Details

analyze4.0ms (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)

sample25.0ms (0.6%)

Algorithm

1×

intervals

Results

6.0ms	196×	body	80	valid
4.0ms	256×	pre	80	true
3.0ms	27×	body	640	valid
3.0ms	18×	body	1280	valid
1.0ms	9×	body	320	valid
0.0ms	6×	body	160	valid

Compiler

Compiled 33 to 29 computations (12.1% saved)

simplify238.0ms (5.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (218.0ms)

Iter	Nodes	Cost
0	4879	19
1	4879	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: 14.0b

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))
1.1b	(+.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` `insert-posit16` `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 → 67

Calls

2 calls:

23.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
13.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

series162.0ms (3.8%)

Counts

2 → 6

Calls

2 calls:

95.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
67.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

simplify112.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	5358	1521

prune96.0ms (2.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	62	11	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	11	74

Merged error: 13.4b

Counts

74 → 11

Compiler

Compiled 1778 to 1000 computations (43.8% saved)

localize11.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
1.1b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite44.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`*-un-lft-identity_binary64`
34×	`add-sqr-sqrt_binary64`
33×	`times-frac_binary64`
24×	`distribute-lft-out_binary64`
23×	`add-cube-cbrt_binary64`
10×	`associate-/r*_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-/l*_binary64`
5×	`add-log-exp_binary64`
4×	`associate-/r/_binary64` `difference-of-squares_binary64`
3×	`pow1_binary64` `insert-posit16`
2×	`flip3-+_binary64` `cbrt-undiv_binary64` `difference-of-sqr-1_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

3 → 95

Calls

3 calls:

17.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
12.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
10.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))

series221.0ms (5.2%)

Counts

3 → 9

Calls

3 calls:

105.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
60.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
56.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))

simplify108.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4928	1744
1	4928	1744

prune152.0ms (3.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	96	8	104
Fresh	10	0	10
Picked	1	0	1
Done	0	0	0
Total	107	8	115

Merged error: 2.9b

Counts

115 → 8

Compiler

Compiled 2891 to 1721 computations (40.5% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.7b	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
0.7b	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
0.7b	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
1.1b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite41.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64`
18×	`add-sqr-sqrt_binary64`
15×	`cbrt-prod_binary64`
9×	`distribute-lft-out_binary64`
7×	`add-cube-cbrt_binary64`
6×	`cbrt-div_binary64` `add-log-exp_binary64`
4×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `insert-posit16`
3×	`flip3-+_binary64` `pow1/3_binary64` `times-frac_binary64` `flip-+_binary64`
2×	`difference-of-sqr-1_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

4 → 67

Calls

4 calls:

17.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
7.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
7.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
7.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))

series508.0ms (11.9%)

Counts

4 → 12

Calls

4 calls:

136.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
134.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
132.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
105.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

simplify209.0ms (4.9%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (181.0ms)

Iter	Nodes	Cost
0	4873	1454
1	4873	1454

prune170.0ms (4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	75	4	79
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	81	6	87

Merged error: 2.9b

Counts

87 → 6

Compiler

Compiled 4049 to 2241 computations (44.7% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.7b	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
0.7b	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
0.7b	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
1.1b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite40.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64`
18×	`add-sqr-sqrt_binary64`
15×	`cbrt-prod_binary64`
9×	`distribute-lft-out_binary64`
7×	`add-cube-cbrt_binary64`
6×	`cbrt-div_binary64` `add-log-exp_binary64`
4×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `insert-posit16`
3×	`flip3-+_binary64` `pow1/3_binary64` `times-frac_binary64` `flip-+_binary64`
2×	`difference-of-sqr-1_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

4 → 67

Calls

4 calls:

17.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
7.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
7.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
7.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))

series515.0ms (12.1%)

Counts

4 → 12

Calls

4 calls:

139.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
136.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
133.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
107.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

simplify210.0ms (4.9%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (182.0ms)

Iter	Nodes	Cost
0	4873	1454
1	4873	1454

prune151.0ms (3.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	77	2	79
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	78	7	85

Merged error: 2.9b

Counts

85 → 7

Compiler

Compiled 3413 to 2153 computations (36.9% saved)

regimes80.0ms (1.9%)

Compiler: Compiled 562 to 394 computations (29.9% saved)

bsearch34.0ms (0.8%)

Steps

Iters	Range		Point
10	3.9544267203064836	1652169842525.6367	102400470.51088828

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify11.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	235	135
1	235	135

end0.0ms (0%)

sample1.0s (24.5%)

Algorithm

1×

intervals

Results

196.0ms	5856×	body	80	valid
146.0ms	8000×	pre	80	true
128.0ms	843×	body	1280	valid
88.0ms	707×	body	640	valid
37.0ms	401×	body	320	valid
12.0ms	193×	body	160	valid

Compiler

Compiled 387 to 269 computations (30.5% saved)

Details

analyze4.0ms (0.1%)

sample25.0ms (0.6%)

simplify238.0ms (5.6%)

prune2.0ms (0.1%)

localize8.0ms (0.2%)

rewrite39.0ms (0.9%)

series162.0ms (3.8%)

simplify112.0ms (2.6%)

prune96.0ms (2.2%)

localize11.0ms (0.3%)

rewrite44.0ms (1%)

series221.0ms (5.2%)

simplify108.0ms (2.5%)

prune152.0ms (3.5%)

localize19.0ms (0.4%)

rewrite41.0ms (1%)

series508.0ms (11.9%)

simplify209.0ms (4.9%)

prune170.0ms (4%)

localize16.0ms (0.4%)

rewrite40.0ms (0.9%)

series515.0ms (12.1%)

simplify210.0ms (4.9%)

prune151.0ms (3.5%)

regimes80.0ms (1.9%)

bsearch34.0ms (0.8%)

simplify11.0ms (0.3%)

end0.0ms (0%)

sample1.0s (24.5%)

Profiling