Details

analyze126.0ms (0.9%)

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)

sample35.0ms (0.2%)

Algorithm

1×

intervals

Results

11.0ms	201×	body	128	valid
6.0ms	256×	pre	128	true
4.0ms	21×	body	1024	valid
3.0ms	18×	body	512	valid
2.0ms	14×	body	256	valid
1.0ms	2×	body	2048	valid

Compiler

Compiled 68 to 50 computations (26.5% saved)

simplify219.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5063	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

Merged error: 26.8b

Counts

2 → 1

Compiler

Compiled 58 to 40 computations (31% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.3b

(/.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))

3.4b

(+.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)

20.7b

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

rewrite99.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`times-frac_binary64_1431`
47×	`*-un-lft-identity_binary64_1425`
25×	`add-cube-cbrt_binary64_1457` `add-sqr-sqrt_binary64_1446`
17×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
14×	`associate-/r/_binary64_1373`
11×	`flip3-+_binary64_1428` `distribute-lft-out_binary64_1378` `flip-+_binary64_1399`
10×	`associate-/l*_binary64_1372`
9×	`associate-/l/_binary64_1374`
7×	`associate-/r*_binary64_1371` `div-inv_binary64_1422` `div-exp_binary64_1473` `cbrt-undiv_binary64_1456`
5×	`add-log-exp_binary64_1461`
4×	`frac-times_binary64_1435`
3×	`flip--_binary64_1400` `pow1_binary64_1483` `flip3--_binary64_1429`
2×	`frac-2neg_binary64_1436` `prod-exp_binary64_1471` `cbrt-unprod_binary64_1455` `clear-num_binary64_1424` `associate-r/_binary64_1369` `associate-l/_binary64_1370`
1×	`sum-log_binary64_1513` `+-commutative_binary64_1357`

Counts

3 → 111

Calls

3 calls:

39.0ms

(+.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)

27.0ms

(/.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))

16.0ms

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

series1.4s (9.6%)

Counts

3 → 9

Calls

3 calls:

697.0ms

(+.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)

585.0ms

(/.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))

119.0ms

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

simplify98.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4937	5261
1	4937	5261

prune237.0ms (1.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	110	10	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	10	121

Merged error: 5.8b

Counts

121 → 10

Compiler

Compiled 5408 to 2838 computations (47.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
0.3b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
3.6b	(.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)))))
5.1b	(+.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)

rewrite167.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

321×	`times-frac_binary64_1431`
290×	`*-un-lft-identity_binary64_1425`
211×	`add-sqr-sqrt_binary64_1446`
140×	`add-cube-cbrt_binary64_1457`
90×	`associate-r_binary64_1367`
44×	`distribute-lft-out_binary64_1378`
31×	`distribute-lft-out--_binary64_1379` `difference-of-squares_binary64_1394`
26×	`associate-/l*_binary64_1372`
24×	`associate-/r/_binary64_1373`
20×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
15×	`flip3-+_binary64_1428` `flip-+_binary64_1399`
12×	`div-inv_binary64_1422`
7×	`associate-/r*_binary64_1371` `div-exp_binary64_1473` `cbrt-undiv_binary64_1456`
6×	`pow1_binary64_1483` `add-log-exp_binary64_1461`
4×	`associate-l_binary64_1368`
3×	`unswap-sqr_binary64_1393` `prod-exp_binary64_1471` `cbrt-unprod_binary64_1455` `div-sub_binary64_1430` `associate-/l/_binary64_1374`
2×	`frac-2neg_binary64_1436` `clear-num_binary64_1424` `associate-*l/_binary64_1370` `frac-times_binary64_1435`
1×	`flip--_binary64_1400` `associate-r/_binary64_1369` `sum-log_binary64_1513` `+-commutative_binary64_1357` `flip3--_binary64_1429` `-commutative_binary64_1358` `pow-prod-down_binary64_1493`

Counts

4 → 295

Calls

4 calls:

50.0ms	(.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)))))
29.0ms	(+.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)
21.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
12.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series1.7s (11.8%)

Counts

4 → 12

Calls

4 calls:

697.0ms	(+.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)
593.0ms	(.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)))))
320.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
110.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify151.0ms (1%)

Algorithm

1×	egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4971	13438
1	4971	13438

prune740.0ms (5.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	302	5	307
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	307	10	317

Merged error: 5.8b

Counts

317 → 10

Compiler

Compiled 14724 to 7770 computations (47.2% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
3.6b	(.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)))))
5.1b	(+.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)
5.1b	(log.f64 (exp.f64 (+.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)))

rewrite156.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

162×	`times-frac_binary64_1431`
151×	`*-un-lft-identity_binary64_1425`
116×	`add-sqr-sqrt_binary64_1446`
90×	`associate-r_binary64_1367`
75×	`add-cube-cbrt_binary64_1457`
22×	`distribute-lft-out_binary64_1378`
16×	`distribute-lft-out--_binary64_1379` `difference-of-squares_binary64_1394`
15×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
12×	`associate-/r/_binary64_1373`
9×	`flip3-+_binary64_1428` `flip-+_binary64_1399`
7×	`pow1_binary64_1483`
6×	`div-inv_binary64_1422` `add-log-exp_binary64_1461`
5×	`associate-/l*_binary64_1372`
4×	`associate-l_binary64_1368` `log-prod_binary64_1508` `log-pow_binary64_1511` `div-exp_binary64_1473` `cbrt-undiv_binary64_1456`
3×	`associate-/r*_binary64_1371` `unswap-sqr_binary64_1393` `prod-exp_binary64_1471` `cbrt-unprod_binary64_1455` `exp-prod_binary64_1474`
2×	`associate-/l/_binary64_1374` `associate-*l/_binary64_1370` `frac-times_binary64_1435`
1×	`flip--_binary64_1400` `frac-2neg_binary64_1436` `clear-num_binary64_1424` `associate-r/_binary64_1369` `div-sub_binary64_1430` `sum-log_binary64_1513` `exp-sum_binary64_1468` `+-commutative_binary64_1357` `rem-log-exp_binary64_1463` `flip3--_binary64_1429` `-commutative_binary64_1358` `pow-prod-down_binary64_1493`

Counts

4 → 184

Calls

4 calls:

50.0ms	(.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)))))
31.0ms	(+.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)
30.0ms	(log.f64 (exp.f64 (+.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)))
12.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series2.5s (17.4%)

Counts

4 → 12

Calls

4 calls:

1.2s	(log.f64 (exp.f64 (+.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)))
667.0ms	(+.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)
590.0ms	(.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)))))
110.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify106.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4948	7173
1	4948	7173

prune433.0ms (3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	195	1	196
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	195	11	206

Merged error: 5.7b

Counts

206 → 11

Compiler

Compiled 9626 to 5275 computations (45.2% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.6b	(.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)))))
3.6b	(.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)))))
5.1b	(+.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)
5.1b	(+.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)

rewrite380.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

294×	`times-frac_binary64_1431`
258×	`*-un-lft-identity_binary64_1425`
188×	`add-sqr-sqrt_binary64_1446`
180×	`associate-r_binary64_1367`
122×	`add-cube-cbrt_binary64_1457`
44×	`distribute-lft-out_binary64_1378`
24×	`distribute-lft-out--_binary64_1379` `difference-of-squares_binary64_1394`
22×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
20×	`associate-/r/_binary64_1373`
16×	`flip3-+_binary64_1428` `flip-+_binary64_1399`
10×	`div-inv_binary64_1422`
8×	`associate-l_binary64_1368` `pow1_binary64_1483` `add-log-exp_binary64_1461`
6×	`unswap-sqr_binary64_1393` `prod-exp_binary64_1471` `cbrt-unprod_binary64_1455` `div-exp_binary64_1473` `cbrt-undiv_binary64_1456`
4×	`associate-*l/_binary64_1370` `frac-times_binary64_1435`
2×	`associate-r/_binary64_1369` `sum-log_binary64_1513` `+-commutative_binary64_1357` `-commutative_binary64_1358` `pow-prod-down_binary64_1493`

Counts

4 → 256

Calls

4 calls:

51.0ms	(.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)))))
46.0ms	(.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)))))
33.0ms	(+.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)
33.0ms	(+.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)

series2.5s (17.1%)

Counts

4 → 12

Calls

4 calls:

672.0ms	(+.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)
665.0ms	(+.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)
575.0ms	(.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)))))
572.0ms	(.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)))))

simplify129.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

268 → 268

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5152	10534

prune1.5s (10.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	268	0	268
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	268	11	279

Merged error: 5.7b

Counts

279 → 11

Compiler

Compiled 21816 to 12009 computations (45% saved)

regimes171.0ms (1.2%)

Compiler: Compiled 2132 to 1368 computations (35.8% saved)

bsearch106.0ms (0.7%)

Steps

Iters	Range		Point
8	8.489737402972492e+210	1.3466033699607912e+215	2.9136664706659033e+211
6	7.678961252145001e+85	1.0656915599992308e+87	9.854544423750154e+86
10	24425790.248319037	4.2719404142716026e+17	2111869904734.4092

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	78	189
1	78	189

end0.0ms (0%)

sample1.5s (10.2%)

Algorithm

1×

intervals

Results

363.0ms	6458×	body	128	valid
182.0ms	8000×	pre	128	true
149.0ms	665×	body	1024	valid
86.0ms	521×	body	512	valid
37.0ms	320×	body	256	valid
10.0ms	36×	body	2048	valid

Compiler

Compiled 693 to 445 computations (35.8% saved)

Details

analyze126.0ms (0.9%)

sample35.0ms (0.2%)

simplify219.0ms (1.5%)

prune3.0ms (0%)

localize13.0ms (0.1%)

rewrite99.0ms (0.7%)

series1.4s (9.6%)

simplify98.0ms (0.7%)

prune237.0ms (1.6%)

localize13.0ms (0.1%)

rewrite167.0ms (1.1%)

series1.7s (11.8%)

simplify151.0ms (1%)

prune740.0ms (5.1%)

localize20.0ms (0.1%)

rewrite156.0ms (1.1%)

series2.5s (17.4%)

simplify106.0ms (0.7%)

prune433.0ms (3%)

localize24.0ms (0.2%)

rewrite380.0ms (2.6%)

series2.5s (17.1%)

simplify129.0ms (0.9%)

prune1.5s (10.3%)

regimes171.0ms (1.2%)

bsearch106.0ms (0.7%)

simplify4.0ms (0%)

end0.0ms (0%)

sample1.5s (10.2%)

Profiling