Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
75%	12.5%	12.5%	5
75%	6.2%	18.8%	6
75%	3.1%	21.9%	7
75%	1.6%	23.5%	8
75%	0.8%	24.3%	9
75%	0.4%	24.6%	10
75%	0.2%	24.8%	11
75%	0.1%	24.9%	12
75%	0%	24.9%	13
75%	0%	25%	14

Compiler

Compiled 10 to 9 computations (10% saved)

sample11.0ms (0.3%)

Algorithm

1×

intervals

Results

6.0ms

256×

body

128

valid

Compiler

Compiled 19 to 18 computations (5.3% saved)

simplify177.0ms (4.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (14.0ms)

Iter	Nodes	Cost
0	279	13
1	279	13

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.1b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 2278821411449471/9007199254740992 (*.f64 x 1080863910568919/9007199254740992))
0.1b	(.f64 x (+.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992)))

rewrite15.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_1783`
4×	`add-log-exp_binary64_1798` `*-un-lft-identity_binary64_1762` `add-cube-cbrt_binary64_1794` `add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797` `pow1_binary64_1820`
3×	`associate-l_binary64_1705` `associate-r_binary64_1704`
2×	`flip3-+_binary64_1765` `flip-+_binary64_1736` `associate-*r/_binary64_1706`
1×	`pow-prod-down_binary64_1830` `prod-exp_binary64_1808` `unswap-sqr_binary64_1730` `+-commutative_binary64_1694` `cbrt-unprod_binary64_1792` `distribute-rgt-in_binary64_1714` `*-commutative_binary64_1695` `distribute-lft-in_binary64_1713` `sum-log_binary64_1850`

Counts

2 → 33

Calls

2 calls:

10.0ms	(.f64 x (+.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992)))
3.0ms	(+.f64 2278821411449471/9007199254740992 (*.f64 x 1080863910568919/9007199254740992))

series127.0ms (3.5%)

Counts

2 → 6

Calls

2 calls:

83.0ms	(.f64 x (+.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992)))
44.0ms	(+.f64 2278821411449471/9007199254740992 (*.f64 x 1080863910568919/9007199254740992))

simplify88.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4813	455
1	4813	455

prune49.0ms (1.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	32	7	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	32	8	40

Merged error: 0.0b

Counts

40 → 8

Compiler

Compiled 665 to 535 computations (19.5% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 x (/.f64 (-.f64 5193027025280559198049186179841/81129638414606681695789005144064 (.f64 x (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))) (-.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992))))
0.1b	(/.f64 (-.f64 5193027025280559198049186179841/81129638414606681695789005144064 (.f64 x (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))) (-.f64 2278821411449471/9007199254740992 (*.f64 x 1080863910568919/9007199254740992)))
0.1b	(.f64 x (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))
0.4b	(*.f64 x 1168266793170336129950248828561/81129638414606681695789005144064)

rewrite40.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_1783`
23×	`*-un-lft-identity_binary64_1762` `add-cube-cbrt_binary64_1794`
19×	`times-frac_binary64_1768` `associate-r_binary64_1704`
18×	`add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797`
13×	`pow1_binary64_1820`
9×	`associate-l_binary64_1705`
6×	`prod-exp_binary64_1808` `cbrt-unprod_binary64_1792`
5×	`pow-prod-down_binary64_1830`
4×	`associate-/r/_binary64_1710` `add-log-exp_binary64_1798`
3×	`flip3--_binary64_1766` `associate-/r_binary64_1708` `unswap-sqr_binary64_1730` `flip--_binary64_1737` `-commutative_binary64_1695` `associate-/l*_binary64_1709`
2×	`associate-/l/_binary64_1711` `div-inv_binary64_1759` `cbrt-undiv_binary64_1793` `div-exp_binary64_1810`
1×	`frac-2neg_binary64_1773` `div-sub_binary64_1767` `clear-num_binary64_1761` `associate-*r/_binary64_1706`

Counts

4 → 102

Calls

4 calls:

11.0ms	(.f64 x (/.f64 (-.f64 5193027025280559198049186179841/81129638414606681695789005144064 (.f64 x (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))) (-.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992))))
9.0ms	(/.f64 (-.f64 5193027025280559198049186179841/81129638414606681695789005144064 (.f64 x (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))) (-.f64 2278821411449471/9007199254740992 (*.f64 x 1080863910568919/9007199254740992)))
5.0ms	(.f64 x (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))
4.0ms	(*.f64 x 1168266793170336129950248828561/81129638414606681695789005144064)

series393.0ms (10.8%)

Counts

4 → 12

Calls

4 calls:

196.0ms	(.f64 x (/.f64 (-.f64 5193027025280559198049186179841/81129638414606681695789005144064 (.f64 x (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))) (-.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992))))
140.0ms	(/.f64 (-.f64 5193027025280559198049186179841/81129638414606681695789005144064 (.f64 x (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))) (-.f64 2278821411449471/9007199254740992 (*.f64 x 1080863910568919/9007199254740992)))
35.0ms	(.f64 x (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))
21.0ms	(*.f64 x 1168266793170336129950248828561/81129638414606681695789005144064)

simplify106.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4838	2071
1	4838	2071

prune161.0ms (4.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	113	9	122

Merged error: 0b

Counts

122 → 9

Compiler

Compiled 2845 to 2232 computations (21.5% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 2278821411449471/9007199254740992 (*.f64 x 1080863910568919/9007199254740992))
0.1b	(.f64 x (/.f64 (-.f64 5193027025280559198049186179841/81129638414606681695789005144064 (.f64 (.f64 x x) 1168266793170336129950248828561/81129638414606681695789005144064)) (-.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992))))
0.1b	(/.f64 (-.f64 5193027025280559198049186179841/81129638414606681695789005144064 (.f64 (.f64 x x) 1168266793170336129950248828561/81129638414606681695789005144064)) (-.f64 2278821411449471/9007199254740992 (*.f64 x 1080863910568919/9007199254740992)))
0.2b	(.f64 (.f64 x x) 1168266793170336129950248828561/81129638414606681695789005144064)

rewrite38.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64_1783`
21×	`*-un-lft-identity_binary64_1762` `add-cube-cbrt_binary64_1794`
19×	`times-frac_binary64_1768`
18×	`associate-r_binary64_1704`
16×	`add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797`
11×	`pow1_binary64_1820`
6×	`add-log-exp_binary64_1798`
5×	`prod-exp_binary64_1808` `cbrt-unprod_binary64_1792`
4×	`associate-/r/_binary64_1710` `flip3--_binary64_1766` `pow-prod-down_binary64_1830` `flip--_binary64_1737` `associate-l_binary64_1705`
3×	`associate-/r_binary64_1708` `unswap-sqr_binary64_1730` `associate-/l_binary64_1709`
2×	`associate-/l/_binary64_1711` `div-inv_binary64_1759` `cbrt-undiv_binary64_1793` `div-exp_binary64_1810` `*-commutative_binary64_1695`
1×	`frac-2neg_binary64_1773` `diff-log_binary64_1851` `div-sub_binary64_1767` `clear-num_binary64_1761` `associate-*r/_binary64_1706` `sub-neg_binary64_1755`

Counts

4 → 96

Calls

4 calls:

11.0ms	(.f64 x (/.f64 (-.f64 5193027025280559198049186179841/81129638414606681695789005144064 (.f64 (.f64 x x) 1168266793170336129950248828561/81129638414606681695789005144064)) (-.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992))))
7.0ms	(/.f64 (-.f64 5193027025280559198049186179841/81129638414606681695789005144064 (.f64 (.f64 x x) 1168266793170336129950248828561/81129638414606681695789005144064)) (-.f64 2278821411449471/9007199254740992 (*.f64 x 1080863910568919/9007199254740992)))
7.0ms	(.f64 (.f64 x x) 1168266793170336129950248828561/81129638414606681695789005144064)
3.0ms	(-.f64 2278821411449471/9007199254740992 (*.f64 x 1080863910568919/9007199254740992))

series413.0ms (11.4%)

Counts

4 → 12

Calls

4 calls:

191.0ms	(.f64 x (/.f64 (-.f64 5193027025280559198049186179841/81129638414606681695789005144064 (.f64 (.f64 x x) 1168266793170336129950248828561/81129638414606681695789005144064)) (-.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992))))
140.0ms	(/.f64 (-.f64 5193027025280559198049186179841/81129638414606681695789005144064 (.f64 (.f64 x x) 1168266793170336129950248828561/81129638414606681695789005144064)) (-.f64 2278821411449471/9007199254740992 (*.f64 x 1080863910568919/9007199254740992)))
46.0ms	(-.f64 2278821411449471/9007199254740992 (*.f64 x 1080863910568919/9007199254740992))
35.0ms	(.f64 (.f64 x x) 1168266793170336129950248828561/81129638414606681695789005144064)

simplify72.0ms (2%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4864	2109
1	4864	2109

prune143.0ms (3.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	108	9	117

Merged error: 0b

Counts

117 → 9

Compiler

Compiled 2720 to 2020 computations (25.7% saved)

localize18.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064)) (cbrt.f64 (*.f64 x 1168266793170336129950248828561/81129638414606681695789005144064)))
0.7b	(cbrt.f64 (*.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))
0.7b	(cbrt.f64 (*.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))
0.7b	(cbrt.f64 (*.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))

rewrite19.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`pow1_binary64_1820`
10×	`add-sqr-sqrt_binary64_1783`
9×	`pow1/3_binary64_1841`
8×	`*-un-lft-identity_binary64_1762` `add-cube-cbrt_binary64_1794`
7×	`cbrt-prod_binary64_1790`
6×	`add-exp-log_binary64_1797`
4×	`add-log-exp_binary64_1798` `swap-sqr_binary64_1729` `add-cbrt-cube_binary64_1795` `associate-l_binary64_1705` `associate-r_binary64_1704`
2×	`pow-sqr_binary64_1735` `pow-prod-down_binary64_1830` `pow-prod-up_binary64_1829`
1×	`prod-exp_binary64_1808` `pow-plus_binary64_1822` `unswap-sqr_binary64_1730` `cbrt-unprod_binary64_1792` `*-commutative_binary64_1695` `pow2_binary64_1840`

Counts

4 → 58

Calls

4 calls:

6.0ms	(.f64 (cbrt.f64 (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064)) (cbrt.f64 (*.f64 x 1168266793170336129950248828561/81129638414606681695789005144064)))
3.0ms	(cbrt.f64 (*.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))
3.0ms	(cbrt.f64 (*.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))
3.0ms	(cbrt.f64 (*.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))

series763.0ms (21%)

Counts

4 → 12

Calls

4 calls:

231.0ms	(.f64 (cbrt.f64 (.f64 x 1168266793170336129950248828561/81129638414606681695789005144064)) (cbrt.f64 (*.f64 x 1168266793170336129950248828561/81129638414606681695789005144064)))
186.0ms	(cbrt.f64 (*.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))
179.0ms	(cbrt.f64 (*.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))
166.0ms	(cbrt.f64 (*.f64 x 1168266793170336129950248828561/81129638414606681695789005144064))

simplify66.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4988	556
1	4988	556

prune107.0ms (3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	70	9	79

Merged error: 0b

Counts

79 → 9

Compiler

Compiled 2057 to 1626 computations (21% saved)

regimes118.0ms (3.3%)

Compiler: Compiled 1075 to 902 computations (16.1% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	76	16
1	76	16

end0.0ms (0%)

sample669.0ms (18.4%)

Algorithm

1×

intervals

Results

202.0ms	8000×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 350 to 294 computations (16% saved)

Details

analyze4.0ms (0.1%)

sample11.0ms (0.3%)

simplify177.0ms (4.9%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

rewrite15.0ms (0.4%)

series127.0ms (3.5%)

simplify88.0ms (2.4%)

prune49.0ms (1.3%)

localize11.0ms (0.3%)

rewrite40.0ms (1.1%)

series393.0ms (10.8%)

simplify106.0ms (2.9%)

prune161.0ms (4.4%)

localize14.0ms (0.4%)

rewrite38.0ms (1%)

series413.0ms (11.4%)

simplify72.0ms (2%)

prune143.0ms (3.9%)

localize18.0ms (0.5%)

rewrite19.0ms (0.5%)

series763.0ms (21%)

simplify66.0ms (1.8%)

prune107.0ms (3%)

regimes118.0ms (3.3%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample669.0ms (18.4%)

Profiling