Details

analyze43.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	14%	86%	0
0%	14%	86%	1
0%	14%	86%	2
0%	14%	86%	3
0%	14%	86%	4
0%	14%	86%	5
0%	14%	86%	6
8.1%	5.9%	86%	7
10.3%	3.7%	86%	8
12.6%	1.5%	86%	9
13.9%	0.1%	86%	10
14%	0%	86%	11
14%	0%	86%	12
14%	0%	86%	13
14%	0%	86%	14

Compiler

Compiled 63 to 34 computations (46% saved)

sample45.0ms (0.1%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
9.0ms	256×	pre	128	true

Compiler

Compiled 116 to 64 computations (44.8% saved)

simplify134.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5395	79

prune4.0ms (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

55.0b

Counts

2 → 1

Compiler

Compiled 106 to 54 computations (49.1% saved)

localize19.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.1b	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
36.2b	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
47.1b	(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

rewrite839.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

38.4b

Rules

86×	`times-frac_binary64_1448`
66×	`flip3-+_binary64_1445` `flip-+_binary64_1416` `associate-/r/_binary64_1388`
61×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
46×	`add-sqr-sqrt_binary64_1464`
44×	`*-un-lft-identity_binary64_1442` `frac-times_binary64_1452`
34×	`associate-*r/_binary64_1384`
30×	`add-cube-cbrt_binary64_1477`
28×	`difference-of-squares_binary64_1411`
22×	`prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `associate-*l/_binary64_1385`
19×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476`
16×	`pow1_binary64_1503`
14×	`associate-/l*_binary64_1387` `difference-of-sqr-1_binary64_1412`
9×	`div-inv_binary64_1439` `associate-/l/_binary64_1389`
7×	`associate-/r*_binary64_1386`
6×	`associate-r_binary64_1382`
4×	`add-log-exp_binary64_1481` `pow-prod-down_binary64_1513` `associate-l_binary64_1383`
3×	`swap-sqr_binary64_1409`
2×	`frac-2neg_binary64_1453` `clear-num_binary64_1441` `distribute-rgt-in_binary64_1392` `distribute-lft-in_binary64_1391` `*-commutative_binary64_1373`
1×	`flip3--_binary64_1446` `flip--_binary64_1417` `pow2_binary64_1523` `pow-prod-up_binary64_1512` `pow-plus_binary64_1505` `pow-sqr_binary64_1415` `unswap-sqr_binary64_1410`

Counts

4 → 228

Calls

4 calls:

42.0ms	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
27.0ms	(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
13.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
13.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

Compiler

Compiled 19221 to 7168 computations (62.7% saved)

series10.5s (21.8%)

Error

10.3b

Counts

4 → 103

Calls

4 calls:

8.8s	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
530.0ms	(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
484.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
245.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

Compiler

Compiled 26437 to 17872 computations (32.4% saved)

simplify218.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

331 → 331

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5013	26298

prune1.3s (2.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	322	9	331
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	323	9	332

Error

8.4b

Counts

332 → 9

Compiler

Compiled 25347 to 11222 computations (55.7% saved)

localize0.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

8.4b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 8.4b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune16.0ms (0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	8	8
Picked	1	1
Done	0	0
Total	9	9

Error

8.4b

Counts

9 → 9

Compiler

Compiled 364 to 224 computations (38.5% saved)

localize20.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (*.f64 2 i)))))
0.1b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (.f64 2 i))))) (/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1)))
35.3b	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
36.0b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (*.f64 2 i))))

rewrite2.0s (4.1%)

Algorithm

1×	rewrite-expression-head

Error

8.4b

Rules

437×	`*-un-lft-identity_binary64_1442`
409×	`times-frac_binary64_1448`
235×	`add-sqr-sqrt_binary64_1464`
150×	`associate-r_binary64_1382`
142×	`add-cube-cbrt_binary64_1477`
122×	`distribute-lft-out_binary64_1393`
74×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
56×	`associate-l_binary64_1383`
48×	`associate-/r/_binary64_1388`
36×	`difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394`
35×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476`
25×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
24×	`div-inv_binary64_1439`
18×	`difference-of-sqr-1_binary64_1412`
17×	`prod-exp_binary64_1491` `cbrt-unprod_binary64_1475`
14×	`associate-/l*_binary64_1387`
13×	`associate-/r*_binary64_1386`
6×	`pow1_binary64_1503` `unswap-sqr_binary64_1410`
5×	`associate-/l/_binary64_1389`
4×	`add-log-exp_binary64_1481`
3×	`frac-2neg_binary64_1453` `clear-num_binary64_1441` `associate-*r/_binary64_1384`
1×	`pow-prod-down_binary64_1513` `frac-times_binary64_1452` `associate-l/_binary64_1385` `flip3--_binary64_1446` `flip--_binary64_1417` `-commutative_binary64_1373`

Counts

4 → 394

Calls

4 calls:

167.0ms	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (.f64 2 i))))) (/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1)))
20.0ms	(/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (*.f64 2 i)))))
13.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
10.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (*.f64 2 i))))

Compiler

Compiled 32200 to 15467 computations (52% saved)

series10.9s (22.5%)

Error

7.9b

Counts

4 → 108

Calls

4 calls:

8.7s	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (.f64 2 i))))) (/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1)))
877.0ms	(/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (*.f64 2 i)))))
420.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (*.f64 2 i))))
254.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))

Compiler

Compiled 31782 to 22014 computations (30.7% saved)

simplify303.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

502 → 502

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5004	38747

prune2.6s (5.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	495	7	502
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	498	13	511

Error

7.9b

Counts

511 → 13

Compiler

Compiled 41092 to 20383 computations (50.4% saved)

localize34.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.3b	(.f64 (/.f64 (sqrt.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))) 1) (.f64 (/.f64 (/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (.f64 i 2)) alpha)) (+.f64 alpha (-.f64 (+.f64 beta (.f64 i 2)) 1))) (/.f64 (sqrt.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (+.f64 (+.f64 beta (.f64 i 2)) alpha))) (+.f64 1 (+.f64 (+.f64 beta (*.f64 i 2)) alpha)))))
35.3b	(/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (+.f64 (+.f64 beta (.f64 i 2)) alpha))
35.3b	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
36.0b	(/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (*.f64 i 2)) alpha))

rewrite897.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

7.9b

Rules

110×	`add-exp-log_binary64_1480`
81×	`add-cbrt-cube_binary64_1478`
71×	`times-frac_binary64_1448`
62×	`*-un-lft-identity_binary64_1442`
46×	`div-exp_binary64_1493`
43×	`associate-l_binary64_1383`
41×	`prod-exp_binary64_1491`
40×	`add-cube-cbrt_binary64_1477` `add-sqr-sqrt_binary64_1464`
30×	`cbrt-undiv_binary64_1476` `sqrt-prod_binary64_1458`
28×	`cbrt-unprod_binary64_1475`
12×	`associate-/r/_binary64_1388` `associate-/r*_binary64_1386`
11×	`distribute-lft-out_binary64_1393`
9×	`pow1_binary64_1503` `flip3-+_binary64_1445` `flip-+_binary64_1416` `associate-*r/_binary64_1384`
7×	`div-inv_binary64_1439` `1-exp_binary64_1486`
6×	`associate-/l/_binary64_1389`
5×	`associate-/l*_binary64_1387` `frac-times_binary64_1452`
4×	`add-log-exp_binary64_1481`
3×	`frac-2neg_binary64_1453` `clear-num_binary64_1441` `pow-prod-down_binary64_1513` `associate-*l/_binary64_1385`
1×	`associate-r_binary64_1382` `*-commutative_binary64_1373`

Counts

4 → 185

Calls

4 calls:

67.0ms	(.f64 (/.f64 (sqrt.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))) 1) (.f64 (/.f64 (/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (.f64 i 2)) alpha)) (+.f64 alpha (-.f64 (+.f64 beta (.f64 i 2)) 1))) (/.f64 (sqrt.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (+.f64 (+.f64 beta (.f64 i 2)) alpha))) (+.f64 1 (+.f64 (+.f64 beta (*.f64 i 2)) alpha)))))
15.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
13.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (+.f64 (+.f64 beta (.f64 i 2)) alpha))
11.0ms	(/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (*.f64 i 2)) alpha))

Compiler

Compiled 18624 to 8957 computations (51.9% saved)

series10.1s (20.9%)

Error

7.9b

Counts

4 → 108

Calls

4 calls:

8.6s	(.f64 (/.f64 (sqrt.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))) 1) (.f64 (/.f64 (/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (.f64 i 2)) alpha)) (+.f64 alpha (-.f64 (+.f64 beta (.f64 i 2)) 1))) (/.f64 (sqrt.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (+.f64 (+.f64 beta (.f64 i 2)) alpha))) (+.f64 1 (+.f64 (+.f64 beta (*.f64 i 2)) alpha)))))
415.0ms	(/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (*.f64 i 2)) alpha))
275.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 i beta))) (+.f64 (+.f64 beta (.f64 i 2)) alpha))
267.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))

Compiler

Compiled 33072 to 22231 computations (32.8% saved)

simplify219.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4951	23218
1	4951	23218

prune1.5s (3.1%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	293	0	293
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	293	13	306

Error

7.9b

Counts

306 → 13

Compiler

Compiled 27435 to 13753 computations (49.9% saved)

regimes1.8s (3.6%)

Accuracy

Total 3.1b remaining (28.9%)

Threshold costs 0b (0%)

Compiler

Compiled 29634 to 17647 computations (40.5% saved)

bsearch33.0ms (0.1%)

Steps

Iters	Range		Point
5	6.417143259536157e+130	2.279755828637448e+131	1.542941599776018e+131

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	111
1	48	111

end0.0ms (0%)

sample4.9s (10.1%)

Algorithm

1×

intervals

Results

673.0ms	8000×	body	128	valid
167.0ms	8000×	pre	128	true

Compiler

Compiled 7437 to 4432 computations (40.4% saved)

Details

analyze43.0ms (0.1%)

sample45.0ms (0.1%)

simplify134.0ms (0.3%)

prune4.0ms (0%)

localize19.0ms (0%)

rewrite839.0ms (1.7%)

series10.5s (21.8%)

simplify218.0ms (0.5%)

prune1.3s (2.6%)

localize0.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0%)

prune16.0ms (0%)

localize20.0ms (0%)

rewrite2.0s (4.1%)

series10.9s (22.5%)

simplify303.0ms (0.6%)

prune2.6s (5.4%)

localize34.0ms (0.1%)

rewrite897.0ms (1.9%)

series10.1s (20.9%)

simplify219.0ms (0.5%)

prune1.5s (3.1%)

regimes1.8s (3.6%)

bsearch33.0ms (0.1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample4.9s (10.1%)

Profiling