Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample22.0ms (0.4%)

Algorithm

1×

intervals

Results

8.0ms	63×	body	1024	valid
4.0ms	138×	body	128	valid
3.0ms	32×	body	512	valid
1.0ms	8×	body	2048	valid
1.0ms	15×	body	256	valid

Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify176.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	681	19
1	681	19

prune2.0ms (0%)

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

29.0b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
0.0b	(/.f64 x (+.f64 x 1))
2.0b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite74.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

148×	`*-un-lft-identity_binary64_1442`
88×	`times-frac_binary64_1448`
85×	`add-sqr-sqrt_binary64_1464`
37×	`add-cube-cbrt_binary64_1477`
34×	`cancel-sign-sub-inv_binary64_1408`
27×	`distribute-lft-out_binary64_1393`
22×	`difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394`
11×	`associate-/r*_binary64_1386`
9×	`difference-of-sqr-1_binary64_1412`
7×	`add-cbrt-cube_binary64_1478` `associate-/l*_binary64_1387` `add-exp-log_binary64_1480`
6×	`associate-/r/_binary64_1388`
5×	`add-log-exp_binary64_1481`
3×	`div-inv_binary64_1439` `flip3--_binary64_1446` `flip--_binary64_1417` `pow1_binary64_1503`
2×	`cbrt-undiv_binary64_1476` `associate-/l/_binary64_1389` `clear-num_binary64_1441` `frac-2neg_binary64_1453` `flip3-+_binary64_1445` `flip-+_binary64_1416` `div-exp_binary64_1493`
1×	`sub-neg_binary64_1435` `frac-sub_binary64_1451` `diff-log_binary64_1534`

Counts

3 → 147

Calls

3 calls:

42.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
9.0ms	(/.f64 x (+.f64 x 1))
8.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))

series63.0ms (1.2%)

Counts

3 → 9

Calls

3 calls:

37.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
13.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
13.0ms	(/.f64 x (+.f64 x 1))

simplify83.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5658	2774

prune200.0ms (3.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	150	6	156
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	151	6	157

Error

0.1b

Counts

157 → 6

Compiler

Compiled 3164 to 2236 computations (29.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(exp.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))
0.0b	(/.f64 x (+.f64 x 1))
1.9b	(log.f64 (exp.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))
2.0b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite176.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Rules

276×	`*-un-lft-identity_binary64_1442`
156×	`times-frac_binary64_1448`
136×	`add-sqr-sqrt_binary64_1464`
102×	`cancel-sign-sub-inv_binary64_1408`
70×	`exp-sum_binary64_1488`
52×	`add-cube-cbrt_binary64_1477`
51×	`distribute-lft-out--_binary64_1394`
49×	`distribute-lft-out_binary64_1393`
38×	`log-prod_binary64_1528`
36×	`difference-of-squares_binary64_1411`
32×	`exp-prod_binary64_1494`
17×	`log-pow_binary64_1531`
12×	`difference-of-sqr-1_binary64_1412`
9×	`add-log-exp_binary64_1481`
8×	`associate-/r/_binary64_1388`
6×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
5×	`pow1_binary64_1503`
4×	`associate-/r*_binary64_1386` `div-inv_binary64_1439` `flip3--_binary64_1446` `flip--_binary64_1417`
3×	`sub-neg_binary64_1435` `associate-/l*_binary64_1387`
2×	`rem-exp-log_binary64_1482` `diff-log_binary64_1534` `exp-diff_binary64_1490`
1×	`cbrt-undiv_binary64_1476` `clear-num_binary64_1441` `rem-log-exp_binary64_1483` `frac-sub_binary64_1451` `frac-2neg_binary64_1453` `flip3-+_binary64_1445` `flip-+_binary64_1416` `log-div_binary64_1529` `div-exp_binary64_1493`

Counts

4 → 217

Calls

4 calls:

51.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))
43.0ms	(exp.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))
43.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
5.0ms	(/.f64 x (+.f64 x 1))

series129.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

50.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))
33.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
33.0ms	(exp.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))
12.0ms	(/.f64 x (+.f64 x 1))

simplify101.0ms (2%)

Algorithm

1×	egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5068	4560

prune279.0ms (5.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	227	2	229
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	229	6	235

Error

0.1b

Counts

235 → 6

Compiler

Compiled 4781 to 3463 computations (27.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (exp.f64 (/.f64 x (+.f64 x 1))) (exp.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))))
0.0b	(/.f64 x (+.f64 x 1))
0.0b	(exp.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))
1.9b	(log.f64 (/.f64 (exp.f64 (/.f64 x (+.f64 x 1))) (exp.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))))

rewrite88.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

166×	`*-un-lft-identity_binary64_1442`
90×	`times-frac_binary64_1448`
70×	`exp-prod_binary64_1494`
56×	`add-sqr-sqrt_binary64_1464`
40×	`add-cube-cbrt_binary64_1477`
27×	`distribute-lft-out_binary64_1393`
18×	`pow-div_binary64_1517`
13×	`log-prod_binary64_1528`
12×	`distribute-lft-out--_binary64_1394`
10×	`log-pow_binary64_1531`
8×	`add-cbrt-cube_binary64_1478` `difference-of-squares_binary64_1411`
7×	`associate-/r*_binary64_1386` `add-exp-log_binary64_1480`
6×	`associate-/l*_binary64_1387`
5×	`add-log-exp_binary64_1481` `pow1_binary64_1503`
4×	`div-inv_binary64_1439` `associate-/r/_binary64_1388` `difference-of-sqr-1_binary64_1412`
3×	`div-exp_binary64_1493`
2×	`cbrt-undiv_binary64_1476` `clear-num_binary64_1441` `rem-log-exp_binary64_1483` `frac-2neg_binary64_1453`
1×	`rem-exp-log_binary64_1482` `flip3--_binary64_1446` `flip--_binary64_1417` `flip3-+_binary64_1445` `flip-+_binary64_1416` `log-div_binary64_1529`

Counts

4 → 144

Calls

4 calls:

30.0ms	(log.f64 (/.f64 (exp.f64 (/.f64 x (+.f64 x 1))) (exp.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))))
27.0ms	(/.f64 (exp.f64 (/.f64 x (+.f64 x 1))) (exp.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))))
10.0ms	(exp.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))
5.0ms	(/.f64 x (+.f64 x 1))

series116.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

55.0ms	(log.f64 (/.f64 (exp.f64 (/.f64 x (+.f64 x 1))) (exp.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))))
31.0ms	(/.f64 (exp.f64 (/.f64 x (+.f64 x 1))) (exp.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))))
17.0ms	(exp.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))
13.0ms	(/.f64 x (+.f64 x 1))

simplify88.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4949	3091
1	4949	3091

prune202.0ms (3.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	156	6	162

Error

0.1b

Counts

162 → 6

Compiler

Compiled 3753 to 2821 computations (24.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
0.0b	(*.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1)))
0.0b	(*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
1.9b	(-.f64 (.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))

rewrite175.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Rules

434×	`*-un-lft-identity_binary64_1442`
272×	`times-frac_binary64_1448`
228×	`add-sqr-sqrt_binary64_1464`
100×	`add-cube-cbrt_binary64_1477`
96×	`swap-sqr_binary64_1409`
93×	`distribute-lft-out_binary64_1393`
53×	`difference-of-squares_binary64_1411`
52×	`associate-r_binary64_1382` `associate-l_binary64_1383`
36×	`distribute-lft-out--_binary64_1394`
32×	`difference-of-sqr-1_binary64_1412`
28×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
18×	`pow1_binary64_1503`
16×	`associate-/r/_binary64_1388`
9×	`frac-sub_binary64_1451`
8×	`associate-r/_binary64_1384` `cbrt-undiv_binary64_1476` `cbrt-unprod_binary64_1475` `div-inv_binary64_1439` `add-log-exp_binary64_1481` `frac-times_binary64_1452` `prod-exp_binary64_1491` `associate-l/_binary64_1385` `div-exp_binary64_1493` `unswap-sqr_binary64_1410`
5×	`flip3--_binary64_1446` `flip--_binary64_1417` `flip3-+_binary64_1445` `flip-+_binary64_1416`
2×	`pow2_binary64_1523` `pow-plus_binary64_1505` `pow-prod-down_binary64_1513` `*-commutative_binary64_1373` `pow-sqr_binary64_1415` `pow-prod-up_binary64_1512`
1×	`cancel-sign-sub-inv_binary64_1408` `sum-log_binary64_1533` `sub-neg_binary64_1435` `+-commutative_binary64_1372` `diff-log_binary64_1534` `frac-add_binary64_1450`

Counts

4 → 299

Calls

4 calls:

40.0ms	(*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
38.0ms	(+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
22.0ms	(*.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1)))
14.0ms	(-.f64 (.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))

series112.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

50.0ms	(-.f64 (.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))
30.0ms	(+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
16.0ms	(*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
15.0ms	(*.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1)))

simplify128.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

311 → 311

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5017	7255

prune1.1s (20.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	307	4	311
Fresh	3	1	4
Picked	1	0	1
Done	0	1	1
Total	311	6	317

Error

0.1b

Counts

317 → 6

Compiler

Compiled 14425 to 10322 computations (28.4% saved)

regimes217.0ms (4.2%)

Accuracy

Total 0.2b remaining (86.4%)

Threshold costs 0.2b (86.4%)

Compiler

Compiled 2473 to 1877 computations (24.1% saved)

bsearch2.0ms (0%)

Compiler: Compiled 13 to 10 computations (23.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	84	69
1	84	69

end0.0ms (0%)

sample1.6s (31.5%)

Algorithm

1×

intervals

Results

262.0ms	2059×	body	1024	valid
142.0ms	4223×	body	128	valid
91.0ms	1004×	body	512	valid
33.0ms	520×	body	256	valid
30.0ms	194×	body	2048	valid

Compiler

Compiled 1195 to 907 computations (24.1% saved)

Details

analyze4.0ms (0.1%)

sample22.0ms (0.4%)

simplify176.0ms (3.4%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite74.0ms (1.4%)

series63.0ms (1.2%)

simplify83.0ms (1.6%)

prune200.0ms (3.9%)

localize9.0ms (0.2%)

rewrite176.0ms (3.4%)

series129.0ms (2.5%)

simplify101.0ms (2%)

prune279.0ms (5.4%)

localize11.0ms (0.2%)

rewrite88.0ms (1.7%)

series116.0ms (2.2%)

simplify88.0ms (1.7%)

prune202.0ms (3.9%)

localize12.0ms (0.2%)

rewrite175.0ms (3.4%)

series112.0ms (2.2%)

simplify128.0ms (2.5%)

prune1.1s (20.7%)

regimes217.0ms (4.2%)

bsearch2.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.6s (31.5%)

Profiling