Details

analyze1.1s (7.3%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4810	96
1	4810	96
0	3	3
1	3	3

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample73.0ms (0.5%)

Algorithm

1×

intervals

Results

15.0ms	167×	body	128	valid
12.0ms	27×	body	2048	valid
9.0ms	25×	body	1024	valid
8.0ms	14×	body	4096	valid
5.0ms	16×	body	512	valid
2.0ms	20×	body	128	nan
1.0ms	7×	body	256	valid
1.0ms	11×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify371.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (361.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

32.9b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
20.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite231.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

32.6b

Rules

24×	`*-un-lft-identity_binary64_1442`
15×	`add-sqr-sqrt_binary64_1464`
14×	`add-cube-cbrt_binary64_1477`
12×	`times-frac_binary64_1448`
8×	`add-log-exp_binary64_1481`
6×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
5×	`pow1_binary64_1503` `distribute-lft-out_binary64_1393`
4×	`associate-/l*_binary64_1387`
3×	`sqrt-prod_binary64_1458` `associate-/r*_binary64_1386`
2×	`flip3--_binary64_1446` `sqrt-div_binary64_1459` `flip--_binary64_1417` `flip3-+_binary64_1445` `flip-+_binary64_1416` `associate-/l/_binary64_1389`
1×	`pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `sum-log_binary64_1533` `+-commutative_binary64_1372` `diff-log_binary64_1534` `sub-neg_binary64_1435` `cancel-sign-sub-inv_binary64_1408` `div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `div-inv_binary64_1439`

Counts

4 → 72

Calls

4 calls:

13.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 2053 to 1050 computations (48.9% saved)

series1.1s (7.6%)

Error

5.6b

Counts

4 → 76

Calls

4 calls:

268.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
257.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
231.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
227.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 3466 to 2621 computations (24.4% saved)

simplify92.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5033	3065

prune228.0ms (1.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	137	11	148
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	138	11	149

Error

5.5b

Counts

149 → 11

Compiler

Compiled 3214 to 1717 computations (46.6% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
20.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite328.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

5.5b

Rules

102×	`times-frac_binary64_1448`
82×	`*-un-lft-identity_binary64_1442`
57×	`add-sqr-sqrt_binary64_1464`
56×	`add-cube-cbrt_binary64_1477`
18×	`associate-/r*_binary64_1386`
15×	`add-exp-log_binary64_1480`
13×	`distribute-lft-out_binary64_1393`
9×	`add-cbrt-cube_binary64_1478` `associate-/r/_binary64_1388`
8×	`add-log-exp_binary64_1481`
7×	`div-exp_binary64_1493`
6×	`pow1_binary64_1503`
5×	`flip3-+_binary64_1445` `flip-+_binary64_1416` `div-inv_binary64_1439`
3×	`sqrt-prod_binary64_1458` `cbrt-undiv_binary64_1476` `associate-/l*_binary64_1387`
2×	`flip3--_binary64_1446` `sqrt-div_binary64_1459` `flip--_binary64_1417` `1-exp_binary64_1486` `rec-exp_binary64_1492`
1×	`pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `sum-log_binary64_1533` `+-commutative_binary64_1372` `diff-log_binary64_1534` `sub-neg_binary64_1435` `cancel-sign-sub-inv_binary64_1408` `inv-pow_binary64_1527` `pow-flip_binary64_1516` `frac-2neg_binary64_1453` `clear-num_binary64_1441`

Counts

4 → 135

Calls

4 calls:

12.0ms	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 4590 to 2591 computations (43.6% saved)

series1.2s (8.2%)

Error

5.5b

Counts

4 → 76

Calls

4 calls:

304.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
282.0ms	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
270.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
250.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 3744 to 2901 computations (22.5% saved)

simplify94.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4992	5551
1	4992	5551

prune351.0ms (2.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	209	2	211
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	212	10	222

Error

5.5b

Counts

222 → 10

Compiler

Compiled 5403 to 3006 computations (44.4% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
20.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite228.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

5.5b

Rules

21×	`add-sqr-sqrt_binary64_1464`
18×	`*-un-lft-identity_binary64_1442`
13×	`add-exp-log_binary64_1480` `add-cube-cbrt_binary64_1477` `associate-r_binary64_1382`
11×	`times-frac_binary64_1448`
9×	`add-cbrt-cube_binary64_1478`
8×	`add-log-exp_binary64_1481`
7×	`pow1_binary64_1503`
4×	`prod-exp_binary64_1491` `associate-l_binary64_1383`
3×	`sqrt-prod_binary64_1458` `flip3-+_binary64_1445` `flip-+_binary64_1416` `unswap-sqr_binary64_1410`
2×	`flip3--_binary64_1446` `sqrt-div_binary64_1459` `flip--_binary64_1417` `distribute-lft-out_binary64_1393` `div-exp_binary64_1493` `cbrt-unprod_binary64_1475` `frac-times_binary64_1452` `associate-*l/_binary64_1385`
1×	`pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `sum-log_binary64_1533` `+-commutative_binary64_1372` `diff-log_binary64_1534` `sub-neg_binary64_1435` `cancel-sign-sub-inv_binary64_1408` `pow-prod-down_binary64_1513` `1-exp_binary64_1486` `rec-exp_binary64_1492` `cbrt-undiv_binary64_1476` `un-div-inv_binary64_1440` `associate-r/_binary64_1384` `div-inv_binary64_1439` `-commutative_binary64_1373`

Counts

4 → 80

Calls

4 calls:

18.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
13.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
7.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 2417 to 1345 computations (44.4% saved)

series1.2s (8.1%)

Error

5.5b

Counts

4 → 76

Calls

4 calls:

309.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
303.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
265.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
226.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 3744 to 2908 computations (22.3% saved)

simplify95.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4968	3105
1	4968	3105

prune221.0ms (1.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	156	10	166

Error

5.5b

Counts

166 → 10

Compiler

Compiled 3473 to 1977 computations (43.1% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
20.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
20.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
20.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite212.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

5.5b

Rules

10×	`add-sqr-sqrt_binary64_1464`
9×	`sqrt-prod_binary64_1458` `*-un-lft-identity_binary64_1442`
7×	`pow1_binary64_1503` `add-cube-cbrt_binary64_1477`
6×	`add-log-exp_binary64_1481` `sqrt-div_binary64_1459`
4×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
3×	`pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `flip3--_binary64_1446` `flip--_binary64_1417` `rem-sqrt-square_binary64_1455`
1×	`sum-log_binary64_1533` `flip3-+_binary64_1445` `flip-+_binary64_1416` `distribute-lft-out_binary64_1393` `+-commutative_binary64_1372`

Counts

4 → 57

Calls

4 calls:

12.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
9.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 3228 to 1668 computations (48.3% saved)

series1.2s (8%)

Error

5.5b

Counts

4 → 79

Calls

4 calls:

270.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
252.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
251.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
229.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))

Compiler

Compiled 9568 to 5982 computations (37.5% saved)

simplify65.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4983	2633
1	4983	2633

prune397.0ms (2.7%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	136	10	146

Error

5.5b

Counts

146 → 10

Compiler

Compiled 6691 to 3468 computations (48.2% saved)

regimes1.6s (11.2%)

Accuracy

Total 3.3b remaining (37%)

Threshold costs 0b (0%)

Compiler

Compiled 7416 to 5382 computations (27.4% saved)

bsearch119.0ms (0.8%)

Steps

Iters	Range	Point
9	1.9104625263991283e+43	3.065541182071303e+49	3.0185045942898314e+49
9	-2.1847048076737034e-284	-2.43617909668472e-289	-2.535008326067869e-289
9	-3.827397424457087e+119	-6.300932638438881e+110	-3.4633822406296006e+113

Iters

Range

Point

1.9104625263991283e+43

3.065541182071303e+49

3.0185045942898314e+49

-2.1847048076737034e-284

-2.43617909668472e-289

-2.535008326067869e-289

-3.827397424457087e+119

-6.300932638438881e+110

-3.4633822406296006e+113

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	127	103
1	127	103

end0.0ms (0%)

sample4.0s (27.6%)

Algorithm

1×

intervals

Results

358.0ms	1140×	body	2048	valid
349.0ms	5202×	body	128	valid
287.0ms	165×	body	256	valid
178.0ms	724×	body	1024	valid
148.0ms	399×	body	4096	valid
68.0ms	370×	body	512	valid
44.0ms	675×	body	128	nan
23.0ms	372×	body	128	invalid

Compiler

Compiled 1973 to 1424 computations (27.8% saved)

Details

analyze1.1s (7.3%)

sample73.0ms (0.5%)

simplify371.0ms (2.5%)

prune5.0ms (0%)

localize16.0ms (0.1%)

rewrite231.0ms (1.6%)

series1.1s (7.6%)

simplify92.0ms (0.6%)

prune228.0ms (1.6%)

localize16.0ms (0.1%)

rewrite328.0ms (2.2%)

series1.2s (8.2%)

simplify94.0ms (0.6%)

prune351.0ms (2.4%)

localize24.0ms (0.2%)

rewrite228.0ms (1.6%)

series1.2s (8.1%)

simplify95.0ms (0.6%)

prune221.0ms (1.5%)

localize32.0ms (0.2%)

rewrite212.0ms (1.5%)

series1.2s (8%)

simplify65.0ms (0.4%)

prune397.0ms (2.7%)

regimes1.6s (11.2%)

bsearch119.0ms (0.8%)

simplify4.0ms (0%)

end0.0ms (0%)

sample4.0s (27.6%)

Profiling