Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample26.0ms (0.7%)

Algorithm

1×

intervals

Results

8.0ms	138×	body	128	valid
7.0ms	63×	body	1024	valid
4.0ms	32×	body	512	valid
1.0ms	18×	body	256	valid
1.0ms	5×	body	2048	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify98.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune2.0ms (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

Error

29.2b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.9b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
1.9b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_1464` `sqrt-prod_binary64_1458`
10×	`*-un-lft-identity_binary64_1442`
6×	`cancel-sign-sub-inv_binary64_1408`
4×	`difference-of-squares_binary64_1411`
3×	`add-log-exp_binary64_1481` `add-cube-cbrt_binary64_1477` `distribute-lft-out--_binary64_1394`
1×	`add-cbrt-cube_binary64_1478` `sub-neg_binary64_1435` `flip3--_binary64_1446` `add-exp-log_binary64_1480` `distribute-lft-out_binary64_1393` `flip--_binary64_1417` `diff-log_binary64_1534` `pow1_binary64_1503`

Counts

1 → 24

Calls

2 calls:

10.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series34.0ms (1%)

Counts

1 → 3

Calls

1 calls:

34.0ms

(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 88 to 74 computations (15.9% saved)

simplify60.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5280	397

prune47.0ms (1.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	25	2	27
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	2	28

Error

0.1b

Counts

28 → 2

Compiler

Compiled 335 to 218 computations (34.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite23.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`*-un-lft-identity_binary64_1442`
20×	`distribute-lft-out_binary64_1393` `sqrt-prod_binary64_1458`
18×	`times-frac_binary64_1448`
13×	`add-sqr-sqrt_binary64_1464` `add-cube-cbrt_binary64_1477`
6×	`associate-/r*_binary64_1386` `add-exp-log_binary64_1480`
4×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481`
3×	`associate-/l*_binary64_1387` `pow1_binary64_1503`
2×	`associate-/r/_binary64_1388` `flip3-+_binary64_1445` `flip-+_binary64_1416` `div-exp_binary64_1493`
1×	`inv-pow_binary64_1527` `cbrt-undiv_binary64_1476` `sum-log_binary64_1533` `div-inv_binary64_1439` `clear-num_binary64_1441` `1-exp_binary64_1486` `+-commutative_binary64_1372` `rec-exp_binary64_1492` `pow-flip_binary64_1516` `frac-2neg_binary64_1453`

Counts

2 → 59

Calls

4 calls:

11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

series32.0ms (0.9%)

Counts

2 → 6

Calls

2 calls:

18.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
14.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 84 to 84 computations (0% saved)

simplify105.0ms (3%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4780	1037
1	4780	1037

prune91.0ms (2.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	60	5	65
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	60	7	67

Error

0.0b

Counts

67 → 7

Compiler

Compiled 1014 to 741 computations (26.9% saved)

localize10.0ms (0.3%)

Local error

Found 8 expressions with local error:

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

rewrite118.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Rules

310×	`*-un-lft-identity_binary64_1442`
290×	`sqrt-prod_binary64_1458`
172×	`times-frac_binary64_1448`
144×	`add-sqr-sqrt_binary64_1464`
116×	`distribute-lft-out_binary64_1393`
88×	`add-cube-cbrt_binary64_1477`
43×	`swap-sqr_binary64_1409`
31×	`pow1_binary64_1503`
27×	`sqrt-pow1_binary64_1460` `associate-r_binary64_1382` `associate-l_binary64_1383`
16×	`unswap-sqr_binary64_1410`
14×	`associate-/r/_binary64_1388` `add-exp-log_binary64_1480`
12×	`associate-/r*_binary64_1386`
11×	`inv-pow_binary64_1527` `pow-flip_binary64_1516`
10×	`add-cbrt-cube_binary64_1478`
9×	`rem-sqrt-square_binary64_1455` `div-inv_binary64_1439` `pow1/2_binary64_1522` `pow-prod-up_binary64_1512`
7×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
6×	`associate-/l*_binary64_1387`
5×	`pow-prod-down_binary64_1513` `pow-sqr_binary64_1415` `sqrt-div_binary64_1459`
4×	`add-log-exp_binary64_1481` `div-exp_binary64_1493`
3×	`sqr-abs_binary64_1457`
2×	`cbrt-undiv_binary64_1476` `clear-num_binary64_1441` `1-exp_binary64_1486` `rec-exp_binary64_1492` `frac-2neg_binary64_1453`
1×	`pow2_binary64_1523` `associate-r/_binary64_1384` `cbrt-unprod_binary64_1475` `pow-plus_binary64_1505` `-commutative_binary64_1373` `sqrt-unprod_binary64_1462` `frac-times_binary64_1452` `prod-exp_binary64_1491` `rem-square-sqrt_binary64_1454` `associate-*l/_binary64_1385`

Counts

4 → 281

Calls

8 calls:

47.0ms	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
11.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

series98.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

28.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
26.0ms	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
22.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
21.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

Compiler

Compiled 404 to 368 computations (8.9% saved)

simplify126.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5824	5963

prune504.0ms (14.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	288	5	293
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	290	10	300

Error

0.0b

Counts

300 → 10

Compiler

Compiled 7002 to 5179 computations (26% saved)

localize10.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.1b	(sqrt.f64 (pow.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 4))
0.1b	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.1b	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.1b	(sqrt.f64 (pow.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 4))
0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.4b	(pow.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 4)

rewrite77.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

158×	`sqrt-prod_binary64_1458`
142×	`*-un-lft-identity_binary64_1442`
76×	`times-frac_binary64_1448`
59×	`add-sqr-sqrt_binary64_1464`
58×	`unpow-prod-down_binary64_1521`
52×	`distribute-lft-out_binary64_1393`
49×	`add-cube-cbrt_binary64_1477`
10×	`pow1_binary64_1503`
9×	`rem-sqrt-square_binary64_1455` `add-exp-log_binary64_1480`
8×	`associate-/r/_binary64_1388`
7×	`sqrt-pow1_binary64_1460`
6×	`associate-/r*_binary64_1386` `add-cbrt-cube_binary64_1478`
5×	`pow-pow_binary64_1514`
4×	`div-inv_binary64_1439` `add-log-exp_binary64_1481` `flip3-+_binary64_1445` `flip-+_binary64_1416`
3×	`inv-pow_binary64_1527` `associate-/l*_binary64_1387` `pow-unpow_binary64_1519` `pow-flip_binary64_1516` `sqr-pow_binary64_1414` `pow1/2_binary64_1522`
2×	`div-exp_binary64_1493`
1×	`cbrt-undiv_binary64_1476` `pow-exp_binary64_1510` `clear-num_binary64_1441` `1-exp_binary64_1486` `rec-exp_binary64_1492` `sqrt-div_binary64_1459` `frac-2neg_binary64_1453` `sqrt-pow2_binary64_1461` `pow-to-exp_binary64_1511`

Counts

4 → 176

Calls

8 calls:

20.0ms	(sqrt.f64 (pow.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 4))
16.0ms	(pow.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 4)
12.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

series106.0ms (3%)

Counts

4 → 12

Calls

4 calls:

38.0ms	(pow.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 4)
25.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
23.0ms	(sqrt.f64 (pow.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 4))
20.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

Compiler

Compiled 268 to 268 computations (0% saved)

simplify102.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4873	3775
1	4873	3775

prune235.0ms (6.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	186	2	188
Fresh	2	6	8
Picked	0	1	1
Done	1	0	1
Total	189	9	198

Error

0.0b

Counts

198 → 9

Compiler

Compiled 3327 to 2586 computations (22.3% saved)

simplify15.0ms (0.4%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	155	1087
1	155	1087

regimes72.0ms (2.1%)

Compiler: Compiled 672 to 557 computations (17.1% saved)

bsearch0.0ms (0%)

regimes10.0ms (0.3%)

Compiler: Compiled 12 to 14 computations (-16.7% saved)

bsearch0.0ms (0%)

regimes7.0ms (0.2%)

Accuracy

Total 0.2b remaining (95.5%)

Threshold costs 0.2b (95.5%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch2.0ms (0.1%)

Compiler: Compiled 17 to 16 computations (5.9% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	26
1	21	26

end0.0ms (0%)

sample1.4s (41.3%)

Algorithm

1×

intervals

Results

220.0ms	1999×	body	1024	valid
128.0ms	4295×	body	128	valid
79.0ms	981×	body	512	valid
30.0ms	223×	body	2048	valid
26.0ms	502×	body	256	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 704 to 587 computations (16.6% saved)

Pareto

-0.9497068181173958

Details

analyze3.0ms (0.1%)

sample26.0ms (0.7%)

simplify98.0ms (2.8%)

prune2.0ms (0.1%)

localize5.0ms (0.1%)

rewrite12.0ms (0.3%)

series34.0ms (1%)

simplify60.0ms (1.7%)

prune47.0ms (1.3%)

localize8.0ms (0.2%)

rewrite23.0ms (0.7%)

series32.0ms (0.9%)

simplify105.0ms (3%)

prune91.0ms (2.6%)

localize10.0ms (0.3%)

rewrite118.0ms (3.4%)

series98.0ms (2.8%)

simplify126.0ms (3.6%)

prune504.0ms (14.5%)

localize10.0ms (0.3%)

rewrite77.0ms (2.2%)

series106.0ms (3%)

simplify102.0ms (2.9%)

prune235.0ms (6.8%)

simplify15.0ms (0.4%)

regimes72.0ms (2.1%)

bsearch0.0ms (0%)

regimes10.0ms (0.3%)

bsearch0.0ms (0%)

regimes7.0ms (0.2%)

bsearch2.0ms (0.1%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.4s (41.3%)

Profiling