beta) 16)))))))) (.f64 (.f64 alpha (pow.f64 (pow.f64 alpha 3) 3)) (+.f64 (.f64 (pow.f64 alpha 4) (.f64 beta 6)) (.f64 (.f64 alpha alpha) (.f64 (.f64 alpha alpha) (+.f64 4 (.f64 2 (.f64 beta beta)))))))) (.f64 (pow.f64 alpha 6) (*.f64 alpha (pow.f64 (pow.f64 alpha 3) 3))))) 2)
	44.3b	(/.f64 (-.f64 2 (+.f64 (/.f64 2 beta) (*.f64 2 (/.f64 alpha beta)))) 2)
	43.2b	(/.f64 (/.f64 (+.f64 2 (*.f64 2 beta)) alpha) 2)
	18.5b	(/.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1) 2)
	44.1b	(/.f64 (+.f64 (-.f64 (+.f64 (/.f64 2 alpha) (.f64 (/.f64 beta alpha) (-.f64 2 (/.f64 6 alpha)))) (/.f64 4 (.f64 alpha alpha))) (.f64 (.f64 (/.f64 beta alpha) (/.f64 beta alpha)) -2)) 2)

Compiler

Compiled 4095 to 2282 computations (44.3% saved)

regimes3.0s (38.4%)

Accuracy

Total 0.0b remaining (40.7%)

Threshold costs 0.0b (40.7%)

Compiler

Compiled 65110 to 42335 computations (35% saved)

bsearch19.0ms (0.2%)

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

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

22×	`+-commutative_binary64`
16×	`*-commutative_binary64`
12×	`sub-neg_binary64`
10×	`neg-mul-1_binary64` `neg-sub0_binary64`
5×	`distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	137
1	71	137
2	82	137
3	103	137
4	129	137
5	144	137
6	154	137
7	158	137
8	159	137
9	155	137

end2.0ms (0%)

Compiler: Compiled 94 to 60 computations (36.2% saved)

sample1.1s (13.5%)

Algorithm

1×

intervals

Results

211.0ms	5981×	body	128	valid
135.0ms	1030×	body	1024	valid
124.0ms	8000×	pre	128	true
62.0ms	588×	body	512	valid
19.0ms	301×	body	256	valid
16.0ms	100×	body	2048	valid

Compiler

Compiled 287 to 199 computations (30.7% saved)

Iter	Nodes	Cost
0	49	137
1	71	137
2	82	137
3	103	137
4	129	137
5	144	137
6	154	137
7	158	137
8	159	137
9	155	137

Iter	Nodes	Cost
0	49	137
1	71	137
2	82	137
3	103	137
4	129	137
5	144	137
6	154	137
7	158	137
8	159	137
9	155	137

Details

analyze317.0ms (4%)

sample32.0ms (0.4%)

simplify260.0ms (3.3%)

prune3.0ms (0%)

localize8.0ms (0.1%)

rewrite106.0ms (1.3%)

series150.0ms (1.9%)

simplify117.0ms (1.5%)

prune67.0ms (0.9%)

localize6.0ms (0.1%)

rewrite34.0ms (0.4%)

series25.0ms (0.3%)

simplify80.0ms (1%)

prune19.0ms (0.2%)

localize35.0ms (0.4%)

rewrite694.0ms (8.8%)

series274.0ms (3.5%)

simplify344.0ms (4.4%)

prune487.0ms (6.2%)

localize17.0ms (0.2%)

rewrite260.0ms (3.3%)

series145.0ms (1.8%)

simplify181.0ms (2.3%)

prune111.0ms (1.4%)

regimes3.0s (38.4%)

bsearch19.0ms (0.2%)

simplify10.0ms (0.1%)

end2.0ms (0%)

sample1.1s (13.5%)

Profiling

Iter	Nodes	Cost
0	49	137
1	71	137
2	82	137
3	103	137
4	129	137
5	144	137
6	154	137
7	158	137
8	159	137
9	155	137