Details

analyze65.0ms (1.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
40.6%	59.3%	0.1%	6
53.1%	45.3%	1.7%	7
64%	31.2%	4.8%	8
70.2%	21.9%	7.9%	9
75.7%	15.2%	9.1%	10
78.8%	10.5%	10.6%	11
81.6%	7.5%	10.9%	12
83.1%	5.2%	11.7%	13
84.5%	3.7%	11.8%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample13.0ms (0.3%)

Algorithm

1×

intervals

Results

5.0ms	256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 15 to 13 computations (13.3% saved)

simplify102.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	45	10
1	45	10

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

Error

0.0b

Counts

2 → 1

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize5.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 (*.f64 x y) x) y)
0.0b	(+.f64 (*.f64 x y) x)
0.0b	(+.f64 (*.f64 x y) x)
0.0b	(+.f64 (+.f64 (*.f64 x y) x) y)

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-log-exp_binary64_1822`
4×	`*-un-lft-identity_binary64_1783` `sum-log_binary64_1874`
2×	`add-cbrt-cube_binary64_1819` `+-commutative_binary64_1713` `add-sqr-sqrt_binary64_1805` `add-exp-log_binary64_1821` `add-cube-cbrt_binary64_1818` `flip-+_binary64_1757` `flip3-+_binary64_1786` `pow1_binary64_1844`
1×	`distribute-lft-out_binary64_1734` `associate-+l+_binary64_1716`

Counts

2 → 25

Calls

4 calls:

8.0ms	(+.f64 (+.f64 (*.f64 x y) x) y)
5.0ms	(+.f64 (*.f64 x y) x)
0.0ms	(+.f64 (*.f64 x y) x)
0.0ms	(+.f64 (+.f64 (*.f64 x y) x) y)

series115.0ms (2.8%)

Counts

2 → 21

Calls

2 calls:

67.0ms	(+.f64 (+.f64 (*.f64 x y) x) y)
47.0ms	(+.f64 (*.f64 x y) x)

Compiler

Compiled 203 to 161 computations (20.7% saved)

simplify45.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4983	484
1	4983	484

prune30.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	43	3	46
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	43	4	47

Error

Counts

47 → 4

Compiler

Compiled 500 to 118 computations (76.4% saved)

localize12.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 y (+.f64 x (*.f64 x y)))
0.0b	(+.f64 x (*.f64 x y))
0.0b	(+.f64 x (*.f64 x y))
0.0b	(+.f64 x (*.f64 x y))
0.6b	(.f64 (cbrt.f64 (+.f64 y (+.f64 x (.f64 x y)))) (cbrt.f64 (+.f64 y (+.f64 x (*.f64 x y)))))
0.6b	(cbrt.f64 (+.f64 y (+.f64 x (*.f64 x y))))
0.6b	(cbrt.f64 (+.f64 y (+.f64 x (*.f64 x y))))
0.6b	(cbrt.f64 (+.f64 y (+.f64 x (*.f64 x y))))

rewrite42.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`cbrt-prod_binary64_1814`
35×	`*-un-lft-identity_binary64_1783`
23×	`add-sqr-sqrt_binary64_1805`
18×	`cbrt-div_binary64_1815`
15×	`add-cube-cbrt_binary64_1818`
11×	`pow1_binary64_1844`
9×	`swap-sqr_binary64_1750` `distribute-lft-out_binary64_1734` `flip-+_binary64_1757` `flip3-+_binary64_1786` `pow1/3_binary64_1865`
7×	`associate-l_binary64_1724` `associate-r_binary64_1723`
6×	`add-exp-log_binary64_1821`
4×	`add-cbrt-cube_binary64_1819` `frac-times_binary64_1793` `unswap-sqr_binary64_1751` `add-log-exp_binary64_1822`
2×	`associate-r/_binary64_1725` `pow-prod-up_binary64_1853` `associate-l/_binary64_1726` `pow-sqr_binary64_1756` `pow-prod-down_binary64_1854`
1×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `pow-plus_binary64_1846` `*-commutative_binary64_1714` `pow2_binary64_1864`

Counts

4 → 95

Calls

8 calls:

16.0ms	(.f64 (cbrt.f64 (+.f64 y (+.f64 x (.f64 x y)))) (cbrt.f64 (+.f64 y (+.f64 x (*.f64 x y)))))
5.0ms	(cbrt.f64 (+.f64 y (+.f64 x (*.f64 x y))))
5.0ms	(cbrt.f64 (+.f64 y (+.f64 x (*.f64 x y))))
5.0ms	(cbrt.f64 (+.f64 y (+.f64 x (*.f64 x y))))
0.0ms	(+.f64 x (*.f64 x y))

series1.3s (31.8%)

Counts

4 → 72

Calls

4 calls:

552.0ms	(.f64 (cbrt.f64 (+.f64 y (+.f64 x (.f64 x y)))) (cbrt.f64 (+.f64 y (+.f64 x (*.f64 x y)))))
258.0ms	(cbrt.f64 (+.f64 y (+.f64 x (*.f64 x y))))
252.0ms	(cbrt.f64 (+.f64 y (+.f64 x (*.f64 x y))))
247.0ms	(cbrt.f64 (+.f64 y (+.f64 x (*.f64 x y))))

Compiler

Compiled 6704 to 5092 computations (24% saved)

simplify104.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5002	7189

prune268.0ms (6.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	167	4	171

Error

Counts

171 → 4

Compiler

Compiled 7478 to 2716 computations (63.7% saved)

localize11.0ms (0.3%)

Local error

Found 8 expressions with local error:

1.7b	(.f64 x (-.f64 (.f64 x (*.f64 y y)) x))
0.0b	(-.f64 (*.f64 x y) x)
0.0b	(-.f64 (.f64 x (.f64 y y)) x)
0.0b	(+.f64 (/.f64 (.f64 x (-.f64 (.f64 x (.f64 y y)) x)) (-.f64 (.f64 x y) x)) y)
0.0b	(-.f64 (*.f64 x y) x)
1.7b	(.f64 x (-.f64 (.f64 x (*.f64 y y)) x))
10.1b	(.f64 x (.f64 y y))
27.8b	(/.f64 (.f64 x (-.f64 (.f64 x (.f64 y y)) x)) (-.f64 (.f64 x y) x))

rewrite49.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
15×	`add-sqr-sqrt_binary64_1805`
12×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
11×	`pow1_binary64_1844`
9×	`cancel-sign-sub-inv_binary64_1749`
6×	`associate-l_binary64_1724` `add-log-exp_binary64_1822`
5×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832`
4×	`flip3--_binary64_1787` `associate-r/_binary64_1725` `distribute-lft-in_binary64_1732` `distribute-rgt-in_binary64_1733` `pow-prod-down_binary64_1854` `flip--_binary64_1758` `associate-r*_binary64_1723`
3×	`associate-/r*_binary64_1727` `times-frac_binary64_1789` `sub-neg_binary64_1776`
2×	`associate-/l/_binary64_1730` `associate-/r/_binary64_1729` `cbrt-undiv_binary64_1817` `*-commutative_binary64_1714` `div-exp_binary64_1834` `unswap-sqr_binary64_1751`
1×	`associate-/l*_binary64_1728` `div-inv_binary64_1780` `diff-log_binary64_1875` `frac-2neg_binary64_1794` `clear-num_binary64_1782`

Counts

4 → 86

Calls

8 calls:

16.0ms	(/.f64 (.f64 x (-.f64 (.f64 x (.f64 y y)) x)) (-.f64 (.f64 x y) x))
11.0ms	(.f64 x (-.f64 (.f64 x (*.f64 y y)) x))
7.0ms	(.f64 x (.f64 y y))
5.0ms	(-.f64 (*.f64 x y) x)
0.0ms	(+.f64 (/.f64 (.f64 x (-.f64 (.f64 x (.f64 y y)) x)) (-.f64 (.f64 x y) x)) y)

series419.0ms (10.2%)

Counts

4 → 33

Calls

4 calls:

193.0ms	(/.f64 (.f64 x (-.f64 (.f64 x (.f64 y y)) x)) (-.f64 (.f64 x y) x))
117.0ms	(.f64 x (-.f64 (.f64 x (*.f64 y y)) x))
55.0ms	(-.f64 (*.f64 x y) x)
53.0ms	(.f64 x (.f64 y y))

Compiler

Compiled 853 to 595 computations (30.2% saved)

simplify68.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4936	1574
1	4936	1574

prune83.0ms (2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	119	4	123

Error

Counts

123 → 4

Compiler

Compiled 2366 to 511 computations (78.4% saved)

localize9.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b	(sqrt.f64 (+.f64 y (+.f64 x (*.f64 x y))))
0.0b	(sqrt.f64 (+.f64 y (+.f64 x (*.f64 x y))))
0.0b	(+.f64 x (*.f64 x y))
0.0b	(+.f64 x (*.f64 x y))
0.0b	(+.f64 x (*.f64 x y))
0.0b	(+.f64 y (+.f64 x (*.f64 x y)))
0.0b	(+.f64 y (+.f64 x (*.f64 x y)))
0.2b	(.f64 (sqrt.f64 (+.f64 y (+.f64 x (.f64 x y)))) (sqrt.f64 (+.f64 y (+.f64 x (*.f64 x y)))))

rewrite43.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`*-un-lft-identity_binary64_1783`
26×	`add-sqr-sqrt_binary64_1805` `sqrt-prod_binary64_1799`
19×	`pow1_binary64_1844`
16×	`add-log-exp_binary64_1822`
12×	`add-cube-cbrt_binary64_1818` `sqrt-div_binary64_1800`
11×	`swap-sqr_binary64_1750`
9×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
8×	`distribute-lft-out_binary64_1734` `pow1/2_binary64_1863` `sqrt-pow1_binary64_1801`
7×	`associate-l_binary64_1724` `sum-log_binary64_1874` `associate-r_binary64_1723`
6×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
5×	`pow-prod-up_binary64_1853`
4×	`frac-times_binary64_1793` `unswap-sqr_binary64_1751`
3×	`+-commutative_binary64_1713` `pow-sqr_binary64_1756` `pow-prod-down_binary64_1854`
2×	`associate-+r+_binary64_1715` `associate-r/_binary64_1725` `associate-l/_binary64_1726` `rem-sqrt-square_binary64_1796`
1×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `sqrt-unprod_binary64_1803` `pow-plus_binary64_1846` `*-commutative_binary64_1714` `rem-square-sqrt_binary64_1795` `sqr-abs_binary64_1798` `pow2_binary64_1864`

Counts

4 → 102

Calls

8 calls:

17.0ms	(.f64 (sqrt.f64 (+.f64 y (+.f64 x (.f64 x y)))) (sqrt.f64 (+.f64 y (+.f64 x (*.f64 x y)))))
6.0ms	(+.f64 y (+.f64 x (*.f64 x y)))
6.0ms	(+.f64 y (+.f64 x (*.f64 x y)))
3.0ms	(+.f64 x (*.f64 x y))
0.0ms	(sqrt.f64 (+.f64 y (+.f64 x (*.f64 x y))))

series265.0ms (6.4%)

Counts

4 → 45

Calls

4 calls:

72.0ms	(+.f64 y (+.f64 x (*.f64 x y)))
72.0ms	(.f64 (sqrt.f64 (+.f64 y (+.f64 x (.f64 x y)))) (sqrt.f64 (+.f64 y (+.f64 x (*.f64 x y)))))
69.0ms	(+.f64 y (+.f64 x (*.f64 x y)))
52.0ms	(+.f64 x (*.f64 x y))

Compiler

Compiled 925 to 597 computations (35.5% saved)

simplify108.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4944	1947
1	4944	1947

prune89.0ms (2.2%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	147	4	151

Error

Counts

151 → 4

Compiler

Compiled 2589 to 365 computations (85.9% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	58	199
1	58	199

regimes49.0ms (1.2%)

Compiler: Compiled 278 to 186 computations (33.1% saved)

bsearch0.0ms (0%)

regimes55.0ms (1.3%)

Compiler: Compiled 40 to 56 computations (-40% saved)

bsearch23.0ms (0.6%)

Steps

Iters	Range		Point
9	0.023951678011460076	231641.11253109007	1.0011536277980586
8	-2600687.916735239	-8711.181044275361	-8842.008692967689

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes23.0ms (0.5%)

Compiler: Compiled 20 to 40 computations (-100% saved)

bsearch0.0ms (0%)

regimes44.0ms (1.1%)

Compiler: Compiled 14 to 34 computations (-142.9% saved)

bsearch23.0ms (0.5%)

Steps

Iters	Range		Point
9	1.4138309916814137e-28	8.258169334887751e-22	2.186793663736364e-28
8	-1.5387427850253125e-11	-2.6216656509947444e-15	-2.7526187059993937e-15

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes17.0ms (0.4%)

Compiler: Compiled 12 to 30 computations (-150% saved)

bsearch0.0ms (0%)

regimes17.0ms (0.4%)

Accuracy

Total 0.0b remaining (64.5%)

Threshold costs 0.0b (64.5%)

Compiler

Compiled 10 to 26 computations (-160% saved)

bsearch4.0ms (0.1%)

Compiler: Compiled 44 to 32 computations (27.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	56
1	34	56

end0.0ms (0%)

sample587.0ms (14.2%)

Algorithm

1×

intervals

Results

175.0ms	8000×	body	128	valid
2.0ms	74×	body	128	invalid

Compiler

Compiled 185 to 130 computations (29.7% saved)

Pareto

0.6724330561194564

Details

analyze65.0ms (1.6%)

sample13.0ms (0.3%)

simplify102.0ms (2.5%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite14.0ms (0.3%)

series115.0ms (2.8%)

simplify45.0ms (1.1%)

prune30.0ms (0.7%)

localize12.0ms (0.3%)

rewrite42.0ms (1%)

series1.3s (31.8%)

simplify104.0ms (2.5%)

prune268.0ms (6.5%)

localize11.0ms (0.3%)

rewrite49.0ms (1.2%)

series419.0ms (10.2%)

simplify68.0ms (1.7%)

prune83.0ms (2%)

localize9.0ms (0.2%)

rewrite43.0ms (1%)

series265.0ms (6.4%)

simplify108.0ms (2.6%)

prune89.0ms (2.2%)

simplify6.0ms (0.1%)

regimes49.0ms (1.2%)

bsearch0.0ms (0%)

regimes55.0ms (1.3%)

bsearch23.0ms (0.6%)

regimes23.0ms (0.5%)

bsearch0.0ms (0%)

regimes44.0ms (1.1%)

bsearch23.0ms (0.5%)

regimes17.0ms (0.4%)

bsearch0.0ms (0%)

regimes17.0ms (0.4%)

bsearch4.0ms (0.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample587.0ms (14.2%)

Profiling