Details

analyze154.0ms (1.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	28.1%	71.9%	0
0%	28.1%	71.9%	1
0%	28.1%	71.9%	2
0%	28.1%	71.9%	3
3.5%	24.6%	71.9%	4
5.3%	22.8%	71.9%	5
10.5%	17.5%	71.9%	6
14%	14%	71.9%	7
19.1%	9%	71.9%	8
24.6%	3.5%	71.9%	9
25.1%	3%	71.9%	10
25.8%	2.3%	71.9%	11
26.3%	1.8%	71.9%	12
26.6%	1.5%	71.9%	13
26.9%	1.2%	71.9%	14

Compiler

Compiled 39 to 27 computations (30.8% saved)

sample39.0ms (0.3%)

Algorithm

1×

intervals

Results

11.0ms	207×	body	128	valid
8.0ms	25×	body	1024	valid
6.0ms	256×	pre	128	true
2.0ms	13×	body	512	valid
1.0ms	8×	body	256	valid
1.0ms	3×	body	2048	valid

Compiler

Compiled 68 to 50 computations (26.5% saved)

simplify193.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	5371	43

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

25.3b

Counts

2 → 1

Compiler

Compiled 58 to 40 computations (31% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b

(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))

1.0b

(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

20.5b

(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

rewrite155.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`times-frac_binary64_1448`
47×	`*-un-lft-identity_binary64_1442`
25×	`add-sqr-sqrt_binary64_1464` `add-cube-cbrt_binary64_1477`
17×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
14×	`associate-/r/_binary64_1388`
11×	`distribute-lft-out_binary64_1393` `flip3-+_binary64_1445` `flip-+_binary64_1416`
10×	`associate-/l*_binary64_1387`
9×	`associate-/l/_binary64_1389`
7×	`cbrt-undiv_binary64_1476` `associate-/r*_binary64_1386` `div-inv_binary64_1439` `div-exp_binary64_1493`
5×	`add-log-exp_binary64_1481`
4×	`frac-times_binary64_1452`
3×	`flip3--_binary64_1446` `flip--_binary64_1417` `pow1_binary64_1503`
2×	`associate-r/_binary64_1384` `cbrt-unprod_binary64_1475` `clear-num_binary64_1441` `frac-2neg_binary64_1453` `prod-exp_binary64_1491` `associate-l/_binary64_1385`
1×	`sum-log_binary64_1533` `+-commutative_binary64_1372`

Counts

3 → 111

Calls

3 calls:

60.0ms

(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

44.0ms

(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))

19.0ms

(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series904.0ms (6.6%)

Counts

3 → 9

Calls

3 calls:

438.0ms

(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

373.0ms

(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))

92.0ms

(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify193.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (107.0ms)

Iter	Nodes	Cost
0	4941	5261
1	4941	5261

prune292.0ms (2.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	113	7	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	114	7	121

Error

4.5b

Counts

121 → 7

Compiler

Compiled 5248 to 2745 computations (47.7% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.1b	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
2.3b	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
2.3b	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))

rewrite234.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

321×	`times-frac_binary64_1448`
290×	`*-un-lft-identity_binary64_1442`
211×	`add-sqr-sqrt_binary64_1464`
140×	`add-cube-cbrt_binary64_1477`
90×	`associate-r_binary64_1382`
44×	`distribute-lft-out_binary64_1393`
31×	`difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394`
26×	`associate-/l*_binary64_1387`
24×	`associate-/r/_binary64_1388`
20×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
15×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
12×	`div-inv_binary64_1439`
7×	`cbrt-undiv_binary64_1476` `associate-/r*_binary64_1386` `div-exp_binary64_1493`
6×	`add-log-exp_binary64_1481` `pow1_binary64_1503`
4×	`associate-l_binary64_1383`
3×	`cbrt-unprod_binary64_1475` `associate-/l/_binary64_1389` `prod-exp_binary64_1491` `div-sub_binary64_1447` `unswap-sqr_binary64_1410`
2×	`clear-num_binary64_1441` `frac-2neg_binary64_1453` `frac-times_binary64_1452` `associate-*l/_binary64_1385`
1×	`associate-r/_binary64_1384` `sum-log_binary64_1533` `flip3--_binary64_1446` `+-commutative_binary64_1372` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `flip--_binary64_1417`

Counts

4 → 295

Calls

4 calls:

72.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
58.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
28.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
11.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series1.1s (8.2%)

Counts

4 → 12

Calls

4 calls:

483.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
378.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
201.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
66.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify197.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5014	13438

prune950.0ms (6.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	304	3	307
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	307	7	314

Error

4.5b

Counts

314 → 7

Compiler

Compiled 14545 to 7666 computations (47.3% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.1b	(.f64 (+.f64 alpha beta) (/.f64 (log.f64 (exp.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
1.5b	(log.f64 (exp.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
2.3b	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (log.f64 (exp.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

rewrite208.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

191×	`times-frac_binary64_1448`
181×	`*-un-lft-identity_binary64_1442`
134×	`add-sqr-sqrt_binary64_1464`
110×	`log-pow_binary64_1531`
106×	`associate-r_binary64_1382`
105×	`exp-prod_binary64_1494`
91×	`add-cube-cbrt_binary64_1477`
26×	`distribute-lft-out_binary64_1393`
19×	`difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394`
14×	`associate-/r/_binary64_1388`
11×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503`
10×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
7×	`div-inv_binary64_1439`
6×	`add-log-exp_binary64_1481`
5×	`associate-/l*_binary64_1387`
4×	`associate-l_binary64_1383`
3×	`associate-/r*_binary64_1386` `log-prod_binary64_1528`
2×	`cbrt-undiv_binary64_1476` `cbrt-unprod_binary64_1475` `associate-/l/_binary64_1389` `frac-times_binary64_1452` `prod-exp_binary64_1491` `div-sub_binary64_1447` `associate-*l/_binary64_1385` `div-exp_binary64_1493` `unswap-sqr_binary64_1410`
1×	`associate-r/_binary64_1384` `sum-log_binary64_1533` `clear-num_binary64_1441` `rem-log-exp_binary64_1483` `flip3--_binary64_1446` `+-commutative_binary64_1372` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `flip--_binary64_1417` `frac-2neg_binary64_1453` `exp-diff_binary64_1490` `log-div_binary64_1529`

Counts

4 → 215

Calls

4 calls:

61.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (log.f64 (exp.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
56.0ms	(.f64 (+.f64 alpha beta) (/.f64 (log.f64 (exp.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
15.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
15.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series1.4s (10.3%)

Counts

4 → 12

Calls

4 calls:

627.0ms	(.f64 (+.f64 alpha beta) (/.f64 (log.f64 (exp.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
578.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (log.f64 (exp.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
112.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
90.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify187.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5254	7380

prune765.0ms (5.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	226	1	227
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	227	7	234

Error

4.5b

Counts

234 → 7

Compiler

Compiled 10742 to 5849 computations (45.6% saved)

localize40.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.3b	(+.f64 (.f64 (.f64 (+.f64 alpha beta) (.f64 (cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))))) (/.f64 (cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
5.5b	(cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
5.5b	(cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
5.5b	(cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

rewrite152.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`cbrt-prod_binary64_1473`
49×	`add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
45×	`times-frac_binary64_1448`
31×	`add-cube-cbrt_binary64_1477`
9×	`difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394`
6×	`associate-/r/_binary64_1388` `add-log-exp_binary64_1481`
4×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1_binary64_1503`
3×	`cbrt-div_binary64_1474` `div-inv_binary64_1439` `pow1/3_binary64_1524`
1×	`sum-log_binary64_1533` `+-commutative_binary64_1372`

Counts

4 → 101

Calls

4 calls:

95.0ms	(+.f64 (.f64 (.f64 (+.f64 alpha beta) (.f64 (cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))))) (/.f64 (cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
15.0ms	(cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
10.0ms	(cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
9.0ms	(cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

series1.8s (13%)

Counts

4 → 12

Calls

4 calls:

526.0ms	(+.f64 (.f64 (.f64 (+.f64 alpha beta) (.f64 (cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))))) (/.f64 (cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
459.0ms	(cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
422.0ms	(cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
380.0ms	(cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

simplify126.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4919	3861
1	4919	3861

prune388.0ms (2.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	113	7	120

Error

4.5b

Counts

120 → 7

Compiler

Compiled 7276 to 3704 computations (49.1% saved)

regimes1.0s (7.3%)

Accuracy

Total 1.7b remaining (22.8%)

Threshold costs 0b (0%)

Compiler

Compiled 11757 to 7769 computations (33.9% saved)

bsearch7.0ms (0.1%)

Compiler: Compiled 25 to 16 computations (36% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	105
1	48	105

end0.0ms (0%)

sample3.1s (22.9%)

Algorithm

1×

intervals

Results

557.0ms	6485×	body	128	valid
257.0ms	8000×	pre	128	true
243.0ms	697×	body	1024	valid
116.0ms	456×	body	512	valid
54.0ms	307×	body	256	valid
23.0ms	55×	body	2048	valid

Compiler

Compiled 1726 to 1137 computations (34.1% saved)

Details

analyze154.0ms (1.1%)

sample39.0ms (0.3%)

simplify193.0ms (1.4%)

prune3.0ms (0%)

localize13.0ms (0.1%)

rewrite155.0ms (1.1%)

series904.0ms (6.6%)

simplify193.0ms (1.4%)

prune292.0ms (2.1%)

localize12.0ms (0.1%)

rewrite234.0ms (1.7%)

series1.1s (8.2%)

simplify197.0ms (1.4%)

prune950.0ms (6.9%)

localize31.0ms (0.2%)

rewrite208.0ms (1.5%)

series1.4s (10.3%)

simplify187.0ms (1.4%)

prune765.0ms (5.6%)

localize40.0ms (0.3%)

rewrite152.0ms (1.1%)

series1.8s (13%)

simplify126.0ms (0.9%)

prune388.0ms (2.8%)

regimes1.0s (7.3%)

bsearch7.0ms (0.1%)

simplify5.0ms (0%)

end0.0ms (0%)

sample3.1s (22.9%)

Profiling