Details

analyze3.0ms (0.1%)

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 20 to 16 computations (20% saved)

sample27.0ms (0.6%)

Algorithm

1×

intervals

Results

8.0ms	256×	pre	128	true
8.0ms	216×	body	128	valid
2.0ms	18×	body	1024	valid
1.0ms	14×	body	512	valid
0.0ms	6×	body	256	valid
0.0ms	2×	body	2048	valid

Compiler

Compiled 33 to 29 computations (12.1% saved)

simplify139.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (133.0ms)

Iter	Nodes	Cost
0	5139	19

prune2.0ms (0.1%)

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

Merged error: 9.8b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
1.2b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite39.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

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`
6×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
5×	`associate-/r_binary64` `associate-/l_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `pow1_binary64` `associate-/r/_binary64` `div-sub_binary64` `flip-+_binary64`
1×	`flip3--_binary64` `cbrt-undiv_binary64` `associate-+l-_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

2 → 65

Calls

2 calls:

21.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
12.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

series163.0ms (3.7%)

Counts

2 → 6

Calls

2 calls:

95.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
68.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

simplify62.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5223	1488

prune280.0ms (6.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	61	10	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	10	72

Merged error: 9.4b

Counts

72 → 10

Compiler

Compiled 5627 to 3694 computations (34.4% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
1.2b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite86.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`*-un-lft-identity_binary64`
54×	`add-sqr-sqrt_binary64`
37×	`times-frac_binary64`
27×	`add-cube-cbrt_binary64`
24×	`distribute-lft-out_binary64`
16×	`cancel-sign-sub-inv_binary64`
11×	`add-log-exp_binary64`
10×	`associate-/r*_binary64` `difference-of-squares_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-/l*_binary64`
5×	`distribute-lft-out--_binary64`
4×	`pow1_binary64` `associate--r+_binary64` `diff-log_binary64` `difference-of-sqr-1_binary64` `associate-/r/_binary64`
3×	`sub-neg_binary64` `flip3--_binary64` `flip--_binary64`
2×	`flip3-+_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64` `frac-sub_binary64`
1×	`associate--r-_binary64`

Counts

4 → 128

Calls

4 calls:

40.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
16.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
8.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
8.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))

series327.0ms (7.3%)

Counts

4 → 12

Calls

4 calls:

106.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
94.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
66.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
59.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))

simplify71.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4934	2917
1	4934	2917

prune389.0ms (8.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	136	4	140
Fresh	5	4	9
Picked	0	1	1
Done	0	0	0
Total	141	9	150

Merged error: 1.5b

Counts

150 → 9

Compiler

Compiled 8261 to 5357 computations (35.2% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 beta)
0.6b	(cbrt.f64 beta)
0.6b	(cbrt.f64 beta)
1.2b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite25.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
9×	`cbrt-prod_binary64`
8×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64`
4×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64`
3×	`pow1/3_binary64` `cancel-sign-sub-inv_binary64` `times-frac_binary64`
2×	`difference-of-sqr-1_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

4 → 54

Calls

4 calls:

16.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
1.0ms	(cbrt.f64 beta)
1.0ms	(cbrt.f64 beta)
1.0ms	(cbrt.f64 beta)

series603.0ms (13.5%)

Counts

4 → 12

Calls

4 calls:

176.0ms	(cbrt.f64 beta)
160.0ms	(cbrt.f64 beta)
156.0ms	(cbrt.f64 beta)
111.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

simplify87.0ms (2%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4855	741
1	4855	741

prune115.0ms (2.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	66	9	75

Merged error: 1.5b

Counts

75 → 9

Compiler

Compiled 2717 to 1498 computations (44.9% saved)

localize21.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (cbrt.f64 beta))
0.6b	(cbrt.f64 (cbrt.f64 beta))
0.6b	(cbrt.f64 (cbrt.f64 beta))
1.2b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite31.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`cbrt-prod_binary64`
22×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64`
4×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64`
3×	`pow1/3_binary64` `cancel-sign-sub-inv_binary64` `times-frac_binary64`
2×	`difference-of-sqr-1_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

4 → 63

Calls

4 calls:

16.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
2.0ms	(cbrt.f64 (cbrt.f64 beta))
2.0ms	(cbrt.f64 (cbrt.f64 beta))
2.0ms	(cbrt.f64 (cbrt.f64 beta))

series747.0ms (16.7%)

Counts

4 → 12

Calls

4 calls:

223.0ms	(cbrt.f64 (cbrt.f64 beta))
214.0ms	(cbrt.f64 (cbrt.f64 beta))
209.0ms	(cbrt.f64 (cbrt.f64 beta))
101.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

simplify86.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4859	960
1	4859	960

prune138.0ms (3.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	76	8	84

Merged error: 1.5b

Counts

84 → 8

Compiler

Compiled 3558 to 1642 computations (53.9% saved)

regimes52.0ms (1.2%)

Compiler: Compiled 452 to 310 computations (31.4% saved)

bsearch19.0ms (0.4%)

Steps

Iters	Range		Point
7	2.838647906671344e+23	7.88418999901068e+24	2.8666984841737303e+23

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	219	71
1	219	71

end0.0ms (0%)

sample913.0ms (20.4%)

Algorithm

1×

intervals

Results

199.0ms	5982×	body	128	valid
130.0ms	8000×	pre	128	true
124.0ms	993×	body	1024	valid
57.0ms	597×	body	512	valid
21.0ms	338×	body	256	valid
16.0ms	90×	body	2048	valid

Compiler

Compiled 292 to 203 computations (30.5% saved)

Details

analyze3.0ms (0.1%)

sample27.0ms (0.6%)

simplify139.0ms (3.1%)

prune2.0ms (0.1%)

localize8.0ms (0.2%)

rewrite39.0ms (0.9%)

series163.0ms (3.7%)

simplify62.0ms (1.4%)

prune280.0ms (6.3%)

localize12.0ms (0.3%)

rewrite86.0ms (1.9%)

series327.0ms (7.3%)

simplify71.0ms (1.6%)

prune389.0ms (8.7%)

localize16.0ms (0.4%)

rewrite25.0ms (0.6%)

series603.0ms (13.5%)

simplify87.0ms (2%)

prune115.0ms (2.6%)

localize21.0ms (0.5%)

rewrite31.0ms (0.7%)

series747.0ms (16.7%)

simplify86.0ms (1.9%)

prune138.0ms (3.1%)

regimes52.0ms (1.2%)

bsearch19.0ms (0.4%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample913.0ms (20.4%)

Profiling