Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
28.1%	28.1%	43.8%	2
56.2%	0%	43.8%	3

Compiler

Compiled 20 to 16 computations (20% saved)

sample24.0ms (0.4%)

Algorithm

1×

intervals

Results

6.0ms	187×	body	128	valid
4.0ms	256×	pre	128	true
4.0ms	31×	body	1024	valid
2.0ms	19×	body	512	valid
1.0ms	17×	body	256	valid
0.0ms	2×	body	2048	valid

Compiler

Compiled 33 to 29 computations (12.1% saved)

simplify342.0ms (5.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (247.0ms)

Iter	Nodes	Cost
0	5018	19

prune7.0ms (0.1%)

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

16.8b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
1.7b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite35.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64_1442`
26×	`add-sqr-sqrt_binary64_1464`
25×	`times-frac_binary64_1448`
19×	`distribute-lft-out_binary64_1393`
14×	`add-cube-cbrt_binary64_1477`
6×	`difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394`
5×	`associate-/r_binary64_1386` `associate-/l_binary64_1387`
4×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480`
2×	`associate-/l/_binary64_1389` `associate-/r/_binary64_1388` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1_binary64_1503` `div-sub_binary64_1447`
1×	`cbrt-undiv_binary64_1476` `sum-log_binary64_1533` `div-inv_binary64_1439` `clear-num_binary64_1441` `flip3--_binary64_1446` `+-commutative_binary64_1372` `flip--_binary64_1417` `frac-2neg_binary64_1453` `associate-+l-_binary64_1377` `div-exp_binary64_1493`

Counts

2 → 65

Calls

2 calls:

19.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
11.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

series80.0ms (1.4%)

Counts

2 → 6

Calls

2 calls:

47.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
33.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

simplify70.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	6172	1488

prune94.0ms (1.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	59	12	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	12	72

Error

16.1b

Counts

72 → 12

Compiler

Compiled 1753 to 994 computations (43.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
0.0b	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) 2)
1.7b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite108.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`*-un-lft-identity_binary64_1442`
76×	`add-sqr-sqrt_binary64_1464`
47×	`times-frac_binary64_1448`
29×	`add-cube-cbrt_binary64_1477`
18×	`difference-of-squares_binary64_1411`
17×	`distribute-lft-out--_binary64_1394`
16×	`cancel-sign-sub-inv_binary64_1408`
12×	`distribute-lft-out_binary64_1393`
11×	`add-log-exp_binary64_1481`
10×	`associate-/l*_binary64_1387`
8×	`associate-/r*_binary64_1386` `add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
5×	`flip3--_binary64_1446` `flip--_binary64_1417`
4×	`associate-/l/_binary64_1389` `frac-sub_binary64_1451` `difference-of-sqr-1_binary64_1412` `diff-log_binary64_1534` `associate--r+_binary64_1378` `pow1_binary64_1503`
3×	`sub-neg_binary64_1435`
2×	`cbrt-undiv_binary64_1476` `div-inv_binary64_1439` `associate-/r/_binary64_1388` `clear-num_binary64_1441` `frac-2neg_binary64_1453` `div-exp_binary64_1493`
1×	`flip3-+_binary64_1445` `flip-+_binary64_1416` `div-sub_binary64_1447` `associate--r-_binary64_1381`

Counts

4 → 139

Calls

4 calls:

36.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
35.0ms	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) 2)
15.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
8.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))

series180.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

55.0ms	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) 2)
49.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
48.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
27.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))

simplify103.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4907	4383
1	4907	4383

prune226.0ms (3.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	144	7	151
Fresh	10	1	11
Picked	1	0	1
Done	0	0	0
Total	155	8	163

Error

2.8b

Counts

163 → 8

Compiler

Compiled 4674 to 2854 computations (38.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2))) -1) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))) 2)
0.0b	(/.f64 (+.f64 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2))) -1) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))
0.1b	(*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)))
1.7b	(+.f64 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2))) -1)

rewrite205.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Rules

363×	`*-un-lft-identity_binary64_1442`
222×	`times-frac_binary64_1448`
141×	`add-sqr-sqrt_binary64_1464`
113×	`distribute-lft-out_binary64_1393`
81×	`add-cube-cbrt_binary64_1477`
39×	`swap-sqr_binary64_1409`
28×	`distribute-lft-out--_binary64_1394`
21×	`associate-r_binary64_1382` `associate-l_binary64_1383`
20×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
18×	`associate-/l*_binary64_1387`
16×	`difference-of-squares_binary64_1411`
11×	`pow1_binary64_1503`
10×	`associate-/r/_binary64_1388`
7×	`associate-/r*_binary64_1386` `flip3-+_binary64_1445` `flip-+_binary64_1416`
6×	`cbrt-undiv_binary64_1476` `div-inv_binary64_1439` `difference-of-sqr--1_binary64_1413` `add-log-exp_binary64_1481` `div-exp_binary64_1493`
5×	`associate-/l/_binary64_1389`
4×	`cbrt-unprod_binary64_1475` `prod-exp_binary64_1491` `unswap-sqr_binary64_1410`
2×	`clear-num_binary64_1441` `frac-2neg_binary64_1453`
1×	`pow2_binary64_1523` `associate-r/_binary64_1384` `sum-log_binary64_1533` `pow-plus_binary64_1505` `flip3--_binary64_1446` `+-commutative_binary64_1372` `frac-sub_binary64_1451` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `pow-sqr_binary64_1415` `flip--_binary64_1417` `frac-times_binary64_1452` `div-sub_binary64_1447` `pow-prod-up_binary64_1512` `associate-*l/_binary64_1385`

Counts

4 → 236

Calls

4 calls:

72.0ms	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2))) -1) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))) 2)
36.0ms	(/.f64 (+.f64 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2))) -1) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))
27.0ms	(*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)))
21.0ms	(+.f64 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2))) -1)

series330.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

133.0ms	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2))) -1) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))) 2)
95.0ms	(/.f64 (+.f64 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2))) -1) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))
62.0ms	(+.f64 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2))) -1)
39.0ms	(*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)))

simplify141.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4942	9953
1	4942	9953

prune617.0ms (10.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	247	1	248
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	248	8	256

Error

2.8b

Counts

256 → 8

Compiler

Compiled 11583 to 7140 computations (38.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2)
0.5b	(exp.f64 (log.f64 (/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2)))
1.7b	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
7.9b	(log.f64 (/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2))

rewrite141.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

101×	`add-sqr-sqrt_binary64_1464`
94×	`*-un-lft-identity_binary64_1442`
76×	`times-frac_binary64_1448`
50×	`log-prod_binary64_1528`
40×	`add-cube-cbrt_binary64_1477`
31×	`distribute-lft-out--_binary64_1394`
25×	`exp-sum_binary64_1488`
24×	`difference-of-squares_binary64_1411`
9×	`add-exp-log_binary64_1480`
7×	`associate-/l*_binary64_1387`
6×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481` `pow1_binary64_1503`
4×	`associate-/l/_binary64_1389` `exp-prod_binary64_1494`
3×	`associate-/r*_binary64_1386` `cancel-sign-sub-inv_binary64_1408` `div-inv_binary64_1439` `flip3--_binary64_1446` `flip--_binary64_1417`
2×	`rem-log-exp_binary64_1483` `log-pow_binary64_1531` `frac-sub_binary64_1451` `difference-of-sqr-1_binary64_1412` `log-div_binary64_1529` `div-exp_binary64_1493`
1×	`cbrt-undiv_binary64_1476` `sub-neg_binary64_1435` `clear-num_binary64_1441` `rem-exp-log_binary64_1482` `frac-2neg_binary64_1453` `diff-log_binary64_1534` `exp-diff_binary64_1490` `div-sub_binary64_1447`

Counts

4 → 143

Calls

4 calls:

39.0ms	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2)
34.0ms	(exp.f64 (log.f64 (/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2)))
34.0ms	(log.f64 (/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2))
15.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)

series303.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

118.0ms	(log.f64 (/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2))
89.0ms	(exp.f64 (log.f64 (/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2)))
49.0ms	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)) 2)
47.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)

simplify116.0ms (2%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4916	5928
1	4916	5928

prune254.0ms (4.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	150	5	155
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	155	8	163

Error

2.8b

Counts

163 → 8

Compiler

Compiled 5054 to 3267 computations (35.4% saved)

regimes516.0ms (8.9%)

Accuracy

Total 0.1b remaining (3.6%)

Threshold costs 0.1b (3.6%)

Compiler

Compiled 7700 to 5517 computations (28.4% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	227	110
1	227	110

end0.0ms (0%)

sample1.9s (32.2%)

Algorithm

1×

intervals

Results

193.0ms	5894×	body	128	valid
144.0ms	8000×	pre	128	true
129.0ms	1054×	body	1024	valid
56.0ms	585×	body	512	valid
22.0ms	364×	body	256	valid
16.0ms	103×	body	2048	valid

Compiler

Compiled 1620 to 1157 computations (28.6% saved)

Details

analyze3.0ms (0.1%)

sample24.0ms (0.4%)

simplify342.0ms (5.9%)

prune7.0ms (0.1%)

localize8.0ms (0.1%)

rewrite35.0ms (0.6%)

series80.0ms (1.4%)

simplify70.0ms (1.2%)

prune94.0ms (1.6%)

localize12.0ms (0.2%)

rewrite108.0ms (1.9%)

series180.0ms (3.1%)

simplify103.0ms (1.8%)

prune226.0ms (3.9%)

localize14.0ms (0.2%)

rewrite205.0ms (3.5%)

series330.0ms (5.7%)

simplify141.0ms (2.4%)

prune617.0ms (10.6%)

localize13.0ms (0.2%)

rewrite141.0ms (2.4%)

series303.0ms (5.2%)

simplify116.0ms (2%)

prune254.0ms (4.4%)

regimes516.0ms (8.9%)

bsearch3.0ms (0.1%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample1.9s (32.2%)

Profiling