Details

analyze9.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
0%	12.5%	87.5%	2
0%	6.3%	93.7%	3
0%	3.1%	96.9%	4
0%	1.6%	98.4%	5
0%	0.8%	99.2%	6
0%	0.4%	99.6%	7
0%	0.2%	99.8%	8
0.1%	0.1%	99.8%	9
0.1%	0%	99.9%	10
0.1%	0%	99.9%	11
0.1%	0%	99.9%	12
0.1%	0%	99.9%	13
0.1%	0%	99.9%	14

Compiler

Compiled 106 to 71 computations (33% saved)

sample70.0ms (0.6%)

Algorithm

1×

intervals

Results

54.0ms	256×	body	128	valid
3.0ms	264×	pre	128	true
2.0ms	8×	body	128	invalid

Compiler

Compiled 209 to 141 computations (32.5% saved)

simplify270.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (114.0ms)

Iter	Nodes	Cost
0	4937	55
1	4937	55

prune12.0ms (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: 2.6b

Counts

2 → 2

Compiler

Compiled 171 to 121 computations (29.2% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64))
0.4b	(*.f64 (/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
1.0b	(sqrt.f64 PI.f64)
2.6b	(exp.f64 (pow.f64 (fabs.f64 x) 2))

rewrite114.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64_1762`
45×	`add-sqr-sqrt_binary64_1783`
42×	`times-frac_binary64_1768`
36×	`add-cube-cbrt_binary64_1794`
25×	`sqrt-prod_binary64_1777`
22×	`associate-l_binary64_1705`
18×	`frac-add_binary64_1770`
12×	`distribute-lft-out_binary64_1715`
11×	`add-cbrt-cube_binary64_1795`
9×	`add-exp-log_binary64_1797`
8×	`exp-prod_binary64_1811` `associate-r_binary64_1704`
7×	`frac-times_binary64_1772` `associate-*r/_binary64_1706` `pow1_binary64_1820`
6×	`flip3-+_binary64_1765` `associate-/r*_binary64_1708` `flip-+_binary64_1736`
5×	`add-log-exp_binary64_1798`
3×	`div-inv_binary64_1759` `unswap-sqr_binary64_1730` `associate-/l*_binary64_1709` `unpow-prod-down_binary64_1838`
2×	`prod-exp_binary64_1808` `cbrt-undiv_binary64_1793` `div-exp_binary64_1810` `cbrt-unprod_binary64_1792`
1×	`rem-sqrt-square_binary64_1775` `frac-2neg_binary64_1773` `sqr-pow_binary64_1734` `pow-prod-down_binary64_1830` `unpow2_binary64_1824` `clear-num_binary64_1761` `rem-exp-log_binary64_1799` `associate-l/_binary64_1707` `distribute-rgt-in_binary64_1714` `sqrt-pow1_binary64_1779` `-commutative_binary64_1695` `distribute-lft-in_binary64_1713` `pow1/2_binary64_1839`

Counts

4 → 131

Calls

4 calls:

80.0ms	(*.f64 (/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
8.0ms	(/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64))
4.0ms	(exp.f64 (pow.f64 (fabs.f64 x) 2))
1.0ms	(sqrt.f64 PI.f64)

series1.1s (9.7%)

Counts

4 → 10

Calls

4 calls:

930.0ms	(*.f64 (/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
137.0ms	(/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64))
67.0ms	(exp.f64 (pow.f64 (fabs.f64 x) 2))
0.0ms	(sqrt.f64 PI.f64)

simplify100.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5038	6082

prune476.0ms (4.1%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	120	21	141
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	122	21	143

Merged error: 0.7b

Counts

143 → 21

Compiler

Compiled 8004 to 5280 computations (34% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64))
0.4b	(*.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
1.0b	(sqrt.f64 PI.f64)
1.1b	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

rewrite129.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

94×	`times-frac_binary64_1768`
86×	`*-un-lft-identity_binary64_1762`
85×	`add-sqr-sqrt_binary64_1783`
66×	`add-cube-cbrt_binary64_1794`
51×	`sqrt-prod_binary64_1777`
46×	`associate-l_binary64_1705`
44×	`unpow-prod-down_binary64_1838`
18×	`frac-add_binary64_1770`
17×	`add-exp-log_binary64_1797`
16×	`sqr-pow_binary64_1734`
12×	`distribute-lft-out_binary64_1715`
11×	`add-cbrt-cube_binary64_1795`
8×	`pow1_binary64_1820` `associate-r_binary64_1704`
7×	`frac-times_binary64_1772` `unswap-sqr_binary64_1730` `associate-r/_binary64_1706` `associate-/l_binary64_1709`
6×	`flip3-+_binary64_1765` `associate-/r*_binary64_1708` `flip-+_binary64_1736` `div-exp_binary64_1810`
4×	`prod-exp_binary64_1808` `add-log-exp_binary64_1798` `pow-pow_binary64_1831`
3×	`exp-prod_binary64_1811` `div-inv_binary64_1759` `pow-exp_binary64_1827` `pow-to-exp_binary64_1828` `pow-unpow_binary64_1836`
2×	`cbrt-undiv_binary64_1793` `cbrt-unprod_binary64_1792`
1×	`rem-sqrt-square_binary64_1775` `frac-2neg_binary64_1773` `pow-prod-down_binary64_1830` `clear-num_binary64_1761` `associate-l/_binary64_1707` `distribute-rgt-in_binary64_1714` `sqrt-pow1_binary64_1779` `-commutative_binary64_1695` `distribute-lft-in_binary64_1713` `pow1/2_binary64_1839`

Counts

4 → 195

Calls

4 calls:

83.0ms	(*.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
7.0ms	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64))
4.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
1.0ms	(sqrt.f64 PI.f64)

series1.7s (14.1%)

Counts

4 → 10

Calls

4 calls:

1.1s	(*.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
309.0ms	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64))
224.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
0.0ms	(sqrt.f64 PI.f64)

simplify116.0ms (1%)

Algorithm

1×	egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5402	9553

prune610.0ms (5.2%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	181	24	205
Fresh	15	5	20
Picked	1	0	1
Done	0	0	0
Total	197	29	226

Merged error: 0.2b

Counts

226 → 29

Compiler

Compiled 11960 to 6241 computations (47.8% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 15/8 (pow.f64 (fabs.f64 x) 7))
0.3b	(/.f64 1/2 (pow.f64 (fabs.f64 x) 3))
0.4b	(*.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
1.1b	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

rewrite115.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

71×	`*-un-lft-identity_binary64_1762`
61×	`times-frac_binary64_1768`
56×	`add-sqr-sqrt_binary64_1783`
51×	`add-cube-cbrt_binary64_1794`
31×	`unpow-prod-down_binary64_1838`
19×	`associate-/r*_binary64_1708`
18×	`add-exp-log_binary64_1797`
12×	`cube-prod_binary64_1787` `distribute-lft-out_binary64_1715`
11×	`sqr-pow_binary64_1734`
10×	`add-cbrt-cube_binary64_1795`
9×	`frac-add_binary64_1770`
8×	`associate-r_binary64_1704`
7×	`associate-r/_binary64_1706` `associate-l*_binary64_1705`
6×	`div-exp_binary64_1810` `associate-/l*_binary64_1709`
5×	`pow1_binary64_1820`
4×	`cube-mult_binary64_1789` `unpow3_binary64_1825` `pow-exp_binary64_1827` `add-log-exp_binary64_1798` `pow-pow_binary64_1831` `pow-to-exp_binary64_1828`
3×	`exp-prod_binary64_1811` `prod-exp_binary64_1808` `flip3-+_binary64_1765` `flip-+_binary64_1736` `div-inv_binary64_1759` `unswap-sqr_binary64_1730` `pow-unpow_binary64_1836`
2×	`frac-2neg_binary64_1773` `clear-num_binary64_1761` `cbrt-undiv_binary64_1793`
1×	`cbrt-unprod_binary64_1792` `distribute-rgt-in_binary64_1714` `*-commutative_binary64_1695` `distribute-lft-in_binary64_1713`

Counts

4 → 169

Calls

4 calls:

73.0ms	(*.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
6.0ms	(/.f64 1/2 (pow.f64 (fabs.f64 x) 3))
5.0ms	(/.f64 15/8 (pow.f64 (fabs.f64 x) 7))
4.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

series1.4s (12.3%)

Counts

4 → 12

Calls

4 calls:

944.0ms	(*.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
215.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
173.0ms	(/.f64 15/8 (pow.f64 (fabs.f64 x) 7))
113.0ms	(/.f64 1/2 (pow.f64 (fabs.f64 x) 3))

simplify79.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5005	4631

prune590.0ms (5%)

Pruning

29 alts after pruning (28 fresh and 1 done)

	Pruned	Kept	Total
New	175	6	181
Fresh	6	22	28
Picked	0	1	1
Done	0	0	0
Total	181	29	210

Merged error: 0.1b

Counts

210 → 29

Compiler

Compiled 10158 to 6178 computations (39.2% saved)

localize37.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64))
0.7b	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
0.7b	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
1.0b	(sqrt.f64 PI.f64)

rewrite44.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`times-frac_binary64_1768`
54×	`add-sqr-sqrt_binary64_1783`
53×	`*-un-lft-identity_binary64_1762` `add-cube-cbrt_binary64_1794`
27×	`sqrt-prod_binary64_1777` `unpow-prod-down_binary64_1838`
26×	`pow-unpow_binary64_1836`
9×	`sqr-pow_binary64_1734`
8×	`pow-pow_binary64_1831` `add-exp-log_binary64_1797`
7×	`associate-/l*_binary64_1709` `pow1_binary64_1820`
6×	`exp-prod_binary64_1811` `associate-/r*_binary64_1708` `add-cbrt-cube_binary64_1795`
4×	`add-log-exp_binary64_1798`
3×	`div-inv_binary64_1759` `pow-exp_binary64_1827` `div-exp_binary64_1810` `pow-to-exp_binary64_1828`
1×	`rem-sqrt-square_binary64_1775` `frac-2neg_binary64_1773` `clear-num_binary64_1761` `cbrt-undiv_binary64_1793` `sqrt-pow1_binary64_1779` `pow1/2_binary64_1839`

Counts

4 → 142

Calls

4 calls:

7.0ms	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64))
5.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
5.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
2.0ms	(sqrt.f64 PI.f64)

series806.0ms (6.9%)

Counts

4 → 10

Calls

4 calls:

312.0ms	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64))
251.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
242.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
0.0ms	(sqrt.f64 PI.f64)

simplify67.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5330	3547

prune413.0ms (3.5%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	142	10	152
Fresh	9	18	27
Picked	1	0	1
Done	1	0	1
Total	153	28	181

Merged error: 0.1b

Counts

181 → 28

Compiler

Compiled 8398 to 4466 computations (46.8% saved)

regimes237.0ms (2%)

Compiler: Compiled 3440 to 2182 computations (36.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	85
1	38	85

end0.0ms (0%)

sample3.1s (26.5%)

Algorithm

1×

intervals

Results

1.6s	8000×	body	128	valid
102.0ms	8128×	pre	128	true
27.0ms	128×	body	128	invalid

Compiler

Compiled 1874 to 1193 computations (36.3% saved)

Details

analyze9.0ms (0.1%)

sample70.0ms (0.6%)

simplify270.0ms (2.3%)

prune12.0ms (0.1%)

localize26.0ms (0.2%)

rewrite114.0ms (1%)

series1.1s (9.7%)

simplify100.0ms (0.9%)

prune476.0ms (4.1%)

localize29.0ms (0.2%)

rewrite129.0ms (1.1%)

series1.7s (14.1%)

simplify116.0ms (1%)

prune610.0ms (5.2%)

localize30.0ms (0.3%)

rewrite115.0ms (1%)

series1.4s (12.3%)

simplify79.0ms (0.7%)

prune590.0ms (5%)

localize37.0ms (0.3%)

rewrite44.0ms (0.4%)

series806.0ms (6.9%)

simplify67.0ms (0.6%)

prune413.0ms (3.5%)

regimes237.0ms (2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.1s (26.5%)

Profiling