Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	0%	50%	2

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample25.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms	70×	body	1024	valid
6.0ms	142×	body	128	valid
3.0ms	29×	body	512	valid
1.0ms	15×	body	256	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify178.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	75	17
1	75	17

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

Merged error: 17.9b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.2b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.3b	(/.f64 1 (sqrt.f64 x))
2.8b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite81.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

127×	`add-sqr-sqrt_binary64_1821`
118×	`times-frac_binary64_1805`
117×	`*-un-lft-identity_binary64_1799`
76×	`sqrt-prod_binary64_1815`
56×	`add-cube-cbrt_binary64_1834`
27×	`cancel-sign-sub-inv_binary64_1765`
25×	`difference-of-squares_binary64_1768`
13×	`associate-/r*_binary64_1743` `distribute-lft-out--_binary64_1751`
12×	`add-exp-log_binary64_1837`
11×	`distribute-lft-out_binary64_1750`
9×	`pow1_binary64_1860`
8×	`add-cbrt-cube_binary64_1835`
7×	`div-inv_binary64_1796`
6×	`sqrt-div_binary64_1816` `associate-/l*_binary64_1744` `add-log-exp_binary64_1838` `pow-flip_binary64_1873`
4×	`div-exp_binary64_1850` `associate-/r/_binary64_1745`
3×	`pow1/2_binary64_1879` `sqrt-pow1_binary64_1817` `flip3-+_binary64_1802` `flip-+_binary64_1773`
2×	`clear-num_binary64_1798` `rec-exp_binary64_1849` `frac-2neg_binary64_1810` `1-exp_binary64_1843` `cbrt-undiv_binary64_1833` `inv-pow_binary64_1884`
1×	`sub-neg_binary64_1792` `diff-log_binary64_1891` `flip--_binary64_1774` `flip3--_binary64_1803` `frac-sub_binary64_1808` `rem-sqrt-square_binary64_1812`

Counts

4 → 189

Calls

4 calls:

46.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
5.0ms	(/.f64 1 (sqrt.f64 x))
4.0ms	(sqrt.f64 (+.f64 x 1))

series187.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

70.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
58.0ms	(/.f64 1 (sqrt.f64 x))
32.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
26.0ms	(sqrt.f64 (+.f64 x 1))

simplify82.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4913	3696
1	4913	3696

prune604.0ms (11.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	190	11	201
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	190	12	202

Merged error: 17.2b

Counts

202 → 12

Compiler

Compiled 9783 to 7835 computations (19.9% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 x))
0.1b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.2b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
2.8b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite56.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64_1821`
42×	`sqrt-prod_binary64_1815`
38×	`*-un-lft-identity_binary64_1799`
13×	`add-cube-cbrt_binary64_1834`
12×	`difference-of-squares_binary64_1768`
11×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
10×	`associate-/l*_binary64_1744` `times-frac_binary64_1805`
9×	`pow1_binary64_1860` `distribute-lft-out--_binary64_1751`
7×	`associate-r_binary64_1739`
6×	`sqrt-div_binary64_1816` `add-log-exp_binary64_1838` `associate-l_binary64_1740` `cancel-sign-sub-inv_binary64_1765`
5×	`distribute-lft-out_binary64_1750`
4×	`unswap-sqr_binary64_1767` `associate-*r/_binary64_1741`
3×	`pow1/2_binary64_1879` `sqrt-pow1_binary64_1817` `pow-prod-down_binary64_1870` `flip3-+_binary64_1802` `flip-+_binary64_1773`
2×	`div-exp_binary64_1850` `prod-exp_binary64_1848` `flip--_binary64_1774` `associate-/r/_binary64_1745` `flip3--_binary64_1803` `cbrt-undiv_binary64_1833` `associate-/l/_binary64_1746` `cbrt-unprod_binary64_1832`
1×	`div-sub_binary64_1804` `sub-neg_binary64_1792` `clear-num_binary64_1798` `frac-2neg_binary64_1810` `associate-/r_binary64_1743` `diff-log_binary64_1891` `-commutative_binary64_1730` `sqrt-unprod_binary64_1819` `div-inv_binary64_1796` `rem-sqrt-square_binary64_1812`

Counts

4 → 113

Calls

4 calls:

19.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
12.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
10.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
4.0ms	(sqrt.f64 (+.f64 1 x))

series315.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

168.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
72.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
49.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
26.0ms	(sqrt.f64 (+.f64 1 x))

simplify76.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5009	2693

prune202.0ms (3.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	9	1	10
Picked	1	0	1
Done	1	0	1
Total	135	2	137

Merged error: 0.2b

Counts

137 → 2

Compiler

Compiled 3628 to 2485 computations (31.5% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 x))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.2b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.2b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

rewrite69.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

114×	`*-un-lft-identity_binary64_1799`
78×	`times-frac_binary64_1805`
55×	`sqrt-prod_binary64_1815`
49×	`add-sqr-sqrt_binary64_1821`
42×	`distribute-lft-out_binary64_1750`
40×	`add-cube-cbrt_binary64_1834`
32×	`add-exp-log_binary64_1837`
27×	`associate-/l*_binary64_1744`
20×	`add-cbrt-cube_binary64_1835`
14×	`div-exp_binary64_1850`
10×	`pow1_binary64_1860`
8×	`associate-/r/_binary64_1745`
7×	`associate-/r_binary64_1743` `cbrt-undiv_binary64_1833` `associate-r*_binary64_1739`
6×	`sqrt-div_binary64_1816` `associate-l_binary64_1740` `flip3-+_binary64_1802` `flip-+_binary64_1773`
5×	`prod-exp_binary64_1848`
4×	`add-log-exp_binary64_1838` `unswap-sqr_binary64_1767` `associate-*r/_binary64_1741` `div-inv_binary64_1796`
3×	`rec-exp_binary64_1849` `pow1/2_binary64_1879` `1-exp_binary64_1843` `cbrt-unprod_binary64_1832` `sqrt-pow1_binary64_1817` `pow-prod-down_binary64_1870`
2×	`clear-num_binary64_1798` `frac-2neg_binary64_1810`
1×	`pow-flip_binary64_1873` `associate-/l/_binary64_1746` `*-commutative_binary64_1730` `sqrt-unprod_binary64_1819` `rem-sqrt-square_binary64_1812` `inv-pow_binary64_1884`

Counts

4 → 168

Calls

4 calls:

25.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
10.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
4.0ms	(sqrt.f64 (+.f64 1 x))

series297.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

163.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
59.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
47.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
28.0ms	(sqrt.f64 (+.f64 1 x))

simplify102.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4909	4123
1	4909	4123

prune613.0ms (11.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	170	10	180
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	171	11	182

Merged error: 0.0b

Counts

182 → 11

Compiler

Compiled 11134 to 8219 computations (26.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 x))
0.1b	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
0.2b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
0.3b	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))

rewrite70.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

234×	`times-frac_binary64_1805`
162×	`*-un-lft-identity_binary64_1799`
157×	`add-sqr-sqrt_binary64_1821`
120×	`add-cube-cbrt_binary64_1834`
91×	`sqrt-prod_binary64_1815`
49×	`distribute-lft-out_binary64_1750`
21×	`associate-/l*_binary64_1744`
20×	`associate-/r/_binary64_1745`
19×	`add-exp-log_binary64_1837`
13×	`add-cbrt-cube_binary64_1835`
12×	`flip3-+_binary64_1802` `flip-+_binary64_1773`
11×	`associate-/r*_binary64_1743`
10×	`pow1_binary64_1860` `div-inv_binary64_1796`
8×	`div-exp_binary64_1850`
7×	`associate-r_binary64_1739`
6×	`sqrt-div_binary64_1816` `associate-l_binary64_1740`
4×	`add-log-exp_binary64_1838` `unswap-sqr_binary64_1767` `cbrt-undiv_binary64_1833`
3×	`pow1/2_binary64_1879` `sqrt-pow1_binary64_1817` `pow-prod-down_binary64_1870`
2×	`clear-num_binary64_1798` `rec-exp_binary64_1849` `frac-2neg_binary64_1810` `associate-*r/_binary64_1741` `1-exp_binary64_1843`
1×	`prod-exp_binary64_1848` `pow-flip_binary64_1873` `associate-/l/_binary64_1746` `cbrt-unprod_binary64_1832` `*-commutative_binary64_1730` `sqrt-unprod_binary64_1819` `rem-sqrt-square_binary64_1812` `inv-pow_binary64_1884`

Counts

4 → 256

Calls

4 calls:

15.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
11.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
6.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
4.0ms	(sqrt.f64 (+.f64 1 x))

series324.0ms (6%)

Counts

4 → 12

Calls

4 calls:

168.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
85.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
45.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
26.0ms	(sqrt.f64 (+.f64 1 x))

simplify148.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

268 → 268

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4935	9713
1	4935	9713

prune815.0ms (15.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	264	4	268
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	267	12	279

Merged error: 0b

Counts

279 → 12

Compiler

Compiled 13190 to 9751 computations (26.1% saved)

regimes31.0ms (0.6%)

Compiler: Compiled 302 to 233 computations (22.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	25
1	14	25

end0.0ms (0%)

sample1.1s (20.1%)

Algorithm

1×

intervals

Results

334.0ms	2188×	body	1024	valid
172.0ms	4303×	body	128	valid
113.0ms	1010×	body	512	valid
37.0ms	499×	body	256	valid

Compiler

Compiled 343 to 267 computations (22.2% saved)

Details

analyze1.0ms (0%)

sample25.0ms (0.5%)

simplify178.0ms (3.3%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite81.0ms (1.5%)

series187.0ms (3.5%)

simplify82.0ms (1.5%)

prune604.0ms (11.2%)

localize7.0ms (0.1%)

rewrite56.0ms (1%)

series315.0ms (5.8%)

simplify76.0ms (1.4%)

prune202.0ms (3.7%)

localize8.0ms (0.2%)

rewrite69.0ms (1.3%)

series297.0ms (5.5%)

simplify102.0ms (1.9%)

prune613.0ms (11.3%)

localize13.0ms (0.2%)

rewrite70.0ms (1.3%)

series324.0ms (6%)

simplify148.0ms (2.7%)

prune815.0ms (15.1%)

regimes31.0ms (0.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.1s (20.1%)

Profiling