Details

analyze310.0ms (4.6%)

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)

sample35.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms	189×	body	128	valid
7.0ms	41×	body	1024	valid
5.0ms	256×	pre	128	true
2.0ms	17×	body	512	valid
1.0ms	7×	body	256	valid
0.0ms	2×	body	2048	valid

Compiler

Compiled 39 to 29 computations (25.6% saved)

simplify252.0ms (3.8%)

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

prune2.0ms (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

17.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	17.0b	(/.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))
1.8b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite94.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

16.2b

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:

15.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
9.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 1149 to 611 computations (46.8% saved)

series111.0ms (1.7%)

Error

0.0b

Counts

2 → 36

Calls

2 calls:

48.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
35.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 2206 to 1740 computations (21.1% saved)

simplify123.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

435×	`distribute-rgt-in_binary64`
379×	`distribute-lft-in_binary64`
363×	`times-frac_binary64`
342×	`associate-/l*_binary64`
283×	`div-sub_binary64`

Counts

101 → 96

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	245	2893
1	657	2852
2	1985	2726
3	4837	2726
4	5283	2726

prune52.0ms (0.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	93	3	96
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	3	97

Error

Counts

97 → 3

Alt Table

Status	Error	Program
▶	17.0b	(/.f64 (+.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) 3)) 1) 2)
	17.0b	(/.f64 (+.f64 (/.f64 1 (/.f64 (+.f64 alpha (+.f64 2 beta)) (-.f64 beta alpha))) 1) 2)
	45.5b	(/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (.f64 2 (/.f64 beta alpha))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (+.f64 (.f64 6 (/.f64 beta (.f64 alpha alpha))) (.f64 2 (.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))) 2)

Compiler

Compiled 1465 to 891 computations (39.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta)))
0.1b	(pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) 3)
1.8b	(+.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) 3)) 1)
11.9b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) 3))

rewrite185.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

246×	`*-un-lft-identity_binary64`
125×	`times-frac_binary64`
114×	`add-sqr-sqrt_binary64`
79×	`distribute-lft-out_binary64`
68×	`cbrt-prod_binary64`

Counts

4 → 224

Calls

4 calls:

29.0ms	(+.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) 3)) 1)
13.0ms	(pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) 3)
13.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) 3))
9.0ms	(/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta)))

Compiler

Compiled 3302 to 2162 computations (34.5% saved)

series280.0ms (4.2%)

Error

Counts

4 → 69

Calls

4 calls:

78.0ms	(+.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) 3)) 1)
60.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) 3))
50.0ms	(pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) 3)
38.0ms	(/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta)))

Compiler

Compiled 4726 to 3835 computations (18.9% saved)

simplify224.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

216×	`+-commutative_binary64`
184×	`associate--l+_binary64`
177×	`times-frac_binary64`
158×	`associate-/l*_binary64`
153×	`associate-+r+_binary64`

Counts

293 → 242

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	508	8767
1	1371	8290
2	4728	8290
3	4945	8290

prune68.0ms (1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	242	0	242
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	242	3	245

Error

Counts

245 → 3

Alt Table

Status	Error	Program
✓	17.0b	(/.f64 (+.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) 3)) 1) 2)
▶	17.0b	(/.f64 (+.f64 (/.f64 1 (/.f64 (+.f64 alpha (+.f64 2 beta)) (-.f64 beta alpha))) 1) 2)
	45.5b	(/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (.f64 2 (/.f64 beta alpha))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (+.f64 (.f64 6 (/.f64 beta (.f64 alpha alpha))) (.f64 2 (.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))) 2)

Compiler

Compiled 2348 to 1500 computations (36.1% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (+.f64 alpha (+.f64 2 beta)) (-.f64 beta alpha))
0.1b	(/.f64 1 (/.f64 (+.f64 alpha (+.f64 2 beta)) (-.f64 beta alpha)))
1.8b	(+.f64 (/.f64 1 (/.f64 (+.f64 alpha (+.f64 2 beta)) (-.f64 beta alpha))) 1)

rewrite187.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

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

Counts

3 → 212

Calls

3 calls:

31.0ms	(+.f64 (/.f64 1 (/.f64 (+.f64 alpha (+.f64 2 beta)) (-.f64 beta alpha))) 1)
19.0ms	(/.f64 1 (/.f64 (+.f64 alpha (+.f64 2 beta)) (-.f64 beta alpha)))
9.0ms	(/.f64 (+.f64 alpha (+.f64 2 beta)) (-.f64 beta alpha))

Compiler

Compiled 3996 to 2546 computations (36.3% saved)

series133.0ms (2%)

Error

Counts

3 → 48

Calls

3 calls:

47.0ms	(+.f64 (/.f64 1 (/.f64 (+.f64 alpha (+.f64 2 beta)) (-.f64 beta alpha))) 1)
35.0ms	(/.f64 1 (/.f64 (+.f64 alpha (+.f64 2 beta)) (-.f64 beta alpha)))
23.0ms	(/.f64 (+.f64 alpha (+.f64 2 beta)) (-.f64 beta alpha))

Compiler

Compiled 2804 to 2242 computations (20% saved)

simplify260.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

546×	`distribute-rgt-in_binary64`
477×	`times-frac_binary64`
281×	`sub-neg_binary64`
238×	`cancel-sign-sub-inv_binary64`
144×	`+-commutative_binary64`

Counts

260 → 249

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	328	6998
1	811	6567
2	2554	6333
3	4909	6333
4	4992	6333
5	4952	6333

prune73.0ms (1.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	249	0	249
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	249	3	252

Error

Counts

252 → 3

Alt Table

Status	Error	Program
✓	17.0b	(/.f64 (+.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) 3)) 1) 2)
✓	17.0b	(/.f64 (+.f64 (/.f64 1 (/.f64 (+.f64 alpha (+.f64 2 beta)) (-.f64 beta alpha))) 1) 2)
▶	45.5b	(/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (.f64 2 (/.f64 beta alpha))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (+.f64 (.f64 6 (/.f64 beta (.f64 alpha alpha))) (.f64 2 (.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))) 2)

Compiler

Compiled 2616 to 1592 computations (39.1% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.0b	(+.f64 (.f64 6 (/.f64 beta (.f64 alpha alpha))) (.f64 2 (.f64 (/.f64 beta alpha) (/.f64 beta alpha))))
2.4b	(+.f64 (/.f64 4 (.f64 alpha alpha)) (+.f64 (.f64 6 (/.f64 beta (.f64 alpha alpha))) (.f64 2 (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
4.0b	(-.f64 (+.f64 (/.f64 2 alpha) (.f64 2 (/.f64 beta alpha))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (+.f64 (.f64 6 (/.f64 beta (.f64 alpha alpha))) (.f64 2 (.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))
8.8b	(/.f64 beta (*.f64 alpha alpha))

rewrite149.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

42×	`frac-add_binary64`
42×	`associate-*r/_binary64`
32×	`add-log-exp_binary64`
21×	`frac-sub_binary64`
16×	`flip-+_binary64`

Counts

4 → 100

Calls

4 calls:

22.0ms	(-.f64 (+.f64 (/.f64 2 alpha) (.f64 2 (/.f64 beta alpha))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (+.f64 (.f64 6 (/.f64 beta (.f64 alpha alpha))) (.f64 2 (.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))
15.0ms	(+.f64 (/.f64 4 (.f64 alpha alpha)) (+.f64 (.f64 6 (/.f64 beta (.f64 alpha alpha))) (.f64 2 (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
7.0ms	(+.f64 (.f64 6 (/.f64 beta (.f64 alpha alpha))) (.f64 2 (.f64 (/.f64 beta alpha) (/.f64 beta alpha))))
4.0ms	(/.f64 beta (*.f64 alpha alpha))

Compiler

Compiled 7040 to 3102 computations (55.9% saved)

series196.0ms (2.9%)

Error

Counts

4 → 42

Calls

4 calls:

73.0ms	(-.f64 (+.f64 (/.f64 2 alpha) (.f64 2 (/.f64 beta alpha))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (+.f64 (.f64 6 (/.f64 beta (.f64 alpha alpha))) (.f64 2 (.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))
53.0ms	(+.f64 (/.f64 4 (.f64 alpha alpha)) (+.f64 (.f64 6 (/.f64 beta (.f64 alpha alpha))) (.f64 2 (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
37.0ms	(+.f64 (.f64 6 (/.f64 beta (.f64 alpha alpha))) (.f64 2 (.f64 (/.f64 beta alpha) (/.f64 beta alpha))))
17.0ms	(/.f64 beta (*.f64 alpha alpha))

Compiler

Compiled 2636 to 1986 computations (24.7% saved)

simplify198.0ms (3%)

Algorithm

1×	egg-herbie

Rules

444×	`associate-r_binary64`
443×	`times-frac_binary64`
420×	`associate-l_binary64`
394×	`distribute-rgt-in_binary64`
378×	`distribute-lft-in_binary64`

Counts

142 → 121

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	322	9167
1	1099	8372
2	4729	8215
3	5494	8215

prune75.0ms (1.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	121	3	124

Error

Counts

124 → 3

Alt Table

Status	Error	Program
✓	17.0b	(/.f64 (+.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))) 3)) 1) 2)
✓	17.0b	(/.f64 (+.f64 (/.f64 1 (/.f64 (+.f64 alpha (+.f64 2 beta)) (-.f64 beta alpha))) 1) 2)
✓	45.5b	(/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (.f64 2 (/.f64 beta alpha))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (+.f64 (.f64 6 (/.f64 beta (.f64 alpha alpha))) (.f64 2 (.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))) 2)

Compiler

Compiled 4576 to 2259 computations (50.6% saved)

regimes1.5s (21.8%)

Accuracy

Total 0.1b remaining (61.7%)

Threshold costs 0.1b (61.7%)

Compiler

Compiled 10222 to 7451 computations (27.1% saved)

bsearch8.0ms (0.1%)

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

simplify15.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

19×	`+-commutative_binary64`
12×	`*-commutative_binary64`
11×	`sub-neg_binary64`
9×	`neg-sub0_binary64`
9×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	83
1	51	83
2	62	83
3	81	83
4	95	83
5	110	83
6	125	83
7	129	83
8	130	83
9	126	83

end2.0ms (0%)

Compiler: Compiled 58 to 39 computations (32.8% saved)

sample2.2s (32.2%)

Algorithm

1×

intervals

Results

587.0ms	5973×	body	128	valid
392.0ms	1034×	body	1024	valid
269.0ms	8000×	pre	128	true
144.0ms	582×	body	512	valid
56.0ms	320×	body	256	valid
37.0ms	91×	body	2048	valid

Compiler

Compiled 154 to 106 computations (31.2% saved)

Details

analyze310.0ms (4.6%)

sample35.0ms (0.5%)

simplify252.0ms (3.8%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite94.0ms (1.4%)

series111.0ms (1.7%)

simplify123.0ms (1.8%)

prune52.0ms (0.8%)

localize12.0ms (0.2%)

rewrite185.0ms (2.8%)

series280.0ms (4.2%)

simplify224.0ms (3.3%)

prune68.0ms (1%)

localize10.0ms (0.1%)

rewrite187.0ms (2.8%)

series133.0ms (2%)

simplify260.0ms (3.9%)

prune73.0ms (1.1%)

localize19.0ms (0.3%)

rewrite149.0ms (2.2%)

series196.0ms (2.9%)

simplify198.0ms (3%)

prune75.0ms (1.1%)

regimes1.5s (21.8%)

bsearch8.0ms (0.1%)

simplify15.0ms (0.2%)

end2.0ms (0%)

sample2.2s (32.2%)

Profiling