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)

sample24.0ms (0.4%)

Algorithm

1×

intervals

Results

6.0ms	192×	body	128	valid
4.0ms	36×	body	1024	valid
4.0ms	256×	pre	128	true
2.0ms	18×	body	512	valid
1.0ms	9×	body	256	valid
0.0ms	1×	body	2048	valid

Compiler

Compiled 33 to 29 computations (12.1% saved)

simplify340.0ms (6.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (242.0ms)

Iter	Nodes	Cost
0	5018	19

prune6.0ms (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: 15.5b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
2.0b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64_1783`
26×	`add-sqr-sqrt_binary64_1805`
25×	`times-frac_binary64_1789`
19×	`distribute-lft-out_binary64_1734`
14×	`add-cube-cbrt_binary64_1818`
6×	`difference-of-squares_binary64_1752` `distribute-lft-out--_binary64_1735`
5×	`associate-/l_binary64_1728` `associate-/r_binary64_1727`
4×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `add-log-exp_binary64_1822`
2×	`div-sub_binary64_1788` `associate-/l/_binary64_1730` `associate-/r/_binary64_1729` `flip-+_binary64_1757` `flip3-+_binary64_1786` `pow1_binary64_1844`
1×	`flip3--_binary64_1787` `+-commutative_binary64_1713` `div-inv_binary64_1780` `associate-+l-_binary64_1718` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `sum-log_binary64_1874` `div-exp_binary64_1834` `clear-num_binary64_1782` `flip--_binary64_1758`

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))

series214.0ms (3.8%)

Counts

2 → 26

Calls

2 calls:

117.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
97.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 941 to 785 computations (16.6% saved)

simplify63.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5130	2178

prune112.0ms (2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	82	9	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	9	92

Merged error: 12.0b

Counts

92 → 9

Compiler

Compiled 2194 to 1326 computations (39.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(exp.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1))
0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2))
2.0b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1)
2.0b	(log.f64 (exp.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1)))

rewrite82.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`*-un-lft-identity_binary64_1783`
31×	`add-sqr-sqrt_binary64_1805`
25×	`times-frac_binary64_1789`
21×	`distribute-lft-out_binary64_1734`
19×	`add-cube-cbrt_binary64_1818`
9×	`add-log-exp_binary64_1822`
8×	`exp-prod_binary64_1835`
6×	`add-cbrt-cube_binary64_1819` `difference-of-squares_binary64_1752` `add-exp-log_binary64_1821` `distribute-lft-out--_binary64_1735`
5×	`log-pow_binary64_1872` `associate-/l_binary64_1728` `associate-/r_binary64_1727` `pow1_binary64_1844`
4×	`div-sub_binary64_1788` `log-prod_binary64_1869`
3×	`associate-+l-_binary64_1718`
2×	`exp-diff_binary64_1831` `associate-/l/_binary64_1730` `rem-exp-log_binary64_1823` `associate-/r/_binary64_1729` `exp-sum_binary64_1829` `flip-+_binary64_1757` `sum-log_binary64_1874` `flip3-+_binary64_1786`
1×	`flip3--_binary64_1787` `+-commutative_binary64_1713` `div-inv_binary64_1780` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `div-exp_binary64_1834` `clear-num_binary64_1782` `flip--_binary64_1758` `rem-log-exp_binary64_1824` `log-div_binary64_1870`

Counts

4 → 98

Calls

4 calls:

21.0ms	(exp.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1))
21.0ms	(log.f64 (exp.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1)))
19.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1)
11.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2))

series629.0ms (11.3%)

Counts

4 → 52

Calls

4 calls:

216.0ms	(exp.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1))
211.0ms	(log.f64 (exp.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1)))
108.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1)
94.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2))

Compiler

Compiled 2476 to 2068 computations (16.5% saved)

simplify83.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4953	4477
1	4953	4477

prune206.0ms (3.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	148	2	150
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	149	10	159

Merged error: 12.0b

Counts

159 → 10

Compiler

Compiled 4280 to 2746 computations (35.8% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 1 (+.f64 (+.f64 beta alpha) 2))
0.1b	(*.f64 (-.f64 beta alpha) (/.f64 1 (+.f64 (+.f64 beta alpha) 2)))
3.0b	(+.f64 (*.f64 (-.f64 beta alpha) (/.f64 1 (+.f64 (+.f64 beta alpha) 2))) 1)

rewrite52.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`*-un-lft-identity_binary64_1783`
32×	`add-sqr-sqrt_binary64_1805` `times-frac_binary64_1789`
23×	`add-cube-cbrt_binary64_1818`
21×	`distribute-lft-out_binary64_1734` `associate-r_binary64_1723`
16×	`add-exp-log_binary64_1821`
10×	`add-cbrt-cube_binary64_1819`
6×	`pow1_binary64_1844`
5×	`associate-/r_binary64_1727` `associate-l*_binary64_1724` `add-log-exp_binary64_1822`
4×	`associate-/r/_binary64_1729` `prod-exp_binary64_1832` `div-exp_binary64_1834`
3×	`associate-/l*_binary64_1728` `flip-+_binary64_1757` `flip3-+_binary64_1786` `unswap-sqr_binary64_1751`
2×	`flip3--_binary64_1787` `cbrt-unprod_binary64_1816` `1-exp_binary64_1827` `div-inv_binary64_1780` `associate-*l/_binary64_1726` `cbrt-undiv_binary64_1817` `frac-times_binary64_1793` `flip--_binary64_1758` `rec-exp_binary64_1833`
1×	`associate-r/_binary64_1725` `difference-of-squares_binary64_1752` `un-div-inv_binary64_1781` `+-commutative_binary64_1713` `inv-pow_binary64_1868` `pow-flip_binary64_1857` `distribute-lft-out--_binary64_1735` `-commutative_binary64_1714` `frac-2neg_binary64_1794` `sum-log_binary64_1874` `clear-num_binary64_1782` `pow-prod-down_binary64_1854`

Counts

3 → 102

Calls

3 calls:

18.0ms	(*.f64 (-.f64 beta alpha) (/.f64 1 (+.f64 (+.f64 beta alpha) 2)))
16.0ms	(+.f64 (*.f64 (-.f64 beta alpha) (/.f64 1 (+.f64 (+.f64 beta alpha) 2))) 1)
8.0ms	(/.f64 1 (+.f64 (+.f64 beta alpha) 2))

series294.0ms (5.3%)

Counts

3 → 41

Calls

3 calls:

121.0ms	(+.f64 (*.f64 (-.f64 beta alpha) (/.f64 1 (+.f64 (+.f64 beta alpha) 2))) 1)
95.0ms	(*.f64 (-.f64 beta alpha) (/.f64 1 (+.f64 (+.f64 beta alpha) 2)))
78.0ms	(/.f64 1 (+.f64 (+.f64 beta alpha) 2))

Compiler

Compiled 1429 to 1188 computations (16.9% saved)

simplify52.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5132	2690

prune158.0ms (2.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	142	1	143
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	143	10	153

Merged error: 12.0b

Counts

153 → 10

Compiler

Compiled 3256 to 2096 computations (35.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (+.f64 beta alpha) 2))) (/.f64 (-.f64 beta alpha) (sqrt.f64 (+.f64 (+.f64 beta alpha) 2))))
0.5b	(/.f64 (-.f64 beta alpha) (sqrt.f64 (+.f64 (+.f64 beta alpha) 2)))
0.6b	(/.f64 1 (sqrt.f64 (+.f64 (+.f64 beta alpha) 2)))
9.1b	(+.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (+.f64 beta alpha) 2))) (/.f64 (-.f64 beta alpha) (sqrt.f64 (+.f64 (+.f64 beta alpha) 2)))) 1)

rewrite132.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

206×	`*-un-lft-identity_binary64_1783`
156×	`add-sqr-sqrt_binary64_1805`
150×	`times-frac_binary64_1789`
101×	`sqrt-prod_binary64_1799`
76×	`add-cube-cbrt_binary64_1818`
54×	`distribute-lft-out_binary64_1734`
46×	`associate-r_binary64_1723`
32×	`add-exp-log_binary64_1821`
30×	`associate-l_binary64_1724`
20×	`add-cbrt-cube_binary64_1819`
17×	`difference-of-squares_binary64_1752` `distribute-lft-out--_binary64_1735`
16×	`associate-/r*_binary64_1727`
15×	`unswap-sqr_binary64_1751`
11×	`div-exp_binary64_1834`
8×	`associate-/r/_binary64_1729` `associate-/l*_binary64_1728` `prod-exp_binary64_1832` `sqrt-div_binary64_1800` `pow1_binary64_1844`
6×	`cbrt-undiv_binary64_1817` `add-log-exp_binary64_1822`
5×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
4×	`cbrt-unprod_binary64_1816` `div-inv_binary64_1780`
3×	`1-exp_binary64_1827` `pow-flip_binary64_1857` `rec-exp_binary64_1833`
2×	`associate-/l/_binary64_1730` `frac-2neg_binary64_1794` `clear-num_binary64_1782`
1×	`flip3--_binary64_1787` `div-sub_binary64_1788` `associate-r/_binary64_1725` `+-commutative_binary64_1713` `inv-pow_binary64_1868` `pow1/2_binary64_1863` `associate-l/_binary64_1726` `*-commutative_binary64_1714` `sum-log_binary64_1874` `frac-times_binary64_1793` `sqrt-pow1_binary64_1801` `pow-prod-down_binary64_1854` `flip--_binary64_1758`

Counts

4 → 251

Calls

4 calls:

53.0ms	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (+.f64 beta alpha) 2))) (/.f64 (-.f64 beta alpha) (sqrt.f64 (+.f64 (+.f64 beta alpha) 2))))
25.0ms	(+.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (+.f64 beta alpha) 2))) (/.f64 (-.f64 beta alpha) (sqrt.f64 (+.f64 (+.f64 beta alpha) 2)))) 1)
13.0ms	(/.f64 (-.f64 beta alpha) (sqrt.f64 (+.f64 (+.f64 beta alpha) 2)))
9.0ms	(/.f64 1 (sqrt.f64 (+.f64 (+.f64 beta alpha) 2)))

series459.0ms (8.2%)

Counts

4 → 50

Calls

4 calls:

149.0ms	(/.f64 (-.f64 beta alpha) (sqrt.f64 (+.f64 (+.f64 beta alpha) 2)))
118.0ms	(+.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (+.f64 beta alpha) 2))) (/.f64 (-.f64 beta alpha) (sqrt.f64 (+.f64 (+.f64 beta alpha) 2)))) 1)
100.0ms	(/.f64 1 (sqrt.f64 (+.f64 (+.f64 beta alpha) 2)))
91.0ms	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (+.f64 beta alpha) 2))) (/.f64 (-.f64 beta alpha) (sqrt.f64 (+.f64 (+.f64 beta alpha) 2))))

Compiler

Compiled 2297 to 1920 computations (16.4% saved)

simplify125.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

301 → 301

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4961	8110
1	4961	8110

prune497.0ms (8.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	298	3	301
Fresh	3	4	7
Picked	1	0	1
Done	0	2	2
Total	302	9	311

Merged error: 12.0b

Counts

311 → 9

Compiler

Compiled 9358 to 5739 computations (38.7% saved)

regimes423.0ms (7.6%)

Compiler: Compiled 4936 to 3688 computations (25.3% saved)

bsearch2.0ms (0%)

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

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	75
1	50	75

end0.0ms (0%)

sample1.5s (27.5%)

Algorithm

1×

intervals

Results

204.0ms	5971×	body	128	valid
143.0ms	8000×	pre	128	true
123.0ms	985×	body	1024	valid
57.0ms	612×	body	512	valid
21.0ms	328×	body	256	valid
16.0ms	104×	body	2048	valid

Compiler

Compiled 1015 to 751 computations (26% saved)

Details

analyze3.0ms (0.1%)

sample24.0ms (0.4%)

simplify340.0ms (6.1%)

prune6.0ms (0.1%)

localize8.0ms (0.1%)

rewrite36.0ms (0.6%)

series214.0ms (3.8%)

simplify63.0ms (1.1%)

prune112.0ms (2%)

localize14.0ms (0.2%)

rewrite82.0ms (1.5%)

series629.0ms (11.3%)

simplify83.0ms (1.5%)

prune206.0ms (3.7%)

localize9.0ms (0.2%)

rewrite52.0ms (0.9%)

series294.0ms (5.3%)

simplify52.0ms (0.9%)

prune158.0ms (2.8%)

localize12.0ms (0.2%)

rewrite132.0ms (2.4%)

series459.0ms (8.2%)

simplify125.0ms (2.3%)

prune497.0ms (8.9%)

regimes423.0ms (7.6%)

bsearch2.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.5s (27.5%)

Profiling