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
50%	25%	25%	4
62.5%	12.5%	25%	5
68.7%	6.2%	25%	6
71.8%	3.1%	25%	7
73.4%	1.6%	25%	8
74.2%	0.8%	25%	9
74.6%	0.4%	25%	10
74.8%	0.2%	25%	11
74.9%	0.1%	25%	12
74.9%	0%	25%	13
74.9%	0%	25.1%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample11.0ms (0.4%)

Algorithm

1×

intervals

Results

5.0ms

256×

body

128

valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify104.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	16	10
1	16	10

prune6.0ms (0.2%)

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

Error

0.0b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize4.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (.f64 (.f64 x x) 2) 1)
0.0b	(.f64 (.f64 x x) 2)
0.0b	(.f64 (.f64 x x) 2)
0.0b	(-.f64 (.f64 (.f64 x x) 2) 1)

rewrite15.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `pow1_binary64_1844`
5×	`add-sqr-sqrt_binary64_1805`
4×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783` `add-log-exp_binary64_1822`
3×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `cancel-sign-sub-inv_binary64_1749` `pow-prod-down_binary64_1854` `associate-r_binary64_1723`
1×	`flip3--_binary64_1787` `associate-l_binary64_1724` `diff-log_binary64_1875` `*-commutative_binary64_1714` `unswap-sqr_binary64_1751` `flip--_binary64_1758` `sub-neg_binary64_1776`

Counts

2 → 33

Calls

4 calls:

7.0ms	(-.f64 (.f64 (.f64 x x) 2) 1)
6.0ms	(.f64 (.f64 x x) 2)
0.0ms	(.f64 (.f64 x x) 2)
0.0ms	(-.f64 (.f64 (.f64 x x) 2) 1)

series72.0ms (2.4%)

Counts

2 → 9

Calls

2 calls:

46.0ms	(-.f64 (.f64 (.f64 x x) 2) 1)
25.0ms	(.f64 (.f64 x x) 2)

Compiler

Compiled 95 to 96 computations (-1.1% saved)

simplify78.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4921	391
1	4921	391

prune36.0ms (1.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	40	2	42
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	40	3	43

Error

0.0b

Counts

43 → 3

Compiler

Compiled 431 to 293 computations (32% saved)

localize7.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.4b	(*.f64 x (sqrt.f64 2))
0.4b	(.f64 (.f64 x (*.f64 x (sqrt.f64 2))) (sqrt.f64 2))
0.2b	(.f64 x (.f64 x (sqrt.f64 2)))
0.0b	(-.f64 (.f64 (.f64 x (*.f64 x (sqrt.f64 2))) (sqrt.f64 2)) 1)
0.0b	(-.f64 (.f64 (.f64 x (*.f64 x (sqrt.f64 2))) (sqrt.f64 2)) 1)
0.2b	(.f64 x (.f64 x (sqrt.f64 2)))
0.4b	(.f64 (.f64 x (*.f64 x (sqrt.f64 2))) (sqrt.f64 2))
0.4b	(*.f64 x (sqrt.f64 2))

rewrite37.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `pow1_binary64_1844`
15×	`add-sqr-sqrt_binary64_1805`
13×	`associate-r_binary64_1723`
11×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
10×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `pow-prod-down_binary64_1854`
7×	`associate-l_binary64_1724` `sqrt-prod_binary64_1799`
6×	`add-log-exp_binary64_1822`
3×	`cancel-sign-sub-inv_binary64_1749` `*-commutative_binary64_1714`
2×	`unswap-sqr_binary64_1751`
1×	`flip3--_binary64_1787` `diff-log_binary64_1875` `flip--_binary64_1758` `sub-neg_binary64_1776`

Counts

4 → 78

Calls

8 calls:

10.0ms	(.f64 (.f64 x (*.f64 x (sqrt.f64 2))) (sqrt.f64 2))
9.0ms	(-.f64 (.f64 (.f64 x (*.f64 x (sqrt.f64 2))) (sqrt.f64 2)) 1)
6.0ms	(*.f64 x (sqrt.f64 2))
6.0ms	(.f64 x (.f64 x (sqrt.f64 2)))
0.0ms	(-.f64 (.f64 (.f64 x (*.f64 x (sqrt.f64 2))) (sqrt.f64 2)) 1)

series192.0ms (6.5%)

Counts

4 → 15

Calls

4 calls:

74.0ms	(-.f64 (.f64 (.f64 x (*.f64 x (sqrt.f64 2))) (sqrt.f64 2)) 1)
49.0ms	(.f64 (.f64 x (*.f64 x (sqrt.f64 2))) (sqrt.f64 2))
34.0ms	(.f64 x (.f64 x (sqrt.f64 2)))
34.0ms	(*.f64 x (sqrt.f64 2))

Compiler

Compiled 269 to 264 computations (1.9% saved)

simplify68.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4939	875
1	4939	875

prune71.0ms (2.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	93	3	96

Error

0.0b

Counts

96 → 3

Compiler

Compiled 1180 to 863 computations (26.9% saved)

localize10.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.0b	(*.f64 (pow.f64 x 4) 4)
0.0b	(.f64 (.f64 x x) 2)
0.0b	(+.f64 (*.f64 (pow.f64 x 4) 4) -1)
0.0b	(+.f64 (.f64 (.f64 x x) 2) 1)
0.0b	(+.f64 (*.f64 (pow.f64 x 4) 4) -1)
0.0b	(.f64 (.f64 x x) 2)
0.0b	(*.f64 (pow.f64 x 4) 4)
11.1b	(/.f64 (+.f64 (.f64 (pow.f64 x 4) 4) -1) (+.f64 (.f64 (*.f64 x x) 2) 1))

rewrite38.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_1805`
16×	`add-exp-log_binary64_1821` `add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
13×	`add-cbrt-cube_binary64_1819`
9×	`times-frac_binary64_1789` `pow1_binary64_1844`
8×	`associate-l_binary64_1724`
6×	`prod-exp_binary64_1832` `add-log-exp_binary64_1822` `associate-r_binary64_1723`
4×	`cbrt-unprod_binary64_1816` `unpow-prod-down_binary64_1862` `unswap-sqr_binary64_1751`
3×	`associate-/l_binary64_1728` `flip-+_binary64_1757` `associate-/r_binary64_1727` `flip3-+_binary64_1786` `pow-prod-down_binary64_1854`
2×	`associate-/l/_binary64_1730` `associate-/r/_binary64_1729` `sqr-pow_binary64_1755` `*-commutative_binary64_1714`
1×	`+-commutative_binary64_1713` `div-inv_binary64_1780` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `sum-log_binary64_1874` `div-exp_binary64_1834` `clear-num_binary64_1782` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`

Counts

4 → 86

Calls

8 calls:

12.0ms	(/.f64 (+.f64 (.f64 (pow.f64 x 4) 4) -1) (+.f64 (.f64 (*.f64 x x) 2) 1))
6.0ms	(.f64 (.f64 x x) 2)
6.0ms	(*.f64 (pow.f64 x 4) 4)
5.0ms	(+.f64 (*.f64 (pow.f64 x 4) 4) -1)
0.0ms	(+.f64 (.f64 (.f64 x x) 2) 1)

series226.0ms (7.7%)

Counts

4 → 18

Calls

4 calls:

101.0ms	(/.f64 (+.f64 (.f64 (pow.f64 x 4) 4) -1) (+.f64 (.f64 (*.f64 x x) 2) 1))
66.0ms	(+.f64 (*.f64 (pow.f64 x 4) 4) -1)
32.0ms	(*.f64 (pow.f64 x 4) 4)
28.0ms	(.f64 (.f64 x x) 2)

Compiler

Compiled 358 to 324 computations (9.5% saved)

simplify64.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5325	1558

prune115.0ms (3.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	104	3	107

Error

Counts

107 → 3

Compiler

Compiled 2044 to 1545 computations (24.4% saved)

localize14.0ms (0.5%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 (.f64 x x) 2)
0.0b	(+.f64 (*.f64 4 (pow.f64 x 4)) -1)
0.0b	(+.f64 (.f64 (.f64 x x) 2) 1)
0.0b	(+.f64 (.f64 (.f64 x x) 2) 1)
0.0b	(sqrt.f64 (+.f64 (.f64 (.f64 x x) 2) 1))
0.1b	(/.f64 1 (sqrt.f64 (+.f64 (.f64 (.f64 x x) 2) 1)))
4.6b	(/.f64 (+.f64 (.f64 4 (pow.f64 x 4)) -1) (sqrt.f64 (+.f64 (.f64 (*.f64 x x) 2) 1)))
6.4b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 (.f64 x x) 2) 1))) (/.f64 (+.f64 (.f64 4 (pow.f64 x 4)) -1) (sqrt.f64 (+.f64 (.f64 (.f64 x x) 2) 1))))

rewrite93.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`add-sqr-sqrt_binary64_1805`
94×	`times-frac_binary64_1789`
67×	`*-un-lft-identity_binary64_1783`
61×	`add-cube-cbrt_binary64_1818`
56×	`sqrt-prod_binary64_1799`
32×	`add-exp-log_binary64_1821`
24×	`associate-l_binary64_1724` `associate-r_binary64_1723`
20×	`add-cbrt-cube_binary64_1819`
15×	`unswap-sqr_binary64_1751`
12×	`associate-/r*_binary64_1727`
11×	`div-exp_binary64_1834`
10×	`sqrt-div_binary64_1800`
9×	`pow1_binary64_1844`
8×	`associate-/r/_binary64_1729` `prod-exp_binary64_1832`
6×	`associate-/l*_binary64_1728` `flip-+_binary64_1757` `cbrt-undiv_binary64_1817` `flip3-+_binary64_1786`
4×	`cbrt-unprod_binary64_1816` `div-inv_binary64_1780` `add-log-exp_binary64_1822`
3×	`1-exp_binary64_1827` `pow-flip_binary64_1857` `rec-exp_binary64_1833`
2×	`associate-/l/_binary64_1730` `pow1/2_binary64_1863` `frac-2neg_binary64_1794` `sqrt-pow1_binary64_1801` `clear-num_binary64_1782`
1×	`associate-r/_binary64_1725` `inv-pow_binary64_1868` `associate-l/_binary64_1726` `*-commutative_binary64_1714` `frac-times_binary64_1793` `pow-prod-down_binary64_1854` `rem-sqrt-square_binary64_1796`

Counts

4 → 192

Calls

8 calls:

38.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 (.f64 x x) 2) 1))) (/.f64 (+.f64 (.f64 4 (pow.f64 x 4)) -1) (sqrt.f64 (+.f64 (.f64 (.f64 x x) 2) 1))))
13.0ms	(/.f64 (+.f64 (.f64 4 (pow.f64 x 4)) -1) (sqrt.f64 (+.f64 (.f64 (*.f64 x x) 2) 1)))
10.0ms	(/.f64 1 (sqrt.f64 (+.f64 (.f64 (.f64 x x) 2) 1)))
6.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 x x) 2) 1))
0.0ms	(+.f64 (.f64 (.f64 x x) 2) 1)

series428.0ms (14.5%)

Counts

4 → 42

Calls

4 calls:

141.0ms	(/.f64 (+.f64 (.f64 4 (pow.f64 x 4)) -1) (sqrt.f64 (+.f64 (.f64 (*.f64 x x) 2) 1)))
111.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 (.f64 x x) 2) 1))) (/.f64 (+.f64 (.f64 4 (pow.f64 x 4)) -1) (sqrt.f64 (+.f64 (.f64 (.f64 x x) 2) 1))))
104.0ms	(/.f64 1 (sqrt.f64 (+.f64 (.f64 (.f64 x x) 2) 1)))
71.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 x x) 2) 1))

Compiler

Compiled 1414 to 1259 computations (11% saved)

simplify99.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

234 → 234

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4989	7715
1	4989	7715

prune545.0ms (18.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	234	0	234
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	234	3	237

Error

Counts

237 → 3

Compiler

Compiled 8511 to 6510 computations (23.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	71	193
1	71	193

regimes39.0ms (1.3%)

Compiler: Compiled 270 to 236 computations (12.6% saved)

bsearch0.0ms (0%)

regimes34.0ms (1.2%)

Compiler: Compiled 24 to 26 computations (-8.3% saved)

bsearch7.0ms (0.2%)

Steps

Iters	Range		Point
6	0.4824925384698944	7.384483152514664	0.5108774671848952

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes8.0ms (0.3%)

Compiler: Compiled 5 to 8 computations (-60% saved)

bsearch0.0ms (0%)

regimes7.0ms (0.2%)

Accuracy

Total 0.0b remaining (100%)

Threshold costs 0.0b (100%)

Compiler

Compiled 4 to 6 computations (-50% saved)

bsearch2.0ms (0.1%)

Compiler: Compiled 21 to 18 computations (14.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	29
1	15	29

end0.0ms (0%)

sample502.0ms (17.1%)

Algorithm

1×

intervals

Results

163.0ms	8000×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 160 to 141 computations (11.9% saved)

Pareto

0.44848650990536754

Details

analyze4.0ms (0.1%)

sample11.0ms (0.4%)

simplify104.0ms (3.5%)

prune6.0ms (0.2%)

localize4.0ms (0.1%)

rewrite15.0ms (0.5%)

series72.0ms (2.4%)

simplify78.0ms (2.6%)

prune36.0ms (1.2%)

localize7.0ms (0.2%)

rewrite37.0ms (1.3%)

series192.0ms (6.5%)

simplify68.0ms (2.3%)

prune71.0ms (2.4%)

localize10.0ms (0.3%)

rewrite38.0ms (1.3%)

series226.0ms (7.7%)

simplify64.0ms (2.2%)

prune115.0ms (3.9%)

localize14.0ms (0.5%)

rewrite93.0ms (3.2%)

series428.0ms (14.5%)

simplify99.0ms (3.4%)

prune545.0ms (18.5%)

simplify4.0ms (0.1%)

regimes39.0ms (1.3%)

bsearch0.0ms (0%)

regimes34.0ms (1.2%)

bsearch7.0ms (0.2%)

regimes8.0ms (0.3%)

bsearch0.0ms (0%)

regimes7.0ms (0.2%)

bsearch2.0ms (0.1%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample502.0ms (17.1%)

Profiling