Details

analyze403.0ms (8.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4733	38
1	4733	38
0	2	2
1	2	2

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 (0.5%)

Algorithm

1×

intervals

Results

7.0ms	197×	body	128	valid
4.0ms	256×	pre	128	true
3.0ms	22×	body	1024	valid
2.0ms	24×	body	512	valid
1.0ms	10×	body	256	valid
0.0ms	3×	body	2048	valid

Compiler

Compiled 33 to 29 computations (12.1% saved)

simplify252.0ms (5.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (246.0ms)

Iter	Nodes	Cost
0	5018	19

prune3.0ms (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

Error

14.2b

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)

rewrite36.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64_2124`
26×	`add-sqr-sqrt_binary64_2146`
25×	`times-frac_binary64_2130`
19×	`distribute-lft-out_binary64_2075`
14×	`add-cube-cbrt_binary64_2159`
6×	`difference-of-squares_binary64_2093` `distribute-lft-out--_binary64_2076`
5×	`associate-/l_binary64_2069` `associate-/r_binary64_2068`
4×	`add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
2×	`associate-/r/_binary64_2070` `pow1_binary64_2185` `flip3-+_binary64_2127` `div-sub_binary64_2129` `flip-+_binary64_2098` `associate-/l/_binary64_2071`
1×	`flip--_binary64_2099` `clear-num_binary64_2123` `flip3--_binary64_2128` `cbrt-undiv_binary64_2158` `associate-+l-_binary64_2059` `sum-log_binary64_2215` `+-commutative_binary64_2054` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

2 → 65

Calls

2 calls:

19.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
11.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

series81.0ms (1.6%)

Counts

2 → 6

Calls

2 calls:

50.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
31.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

simplify71.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	6172	1488

prune90.0ms (1.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	63	8	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	8	72

Error

13.5b

Counts

72 → 8

Compiler

Compiled 1667 to 929 computations (44.3% saved)

localize11.0ms (0.2%)

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)

rewrite79.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`*-un-lft-identity_binary64_2124`
54×	`add-sqr-sqrt_binary64_2146`
37×	`times-frac_binary64_2130`
27×	`add-cube-cbrt_binary64_2159`
24×	`distribute-lft-out_binary64_2075`
16×	`cancel-sign-sub-inv_binary64_2090`
11×	`add-log-exp_binary64_2163`
10×	`difference-of-squares_binary64_2093` `associate-/r*_binary64_2068`
8×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
6×	`associate-/l*_binary64_2069`
5×	`distribute-lft-out--_binary64_2076`
4×	`associate-/r/_binary64_2070` `pow1_binary64_2185` `diff-log_binary64_2216` `associate--r+_binary64_2060` `difference-of-sqr-1_binary64_2094`
3×	`flip--_binary64_2099` `flip3--_binary64_2128` `sub-neg_binary64_2117`
2×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `frac-sub_binary64_2133` `flip3-+_binary64_2127` `flip-+_binary64_2098` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`
1×	`associate--r-_binary64_2063`

Counts

4 → 128

Calls

4 calls:

36.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
15.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
8.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
7.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))

series154.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

51.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
48.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
28.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
28.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))

simplify90.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4935	2917
1	4935	2917

prune186.0ms (3.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	133	7	140
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	141	7	148

Error

3.1b

Counts

148 → 7

Compiler

Compiled 3873 to 2310 computations (40.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 (+.f64 alpha beta) 2) beta)
0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
0.5b	(/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) beta))
1.2b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite67.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

185×	`*-un-lft-identity_binary64_2124`
150×	`times-frac_binary64_2130`
92×	`add-sqr-sqrt_binary64_2146`
81×	`add-cube-cbrt_binary64_2159`
60×	`distribute-lft-out_binary64_2075`
27×	`associate-/r*_binary64_2068`
19×	`add-exp-log_binary64_2162`
13×	`add-cbrt-cube_binary64_2160`
11×	`associate-/l*_binary64_2069`
9×	`div-exp_binary64_2175`
7×	`div-inv_binary64_2121`
6×	`add-log-exp_binary64_2163`
5×	`cbrt-undiv_binary64_2158` `pow1_binary64_2185`
4×	`difference-of-squares_binary64_2093`
3×	`clear-num_binary64_2123` `associate-/r/_binary64_2070` `cancel-sign-sub-inv_binary64_2090` `frac-2neg_binary64_2135`
2×	`flip3-+_binary64_2127` `difference-of-sqr-1_binary64_2094` `flip-+_binary64_2098` `1-exp_binary64_2168` `associate-/l/_binary64_2071` `rec-exp_binary64_2174`
1×	`flip--_binary64_2099` `flip3--_binary64_2128` `distribute-lft-out--_binary64_2076` `diff-log_binary64_2216` `sub-neg_binary64_2117` `pow-flip_binary64_2198` `inv-pow_binary64_2209`

Counts

4 → 195

Calls

4 calls:

18.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
11.0ms	(/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) beta))
8.0ms	(/.f64 (+.f64 (+.f64 alpha beta) 2) beta)
7.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))

series132.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

48.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
38.0ms	(/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) beta))
27.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
18.0ms	(/.f64 (+.f64 (+.f64 alpha beta) 2) beta)

simplify116.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4925	3828
1	4925	3828

prune272.0ms (5.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	205	2	207
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	205	9	214

Error

3.1b

Counts

214 → 9

Compiler

Compiled 6007 to 3670 computations (38.9% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
6.1b	(cbrt.f64 (/.f64 (+.f64 (+.f64 alpha beta) 2) beta))
6.1b	(cbrt.f64 (/.f64 (+.f64 (+.f64 alpha beta) 2) beta))
6.1b	(cbrt.f64 (/.f64 (+.f64 (+.f64 alpha beta) 2) beta))

rewrite54.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`*-un-lft-identity_binary64_2124`
57×	`cbrt-prod_binary64_2155`
48×	`times-frac_binary64_2130`
43×	`add-sqr-sqrt_binary64_2146`
32×	`add-cube-cbrt_binary64_2159`
27×	`distribute-lft-out_binary64_2075`
6×	`add-log-exp_binary64_2163`
4×	`difference-of-squares_binary64_2093` `pow1_binary64_2185` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
3×	`cbrt-div_binary64_2156` `cancel-sign-sub-inv_binary64_2090` `pow1/3_binary64_2206` `div-inv_binary64_2121`
2×	`difference-of-sqr-1_binary64_2094`
1×	`flip--_binary64_2099` `flip3--_binary64_2128` `distribute-lft-out--_binary64_2076` `diff-log_binary64_2216` `sub-neg_binary64_2117`

Counts

4 → 105

Calls

4 calls:

14.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
7.0ms	(cbrt.f64 (/.f64 (+.f64 (+.f64 alpha beta) 2) beta))
7.0ms	(cbrt.f64 (/.f64 (+.f64 (+.f64 alpha beta) 2) beta))
7.0ms	(cbrt.f64 (/.f64 (+.f64 (+.f64 alpha beta) 2) beta))

series441.0ms (8.8%)

Counts

4 → 12

Calls

4 calls:

134.0ms	(cbrt.f64 (/.f64 (+.f64 (+.f64 alpha beta) 2) beta))
133.0ms	(cbrt.f64 (/.f64 (+.f64 (+.f64 alpha beta) 2) beta))
127.0ms	(cbrt.f64 (/.f64 (+.f64 (+.f64 alpha beta) 2) beta))
47.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

simplify76.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4893	2682
1	4893	2682

prune249.0ms (5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	114	3	117
Fresh	5	2	7
Picked	1	0	1
Done	0	1	1
Total	120	6	126

Error

3.1b

Counts

126 → 6

Compiler

Compiled 5685 to 3449 computations (39.3% saved)

regimes443.0ms (8.9%)

Accuracy

Total 0.1b remaining (3.9%)

Threshold costs 0.1b (3.9%)

Compiler

Compiled 5875 to 4192 computations (28.6% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	238	110
1	238	110

end0.0ms (0%)

sample1.6s (32.2%)

Algorithm

1×

intervals

Results

201.0ms	6057×	body	128	valid
139.0ms	8000×	pre	128	true
124.0ms	943×	body	1024	valid
56.0ms	576×	body	512	valid
21.0ms	330×	body	256	valid
17.0ms	94×	body	2048	valid

Compiler

Compiled 1254 to 893 computations (28.8% saved)

Details

analyze403.0ms (8.1%)

sample25.0ms (0.5%)

simplify252.0ms (5.1%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

rewrite36.0ms (0.7%)

series81.0ms (1.6%)

simplify71.0ms (1.4%)

prune90.0ms (1.8%)

localize11.0ms (0.2%)

rewrite79.0ms (1.6%)

series154.0ms (3.1%)

simplify90.0ms (1.8%)

prune186.0ms (3.7%)

localize12.0ms (0.2%)

rewrite67.0ms (1.3%)

series132.0ms (2.6%)

simplify116.0ms (2.3%)

prune272.0ms (5.4%)

localize18.0ms (0.4%)

rewrite54.0ms (1.1%)

series441.0ms (8.8%)

simplify76.0ms (1.5%)

prune249.0ms (5%)

regimes443.0ms (8.9%)

bsearch3.0ms (0.1%)

simplify10.0ms (0.2%)

end0.0ms (0%)

sample1.6s (32.2%)

Profiling