Details

analyze9.0ms (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
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50.4%	0.4%	49.2%	10
50.4%	0.2%	49.4%	11
50.4%	0.1%	49.5%	12
50.4%	0%	49.6%	13
50.4%	0%	49.6%	14

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample110.0ms (1.8%)

Algorithm

1×

intervals

Results

83.0ms	139×	body	2048	valid
14.0ms	59×	body	1024	valid
5.0ms	30×	body	512	valid
1.0ms	14×	body	256	valid
1.0ms	14×	body	128	valid

Compiler

Compiled 17 to 16 computations (5.9% saved)

simplify242.0ms (4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5087	13

prune2.0ms (0%)

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: 28.0b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (exp.f64 x) 2)
4.0b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-log-exp_binary64_1798` `*-un-lft-identity_binary64_1762`
4×	`frac-add_binary64_1770` `add-sqr-sqrt_binary64_1783`
3×	`flip3--_binary64_1766` `flip--_binary64_1737`
2×	`diff-log_binary64_1851` `exp-neg_binary64_1806` `neg-sub0_binary64_1757` `distribute-lft-out--_binary64_1716` `exp-diff_binary64_1807` `sub-neg_binary64_1755` `distribute-lft-out_binary64_1715` `add-cube-cbrt_binary64_1794` `add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797` `pow1_binary64_1820` `sum-log_binary64_1850`
1×	`flip3-+_binary64_1765` `flip-+_binary64_1736` `+-commutative_binary64_1694` `difference-of-squares_binary64_1731` `associate-+l-_binary64_1699` `associate-+l+_binary64_1697`

Counts

2 → 33

Calls

2 calls:

9.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
4.0ms	(-.f64 (exp.f64 x) 2)

series70.0ms (1.1%)

Counts

2 → 6

Calls

2 calls:

56.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
15.0ms	(-.f64 (exp.f64 x) 2)

simplify86.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4859	627
1	4859	627

prune49.0ms (0.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	36	3	39
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	37	3	40

Merged error: 0.0b

Counts

40 → 3

Compiler

Compiled 592 to 320 computations (45.9% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x x) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4))))
0.0b	(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/12 (pow.f64 x 4)))
0.0b	(*.f64 1/360 (pow.f64 x 6))
0.1b	(*.f64 1/12 (pow.f64 x 4))

rewrite35.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_1783`
14×	`add-exp-log_binary64_1797` `associate-r_binary64_1704`
11×	`add-log-exp_binary64_1798`
10×	`*-un-lft-identity_binary64_1762` `add-cube-cbrt_binary64_1794`
8×	`add-cbrt-cube_binary64_1795` `unpow-prod-down_binary64_1838`
6×	`prod-exp_binary64_1808` `unswap-sqr_binary64_1730` `associate-l_binary64_1705`
4×	`sqr-pow_binary64_1734` `pow1_binary64_1820` `sum-log_binary64_1850`
2×	`flip3-+_binary64_1765` `flip-+_binary64_1736` `+-commutative_binary64_1694` `pow-exp_binary64_1827` `cbrt-unprod_binary64_1792` `*-commutative_binary64_1695` `pow-to-exp_binary64_1828`
1×	`associate-+r+_binary64_1696`

Counts

4 → 74

Calls

4 calls:

9.0ms	(+.f64 (.f64 x x) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4))))
6.0ms	(*.f64 1/12 (pow.f64 x 4))
6.0ms	(*.f64 1/360 (pow.f64 x 6))
6.0ms	(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/12 (pow.f64 x 4)))

series363.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

192.0ms	(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/12 (pow.f64 x 4)))
63.0ms	(*.f64 1/360 (pow.f64 x 6))
56.0ms	(+.f64 (.f64 x x) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4))))
52.0ms	(*.f64 1/12 (pow.f64 x 4))

simplify72.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4895	1259
1	4895	1259

prune98.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	85	4	89

Merged error: 0.0b

Counts

89 → 4

Compiler

Compiled 1786 to 1258 computations (29.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 1/360 (pow.f64 x 6))
0.1b	(*.f64 1/12 (pow.f64 x 4))
0.1b	(pow.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))) 3)
18.7b	(cbrt.f64 (pow.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))) 3))

rewrite40.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64_1783`
16×	`*-un-lft-identity_binary64_1762` `add-cube-cbrt_binary64_1794`
15×	`add-exp-log_binary64_1797`
14×	`unpow-prod-down_binary64_1838` `associate-r_binary64_1704`
12×	`cbrt-prod_binary64_1790`
9×	`add-cbrt-cube_binary64_1795`
6×	`cube-prod_binary64_1787` `sqr-pow_binary64_1734` `prod-exp_binary64_1808` `unswap-sqr_binary64_1730` `associate-l_binary64_1705`
5×	`pow1_binary64_1820`
4×	`cube-div_binary64_1788` `add-log-exp_binary64_1798`
3×	`pow-exp_binary64_1827` `pow-to-exp_binary64_1828` `pow-unpow_binary64_1836`
2×	`cube-mult_binary64_1789` `flip3-+_binary64_1765` `flip-+_binary64_1736` `unpow3_binary64_1825` `cbrt-unprod_binary64_1792` `*-commutative_binary64_1695` `cbrt-div_binary64_1791`
1×	`rem-cube-cbrt_binary64_1784` `pow1/3_binary64_1841` `pow-pow_binary64_1831` `rem-cbrt-cube_binary64_1785`

Counts

4 → 98

Calls

4 calls:

9.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))) 3))
9.0ms	(pow.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))) 3)
6.0ms	(*.f64 1/360 (pow.f64 x 6))
6.0ms	(*.f64 1/12 (pow.f64 x 4))

series251.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

69.0ms	(pow.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))) 3)
67.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))) 3))
62.0ms	(*.f64 1/360 (pow.f64 x 6))
53.0ms	(*.f64 1/12 (pow.f64 x 4))

simplify70.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4928	2300
1	4928	2300

prune154.0ms (2.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	110	4	114

Merged error: 0.0b

Counts

114 → 4

Compiler

Compiled 2750 to 2023 computations (26.4% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 4 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) (+.f64 -6 (pow.f64 (exp.f64 x) 3))))) (.f64 (exp.f64 x) (+.f64 4 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2)))))
0.0b	(.f64 (exp.f64 x) (+.f64 4 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2))))
0.0b	(pow.f64 (exp.f64 x) 3)
4.2b	(+.f64 4 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) (+.f64 -6 (pow.f64 (exp.f64 x) 3)))))

rewrite40.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_1783`
12×	`*-un-lft-identity_binary64_1762` `add-cube-cbrt_binary64_1794` `add-cbrt-cube_binary64_1795`
9×	`add-exp-log_binary64_1797`
7×	`pow1_binary64_1820`
6×	`add-log-exp_binary64_1798`
4×	`flip3-+_binary64_1765` `flip-+_binary64_1736` `associate-*r/_binary64_1706` `pow-pow_binary64_1831`
3×	`cube-prod_binary64_1787` `exp-prod_binary64_1811` `times-frac_binary64_1768` `associate-/l_binary64_1709` `pow-unpow_binary64_1836` `associate-l_binary64_1705` `unpow-prod-down_binary64_1838` `associate-r*_binary64_1704`
2×	`associate-/r/_binary64_1710` `associate-/l/_binary64_1711` `prod-exp_binary64_1808` `cbrt-undiv_binary64_1793` `div-exp_binary64_1810` `cbrt-unprod_binary64_1792` `distribute-rgt-in_binary64_1714` `distribute-lft-in_binary64_1713` `associate-+r+_binary64_1696`
1×	`frac-2neg_binary64_1773` `cube-mult_binary64_1789` `rem-cube-cbrt_binary64_1784` `sqr-pow_binary64_1734` `pow-prod-down_binary64_1830` `clear-num_binary64_1761` `associate-/r_binary64_1708` `div-inv_binary64_1759` `unpow3_binary64_1825` `unswap-sqr_binary64_1730` `+-commutative_binary64_1694` `pow-exp_binary64_1827` `-commutative_binary64_1695` `pow-to-exp_binary64_1828` `sum-log_binary64_1850`

Counts

4 → 86

Calls

4 calls:

11.0ms	(/.f64 (+.f64 4 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) (+.f64 -6 (pow.f64 (exp.f64 x) 3))))) (.f64 (exp.f64 x) (+.f64 4 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2)))))
7.0ms	(.f64 (exp.f64 x) (+.f64 4 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2))))
4.0ms	(+.f64 4 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) (+.f64 -6 (pow.f64 (exp.f64 x) 3)))))
4.0ms	(pow.f64 (exp.f64 x) 3)

series727.0ms (11.9%)

Counts

4 → 12

Calls

4 calls:

475.0ms	(/.f64 (+.f64 4 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) (+.f64 -6 (pow.f64 (exp.f64 x) 3))))) (.f64 (exp.f64 x) (+.f64 4 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2)))))
135.0ms	(+.f64 4 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) (+.f64 -6 (pow.f64 (exp.f64 x) 3)))))
80.0ms	(.f64 (exp.f64 x) (+.f64 4 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2))))
37.0ms	(pow.f64 (exp.f64 x) 3)

simplify73.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5096	2508

prune146.0ms (2.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	98	4	102

Merged error: 0.0b

Counts

102 → 4

Compiler

Compiled 3348 to 1951 computations (41.7% saved)

regimes17.0ms (0.3%)

Compiler: Compiled 109 to 78 computations (28.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	22
1	17	22

end0.0ms (0%)

sample3.4s (55.6%)

Algorithm

1×

intervals

Results

2.4s	4246×	body	2048	valid
469.0ms	1884×	body	1024	valid
140.0ms	1006×	body	512	valid
46.0ms	493×	body	256	valid
17.0ms	371×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 139 to 105 computations (24.5% saved)

Details

analyze9.0ms (0.1%)

sample110.0ms (1.8%)

simplify242.0ms (4%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite17.0ms (0.3%)

series70.0ms (1.1%)

simplify86.0ms (1.4%)

prune49.0ms (0.8%)

localize9.0ms (0.2%)

rewrite35.0ms (0.6%)

series363.0ms (5.9%)

simplify72.0ms (1.2%)

prune98.0ms (1.6%)

localize12.0ms (0.2%)

rewrite40.0ms (0.7%)

series251.0ms (4.1%)

simplify70.0ms (1.1%)

prune154.0ms (2.5%)

localize14.0ms (0.2%)

rewrite40.0ms (0.6%)

series727.0ms (11.9%)

simplify73.0ms (1.2%)

prune146.0ms (2.4%)

regimes17.0ms (0.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.4s (55.6%)

Profiling