Details

analyze2.0ms (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)

sample24.0ms (0.5%)

Algorithm

1×

intervals

Results

7.0ms	198×	body	128	valid
4.0ms	256×	pre	128	true
4.0ms	30×	body	1024	valid
2.0ms	21×	body	512	valid
0.0ms	3×	body	2048	valid
0.0ms	4×	body	256	valid

Compiler

Compiled 33 to 29 computations (12.1% saved)

simplify295.0ms (6.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (122.0ms)

Iter	Nodes	Cost
0	4878	19
1	4878	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

Merged error: 14.6b

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))
1.6b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite38.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64_1762`
26×	`add-sqr-sqrt_binary64_1783`
25×	`times-frac_binary64_1768`
19×	`distribute-lft-out_binary64_1715`
14×	`add-cube-cbrt_binary64_1794`
6×	`distribute-lft-out--_binary64_1716` `difference-of-squares_binary64_1731`
5×	`associate-/r_binary64_1708` `associate-/l_binary64_1709`
4×	`add-log-exp_binary64_1798` `add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797`
2×	`associate-/r/_binary64_1710` `div-sub_binary64_1767` `associate-/l/_binary64_1711` `flip3-+_binary64_1765` `flip-+_binary64_1736` `pow1_binary64_1820`
1×	`flip3--_binary64_1766` `frac-2neg_binary64_1773` `clear-num_binary64_1761` `div-inv_binary64_1759` `+-commutative_binary64_1694` `cbrt-undiv_binary64_1793` `div-exp_binary64_1810` `flip--_binary64_1737` `associate-+l-_binary64_1699` `sum-log_binary64_1850`

Counts

2 → 65

Calls

2 calls:

20.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
11.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

series163.0ms (3.6%)

Counts

2 → 6

Calls

2 calls:

92.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
71.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

simplify64.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5354	1488

prune93.0ms (2.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	60	11	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	11	72

Merged error: 14.0b

Counts

72 → 11

Compiler

Compiled 1719 to 973 computations (43.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) 2)
0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
1.5b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite86.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

100×	`*-un-lft-identity_binary64_1762`
67×	`add-sqr-sqrt_binary64_1783`
58×	`times-frac_binary64_1768`
36×	`add-cube-cbrt_binary64_1794`
24×	`distribute-lft-out_binary64_1715`
13×	`associate-/r_binary64_1708` `distribute-lft-out--_binary64_1716` `associate-/l_binary64_1709`
12×	`difference-of-squares_binary64_1731`
10×	`add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797`
6×	`add-log-exp_binary64_1798`
4×	`associate-/r/_binary64_1710` `associate-/l/_binary64_1711` `pow1_binary64_1820`
3×	`flip3--_binary64_1766` `frac-2neg_binary64_1773` `clear-num_binary64_1761` `div-inv_binary64_1759` `cbrt-undiv_binary64_1793` `div-exp_binary64_1810` `flip--_binary64_1737`
2×	`difference-of-sqr-1_binary64_1732` `flip3-+_binary64_1765` `flip-+_binary64_1736` `frac-sub_binary64_1771`
1×	`diff-log_binary64_1851` `div-sub_binary64_1767` `sub-neg_binary64_1755`

Counts

4 → 140

Calls

4 calls:

39.0ms	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) 2)
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))

series350.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

118.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
107.0ms	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) 2)
63.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
61.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))

simplify78.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5297	3801

prune244.0ms (5.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	142	10	152
Fresh	10	0	10
Picked	1	0	1
Done	0	0	0
Total	153	10	163

Merged error: 2.9b

Counts

163 → 10

Compiler

Compiled 4722 to 2855 computations (39.5% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 alpha (+.f64 (+.f64 alpha beta) 2))
0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
0.0b	(*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)))
1.5b	(+.f64 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2))) -1)

rewrite98.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

244×	`*-un-lft-identity_binary64_1762`
130×	`times-frac_binary64_1768`
96×	`distribute-lft-out_binary64_1715`
84×	`add-sqr-sqrt_binary64_1783`
72×	`add-cube-cbrt_binary64_1794`
39×	`swap-sqr_binary64_1729`
21×	`associate-l_binary64_1705` `associate-r_binary64_1704`
20×	`add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797`
12×	`associate-/r/_binary64_1710`
11×	`pow1_binary64_1820`
10×	`associate-/r*_binary64_1708`
7×	`flip3-+_binary64_1765` `flip-+_binary64_1736`
6×	`div-inv_binary64_1759` `cbrt-undiv_binary64_1793` `add-log-exp_binary64_1798` `div-exp_binary64_1810` `associate-/l*_binary64_1709`
4×	`prod-exp_binary64_1808` `unswap-sqr_binary64_1730` `cbrt-unprod_binary64_1792`
2×	`frac-2neg_binary64_1773` `clear-num_binary64_1761`
1×	`pow-sqr_binary64_1735` `frac-times_binary64_1772` `pow-prod-down_binary64_1830` `pow-prod-up_binary64_1829` `pow-plus_binary64_1822` `difference-of-sqr--1_binary64_1733` `associate-l/_binary64_1707` `+-commutative_binary64_1694` `associate-r/_binary64_1706` `*-commutative_binary64_1695` `sum-log_binary64_1850` `pow2_binary64_1840`

Counts

4 → 195

Calls

4 calls:

28.0ms	(*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)))
22.0ms	(+.f64 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2))) -1)
8.0ms	(/.f64 alpha (+.f64 (+.f64 alpha beta) 2))
8.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))

series351.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

144.0ms	(+.f64 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2))) -1)
88.0ms	(*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)))
60.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
59.0ms	(/.f64 alpha (+.f64 (+.f64 alpha beta) 2))

simplify84.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4967	4168
1	4967	4168

prune421.0ms (9.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	206	1	207
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	207	10	217

Merged error: 2.9b

Counts

217 → 10

Compiler

Compiled 9170 to 5336 computations (41.8% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
0.6b	(exp.f64 (log.f64 (/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2)))
1.5b	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
7.1b	(log.f64 (/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2))

rewrite118.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

91×	`*-un-lft-identity_binary64_1762`
78×	`add-sqr-sqrt_binary64_1783`
66×	`times-frac_binary64_1768`
50×	`log-prod_binary64_1845`
37×	`add-cube-cbrt_binary64_1794`
25×	`exp-sum_binary64_1805`
19×	`distribute-lft-out--_binary64_1716`
16×	`difference-of-squares_binary64_1731`
12×	`distribute-lft-out_binary64_1715`
9×	`add-exp-log_binary64_1797`
6×	`add-log-exp_binary64_1798` `add-cbrt-cube_binary64_1795` `pow1_binary64_1820`
5×	`associate-/r*_binary64_1708`
4×	`exp-prod_binary64_1811`
3×	`div-inv_binary64_1759` `associate-/l*_binary64_1709`
2×	`associate-/r/_binary64_1710` `difference-of-sqr-1_binary64_1732` `log-pow_binary64_1848` `div-exp_binary64_1810` `log-div_binary64_1846` `rem-log-exp_binary64_1800`
1×	`flip3--_binary64_1766` `frac-2neg_binary64_1773` `diff-log_binary64_1851` `flip3-+_binary64_1765` `clear-num_binary64_1761` `flip-+_binary64_1736` `rem-exp-log_binary64_1799` `cbrt-undiv_binary64_1793` `exp-diff_binary64_1807` `flip--_binary64_1737` `sub-neg_binary64_1755`

Counts

4 → 129

Calls

4 calls:

42.0ms	(exp.f64 (log.f64 (/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2)))
35.0ms	(log.f64 (/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2))
17.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
9.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))

series558.0ms (12.3%)

Counts

4 → 12

Calls

4 calls:

228.0ms	(log.f64 (/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2))
171.0ms	(exp.f64 (log.f64 (/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2)))
104.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
54.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))

simplify124.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4869	4513
1	4869	4513

prune207.0ms (4.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	136	5	141
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	144	7	151

Merged error: 2.9b

Counts

151 → 7

Compiler

Compiled 4281 to 2720 computations (36.5% saved)

regimes65.0ms (1.4%)

Compiler: Compiled 488 to 368 computations (24.6% saved)

bsearch15.0ms (0.3%)

Steps

Iters	Range		Point
6	4.408790000714098e+18	4.9724012816074736e+19	4.470683226004296e+18

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	223	80
1	223	80

end0.0ms (0%)

sample990.0ms (21.9%)

Algorithm

1×

intervals

Results

201.0ms	5976×	body	128	valid
144.0ms	8000×	pre	128	true
128.0ms	1006×	body	1024	valid
57.0ms	583×	body	512	valid
23.0ms	115×	body	2048	valid
21.0ms	320×	body	256	valid

Compiler

Compiled 315 to 237 computations (24.8% saved)

Details

analyze2.0ms (0.1%)

sample24.0ms (0.5%)

simplify295.0ms (6.5%)

prune2.0ms (0%)

localize8.0ms (0.2%)

rewrite38.0ms (0.8%)

series163.0ms (3.6%)

simplify64.0ms (1.4%)

prune93.0ms (2.1%)

localize11.0ms (0.2%)

rewrite86.0ms (1.9%)

series350.0ms (7.7%)

simplify78.0ms (1.7%)

prune244.0ms (5.4%)

localize13.0ms (0.3%)

rewrite98.0ms (2.2%)

series351.0ms (7.8%)

simplify84.0ms (1.9%)

prune421.0ms (9.3%)

localize15.0ms (0.3%)

rewrite118.0ms (2.6%)

series558.0ms (12.3%)

simplify124.0ms (2.7%)

prune207.0ms (4.6%)

regimes65.0ms (1.4%)

bsearch15.0ms (0.3%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample990.0ms (21.9%)

Profiling