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)

sample27.0ms (0.2%)

Algorithm

1×

intervals

Results

11.0ms	74×	body	1024	valid
5.0ms	139×	body	128	valid
3.0ms	32×	body	512	valid
1.0ms	11×	body	256	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify106.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	75	17
1	75	17

prune3.0ms (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

17.6b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.1b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.3b	(/.f64 1 (sqrt.f64 x))
1.4b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite347.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

17.1b

Rules

127×	`add-sqr-sqrt_binary64_1464`
118×	`times-frac_binary64_1448`
117×	`*-un-lft-identity_binary64_1442`
76×	`sqrt-prod_binary64_1458`
56×	`add-cube-cbrt_binary64_1477`
27×	`cancel-sign-sub-inv_binary64_1408`
25×	`difference-of-squares_binary64_1411`
13×	`distribute-lft-out--_binary64_1394` `associate-/r*_binary64_1386`
12×	`add-exp-log_binary64_1480`
11×	`distribute-lft-out_binary64_1393`
9×	`pow1_binary64_1503`
8×	`add-cbrt-cube_binary64_1478`
7×	`div-inv_binary64_1439`
6×	`add-log-exp_binary64_1481` `sqrt-div_binary64_1459` `pow-flip_binary64_1516` `associate-/l*_binary64_1387`
4×	`associate-/r/_binary64_1388` `div-exp_binary64_1493`
3×	`flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1/2_binary64_1522` `sqrt-pow1_binary64_1460`
2×	`inv-pow_binary64_1527` `1-exp_binary64_1486` `rec-exp_binary64_1492` `cbrt-undiv_binary64_1476` `frac-2neg_binary64_1453` `clear-num_binary64_1441`
1×	`diff-log_binary64_1534` `frac-sub_binary64_1451` `flip3--_binary64_1446` `sub-neg_binary64_1435` `flip--_binary64_1417` `rem-sqrt-square_binary64_1455`

Counts

4 → 189

Calls

4 calls:

36.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
8.0ms	(/.f64 1 (sqrt.f64 x))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
3.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 3837 to 2945 computations (23.2% saved)

series79.0ms (0.4%)

Error

17.4b

Counts

4 → 14

Calls

4 calls:

25.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
17.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
14.0ms	(sqrt.f64 (+.f64 x 1))
13.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 435 to 360 computations (17.2% saved)

simplify91.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5145	3271

prune244.0ms (1.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	194	9	203
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	195	9	204

Error

17.0b

Counts

204 → 9

Compiler

Compiled 3525 to 2629 computations (25.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
0.3b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
0.3b	(/.f64 1 (sqrt.f64 x))
1.6b	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

rewrite2.2s (12.8%)

Algorithm

1×	rewrite-expression-head

Error

16.9b

Rules

1332×	`*-un-lft-identity_binary64_1442`
1249×	`times-frac_binary64_1448`
725×	`add-sqr-sqrt_binary64_1464`
429×	`distribute-lft-out_binary64_1393`
304×	`sqrt-prod_binary64_1458`
293×	`add-cube-cbrt_binary64_1477`
180×	`distribute-lft-out--_binary64_1394`
168×	`div-inv_binary64_1439`
162×	`difference-of-squares_binary64_1411`
29×	`associate-/r*_binary64_1386`
28×	`associate-/l*_binary64_1387`
18×	`cancel-sign-sub-inv_binary64_1408`
14×	`add-exp-log_binary64_1480`
10×	`add-cbrt-cube_binary64_1478`
8×	`pow1_binary64_1503`
7×	`associate-/r/_binary64_1388`
6×	`add-log-exp_binary64_1481` `pow-flip_binary64_1516`
5×	`div-exp_binary64_1493`
3×	`flip3-+_binary64_1445` `flip-+_binary64_1416` `cbrt-undiv_binary64_1476` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `associate-/l/_binary64_1389`
2×	`frac-sub_binary64_1451` `flip3--_binary64_1446` `flip--_binary64_1417` `inv-pow_binary64_1527` `pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `1-exp_binary64_1486` `rec-exp_binary64_1492` `sqrt-div_binary64_1459`
1×	`diff-log_binary64_1534` `sub-neg_binary64_1435` `div-sub_binary64_1447` `frac-add_binary64_1450`

Counts

4 → 554

Calls

4 calls:

68.0ms	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
19.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))
7.0ms	(/.f64 1 (sqrt.f64 x))
6.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))

Compiler

Compiled 19722 to 15860 computations (19.6% saved)

series130.0ms (0.7%)

Error

5.1b

Counts

4 → 20

Calls

4 calls:

35.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))
33.0ms	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
19.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
15.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 1032 to 847 computations (17.9% saved)

simplify228.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

574 → 574

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5297	21868

prune1.6s (9.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	573	1	574
Fresh	7	1	8
Picked	1	0	1
Done	0	0	0
Total	581	2	583

Error

5.1b

Counts

583 → 2

Compiler

Compiled 17777 to 13863 computations (22% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
0.2b	(/.f64 1 (+.f64 x (*.f64 x x)))
0.3b	(/.f64 1 (sqrt.f64 x))
5.1b	(/.f64 (/.f64 1 (+.f64 x (*.f64 x x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))

rewrite1.7s (9.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

1041×	`times-frac_binary64_1448`
965×	`*-un-lft-identity_binary64_1442`
356×	`distribute-lft-out_binary64_1393`
352×	`add-cube-cbrt_binary64_1477` `add-sqr-sqrt_binary64_1464`
292×	`sqrt-prod_binary64_1458`
109×	`div-inv_binary64_1439`
55×	`distribute-rgt1-in_binary64_1398` `distribute-rgt-out_binary64_1395`
41×	`associate-/r/_binary64_1388`
34×	`associate-/r*_binary64_1386`
30×	`associate-/l*_binary64_1387`
25×	`add-exp-log_binary64_1480`
20×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
15×	`add-cbrt-cube_binary64_1478`
12×	`div-exp_binary64_1493`
9×	`pow1_binary64_1503`
7×	`pow-flip_binary64_1516`
6×	`cbrt-undiv_binary64_1476`
4×	`1-exp_binary64_1486` `rec-exp_binary64_1492` `add-log-exp_binary64_1481` `frac-2neg_binary64_1453` `clear-num_binary64_1441`
3×	`inv-pow_binary64_1527`
2×	`pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `sqrt-div_binary64_1459`
1×	`associate-/l/_binary64_1389` `frac-add_binary64_1450`

Counts

4 → 530

Calls

4 calls:

47.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 x x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
11.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
5.0ms	(/.f64 1 (+.f64 x (*.f64 x x)))
4.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 17492 to 11231 computations (35.8% saved)

series127.0ms (0.7%)

Error

5.1b

Counts

4 → 20

Calls

4 calls:

40.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 x x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
34.0ms	(/.f64 1 (+.f64 x (*.f64 x x)))
18.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
15.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 994 to 776 computations (21.9% saved)

simplify229.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

550 → 550

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4985	18796
1	4985	18796

prune1.1s (6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	543	7	550
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	544	8	552

Error

0.0b

Counts

552 → 8

Compiler

Compiled 15628 to 9645 computations (38.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (+.f64 x 1))
0.2b	(/.f64 x (sqrt.f64 (+.f64 1 x)))
0.3b	(/.f64 (/.f64 1 (+.f64 x 1)) (+.f64 (/.f64 x (sqrt.f64 x)) (/.f64 x (sqrt.f64 (+.f64 1 x)))))
0.5b	(/.f64 x (sqrt.f64 x))

rewrite972.0ms (5.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

840×	`*-un-lft-identity_binary64_1442`
825×	`times-frac_binary64_1448`
319×	`distribute-lft-out_binary64_1393`
297×	`add-cube-cbrt_binary64_1477` `add-sqr-sqrt_binary64_1464`
256×	`sqrt-prod_binary64_1458`
57×	`div-inv_binary64_1439`
37×	`associate-/r/_binary64_1388`
31×	`associate-/r*_binary64_1386`
27×	`associate-/l*_binary64_1387`
21×	`add-exp-log_binary64_1480`
18×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
15×	`add-cbrt-cube_binary64_1478`
10×	`div-exp_binary64_1493`
8×	`pow1_binary64_1503`
6×	`cbrt-undiv_binary64_1476`
4×	`add-log-exp_binary64_1481` `frac-2neg_binary64_1453` `clear-num_binary64_1441`
2×	`pow-div_binary64_1517` `1-exp_binary64_1486` `rec-exp_binary64_1492` `sqrt-div_binary64_1459`
1×	`pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `associate-/l/_binary64_1389` `frac-add_binary64_1450` `inv-pow_binary64_1527` `pow-flip_binary64_1516`

Counts

4 → 427

Calls

4 calls:

48.0ms	(/.f64 (/.f64 1 (+.f64 x 1)) (+.f64 (/.f64 x (sqrt.f64 x)) (/.f64 x (sqrt.f64 (+.f64 1 x)))))
6.0ms	(/.f64 x (sqrt.f64 (+.f64 1 x)))
5.0ms	(/.f64 1 (+.f64 x 1))
5.0ms	(/.f64 x (sqrt.f64 x))

Compiler

Compiled 13137 to 8535 computations (35% saved)

series125.0ms (0.7%)

Error

0.0b

Counts

4 → 20

Calls

4 calls:

39.0ms	(/.f64 (/.f64 1 (+.f64 x 1)) (+.f64 (/.f64 x (sqrt.f64 x)) (/.f64 x (sqrt.f64 (+.f64 1 x)))))
27.0ms	(/.f64 1 (+.f64 x 1))
23.0ms	(/.f64 x (sqrt.f64 (+.f64 1 x)))
18.0ms	(/.f64 x (sqrt.f64 x))

Compiler

Compiled 898 to 659 computations (26.6% saved)

simplify198.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

447 → 447

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4899	13606
1	4899	13606

prune792.0ms (4.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	442	5	447
Fresh	6	1	7
Picked	0	1	1
Done	0	0	0
Total	448	7	455

Error

Counts

455 → 7

Compiler

Compiled 11361 to 7462 computations (34.3% saved)

regimes1.0s (5.7%)

Accuracy

Total 0.3b remaining (100%)

Threshold costs 0.3b (100%)

Compiler

Compiled 13783 to 10891 computations (21% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	24
1	14	24

end0.0ms (0%)

sample6.3s (35.7%)

Algorithm

1×

intervals

Results

337.0ms	2260×	body	1024	valid
171.0ms	4233×	body	128	valid
112.0ms	1046×	body	512	valid
36.0ms	461×	body	256	valid

Compiler

Compiled 6850 to 5410 computations (21% saved)

Details

analyze1.0ms (0%)

sample27.0ms (0.2%)

simplify106.0ms (0.6%)

prune3.0ms (0%)

localize8.0ms (0%)

rewrite347.0ms (2%)

series79.0ms (0.4%)

simplify91.0ms (0.5%)

prune244.0ms (1.4%)

localize12.0ms (0.1%)

rewrite2.2s (12.8%)

series130.0ms (0.7%)

simplify228.0ms (1.3%)

prune1.6s (9.2%)

localize14.0ms (0.1%)

rewrite1.7s (9.5%)

series127.0ms (0.7%)

simplify229.0ms (1.3%)

prune1.1s (6%)

localize11.0ms (0.1%)

rewrite972.0ms (5.5%)

series125.0ms (0.7%)

simplify198.0ms (1.1%)

prune792.0ms (4.5%)

regimes1.0s (5.7%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample6.3s (35.7%)

Profiling