Details

analyze2.2s (7%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5362	451
0	5	5
1	5	5

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	81.1%	18.9%	7
0%	68.6%	31.4%	8
0%	59.2%	40.8%	9
0%	59.2%	40.8%	10
0%	59.2%	40.8%	11
0.4%	49.5%	50.1%	12
0.8%	44.4%	54.8%	13
1.4%	39.9%	58.7%	14

Symmetry

(sort M D)

Compiler

Compiled 36 to 32 computations (11.1% saved)

sample146.0ms (0.5%)

Algorithm

1×

intervals

Results

36.0ms	256×	body	128	valid
32.0ms	258×	body	128	nan
19.0ms	134×	body	128	invalid

Compiler

Compiled 71 to 68 computations (4.2% saved)

simplify36.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5205	41

prune6.0ms (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

26.7b

Counts

2 → 1

Compiler

Compiled 54 to 46 computations (14.8% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.1b	(/.f64 (.f64 M D) (.f64 d 2))
11.1b	(sqrt.f64 (/.f64 d h))
13.2b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
13.2b	(sqrt.f64 (/.f64 d l))

rewrite267.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

12.4b

Rules

84×	`add-exp-log_binary64_1480`
42×	`prod-exp_binary64_1491`
31×	`add-sqr-sqrt_binary64_1464`
30×	`times-frac_binary64_1448`
28×	`add-cbrt-cube_binary64_1478`
26×	`sqrt-prod_binary64_1458`
25×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
20×	`div-exp_binary64_1493`
13×	`associate-r_binary64_1382`
10×	`pow-exp_binary64_1510` `cbrt-unprod_binary64_1475`
8×	`pow1_binary64_1503`
6×	`cbrt-undiv_binary64_1476`
4×	`add-log-exp_binary64_1481` `div-inv_binary64_1439` `rem-sqrt-square_binary64_1455`
2×	`pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `sqrt-div_binary64_1459` `pow-to-exp_binary64_1511`
1×	`pow-prod-down_binary64_1513` `associate-r/_binary64_1384` `associate-l_binary64_1383` `-commutative_binary64_1373` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `associate-/l_binary64_1387` `associate-/r_binary64_1386`

Counts

4 → 115

Calls

4 calls:

10.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
3.0ms	(sqrt.f64 (/.f64 d l))
3.0ms	(sqrt.f64 (/.f64 d h))

Compiler

Compiled 3980 to 1816 computations (54.4% saved)

series1.2s (3.6%)

Error

25.7b

Counts

4 → 36

Calls

4 calls:

825.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
184.0ms	(/.f64 (.f64 M D) (.f64 d 2))
57.0ms	(sqrt.f64 (/.f64 d l))
54.0ms	(sqrt.f64 (/.f64 d h))

Compiler

Compiled 3146 to 2306 computations (26.7% saved)

simplify67.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5039	2413

prune286.0ms (0.9%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	130	21	151
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	131	21	152

Error

13.1b

Counts

152 → 21

Compiler

Compiled 5300 to 2494 computations (52.9% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.6b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
7.1b	(/.f64 (.f64 M D) (.f64 d 2))
13.2b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
13.2b	(sqrt.f64 (/.f64 d l))

rewrite337.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

11.1b

Rules

93×	`add-exp-log_binary64_1480`
48×	`prod-exp_binary64_1491`
37×	`add-cbrt-cube_binary64_1478`
22×	`add-sqr-sqrt_binary64_1464`
20×	`times-frac_binary64_1448` `div-exp_binary64_1493`
19×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
16×	`pow1_binary64_1503` `cbrt-unprod_binary64_1475` `associate-r_binary64_1382`
13×	`sqrt-div_binary64_1459` `sqrt-prod_binary64_1458`
12×	`associate-*r/_binary64_1384`
10×	`pow-exp_binary64_1510`
9×	`frac-times_binary64_1452`
7×	`pow-prod-down_binary64_1513`
6×	`cbrt-undiv_binary64_1476` `associate-*l/_binary64_1385`
4×	`add-log-exp_binary64_1481` `flip3--_binary64_1446` `flip--_binary64_1417`
3×	`div-inv_binary64_1439`
2×	`rem-sqrt-square_binary64_1455` `pow-to-exp_binary64_1511` `associate-l_binary64_1383` `*-commutative_binary64_1373` `sub-neg_binary64_1435` `distribute-rgt-in_binary64_1392` `cancel-sign-sub-inv_binary64_1408` `distribute-lft-in_binary64_1391`
1×	`pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `associate-/l_binary64_1387` `associate-/r_binary64_1386`

Counts

4 → 126

Calls

4 calls:

20.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
11.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
3.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 6223 to 2306 computations (62.9% saved)

series4.5s (14%)

Error

13.1b

Counts

4 → 55

Calls

4 calls:

3.3s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
805.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
211.0ms	(/.f64 (.f64 M D) (.f64 d 2))
60.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 6576 to 4835 computations (26.5% saved)

simplify123.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4947	6103
1	4947	6103

prune394.0ms (1.2%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	172	9	181
Fresh	3	17	20
Picked	1	0	1
Done	0	0	0
Total	176	26	202

Error

13.0b

Counts

202 → 26

Compiler

Compiled 8499 to 3431 computations (59.6% saved)

localize31.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.8b	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
5.6b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
7.1b	(/.f64 (.f64 M D) (.f64 d 2))
13.2b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite510.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

10.0b

Rules

102×	`add-exp-log_binary64_1480`
55×	`prod-exp_binary64_1491`
46×	`add-cbrt-cube_binary64_1478`
37×	`sqrt-div_binary64_1459`
30×	`add-sqr-sqrt_binary64_1464` `associate-*r/_binary64_1384` `times-frac_binary64_1448`
29×	`frac-times_binary64_1452`
25×	`pow1_binary64_1503` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
23×	`cbrt-unprod_binary64_1475`
22×	`sqrt-prod_binary64_1458`
20×	`div-exp_binary64_1493`
16×	`associate-r_binary64_1382` `associate-*l/_binary64_1385`
14×	`pow-prod-down_binary64_1513`
10×	`pow-exp_binary64_1510` `cbrt-prod_binary64_1473`
8×	`flip3--_binary64_1446` `flip--_binary64_1417`
6×	`cbrt-undiv_binary64_1476`
4×	`add-log-exp_binary64_1481`
3×	`div-inv_binary64_1439` `rem-sqrt-square_binary64_1455`
2×	`pow-to-exp_binary64_1511` `associate-l_binary64_1383` `*-commutative_binary64_1373` `sub-neg_binary64_1435` `distribute-rgt-in_binary64_1392` `cancel-sign-sub-inv_binary64_1408` `distribute-lft-in_binary64_1391`
1×	`frac-2neg_binary64_1453` `clear-num_binary64_1441` `associate-/l_binary64_1387` `associate-/r_binary64_1386` `pow1/2_binary64_1522` `sqrt-pow1_binary64_1460`

Counts

4 → 154

Calls

4 calls:

34.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
11.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
8.0ms	(/.f64 (.f64 M D) (.f64 d 2))
4.0ms	(sqrt.f64 (/.f64 d (cbrt.f64 l)))

Compiler

Compiled 9641 to 3786 computations (60.7% saved)

series4.7s (14.6%)

Error

12.5b

Counts

4 → 55

Calls

4 calls:

3.3s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
820.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
224.0ms	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
186.0ms	(/.f64 (.f64 M D) (.f64 d 2))

Compiler

Compiled 7567 to 5465 computations (27.8% saved)

simplify122.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

209 → 209

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4971	8682
1	4971	8682

prune577.0ms (1.8%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	204	5	209
Fresh	4	21	25
Picked	1	0	1
Done	0	0	0
Total	209	26	235

Error

12.0b

Counts

235 → 26

Compiler

Compiled 11932 to 4932 computations (58.7% saved)

localize37.0ms (0.1%)

Local error

Found 4 expressions with local error:

8.1b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (*.f64 (cbrt.f64 (/.f64 h l)) (cbrt.f64 (/.f64 h l))))
15.5b	(cbrt.f64 (/.f64 h l))
15.5b	(cbrt.f64 (/.f64 h l))
15.5b	(cbrt.f64 (/.f64 h l))

rewrite287.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

10.9b

Rules

72×	`add-exp-log_binary64_1480`
46×	`prod-exp_binary64_1491`
39×	`cbrt-prod_binary64_1473`
27×	`times-frac_binary64_1448`
25×	`add-cube-cbrt_binary64_1477` `add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
12×	`add-cbrt-cube_binary64_1478`
10×	`pow-exp_binary64_1510`
9×	`pow1_binary64_1503`
8×	`div-exp_binary64_1493` `cbrt-unprod_binary64_1475`
7×	`cbrt-div_binary64_1474`
4×	`add-log-exp_binary64_1481` `associate-*r/_binary64_1384`
3×	`pow1/3_binary64_1524` `div-inv_binary64_1439` `pow-prod-down_binary64_1513`
2×	`pow-to-exp_binary64_1511`
1×	`frac-times_binary64_1452` `associate-l/_binary64_1385` `associate-l_binary64_1383` `associate-r_binary64_1382` `-commutative_binary64_1373`

Counts

4 → 101

Calls

4 calls:

15.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (*.f64 (cbrt.f64 (/.f64 h l)) (cbrt.f64 (/.f64 h l))))
4.0ms	(cbrt.f64 (/.f64 h l))
2.0ms	(cbrt.f64 (/.f64 h l))
2.0ms	(cbrt.f64 (/.f64 h l))

Compiler

Compiled 6570 to 2120 computations (67.7% saved)

series2.7s (8.4%)

Error

12.0b

Counts

4 → 33

Calls

4 calls:

1.7s	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (*.f64 (cbrt.f64 (/.f64 h l)) (cbrt.f64 (/.f64 h l))))
303.0ms	(cbrt.f64 (/.f64 h l))
302.0ms	(cbrt.f64 (/.f64 h l))
301.0ms	(cbrt.f64 (/.f64 h l))

Compiler

Compiled 6255 to 3971 computations (36.5% saved)

simplify71.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5132	2716

prune333.0ms (1%)

Pruning

28 alts after pruning (27 fresh and 1 done)

	Pruned	Kept	Total
New	131	3	134
Fresh	1	24	25
Picked	0	1	1
Done	0	0	0
Total	132	28	160

Error

10.8b

Counts

160 → 28

Compiler

Compiled 8196 to 2688 computations (67.2% saved)

regimes4.2s (12.9%)

Accuracy

Total 3.8b remaining (29.1%)

Threshold costs 0b (0%)

Compiler

Compiled 48967 to 35628 computations (27.2% saved)

bsearch16.0ms (0.1%)

Compiler: Compiled 35 to 31 computations (11.4% saved)

simplify29.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	149	338
1	149	338

Remove

(sort M D)

Compiler

Compiled 424 to 228 computations (46.2% saved)

end0.0ms (0%)

sample9.0s (27.9%)

Algorithm

1×

intervals

Results

1.2s	8000×	body	128	valid
1.0s	8180×	body	128	nan
698.0ms	4816×	body	128	invalid

Compiler

Compiled 7231 to 5223 computations (27.8% saved)

Details

analyze2.2s (7%)

sample146.0ms (0.5%)

simplify36.0ms (0.1%)

prune6.0ms (0%)

localize18.0ms (0.1%)

rewrite267.0ms (0.8%)

series1.2s (3.6%)

simplify67.0ms (0.2%)

prune286.0ms (0.9%)

localize26.0ms (0.1%)

rewrite337.0ms (1.1%)

series4.5s (14%)

simplify123.0ms (0.4%)

prune394.0ms (1.2%)

localize31.0ms (0.1%)

rewrite510.0ms (1.6%)

series4.7s (14.6%)

simplify122.0ms (0.4%)

prune577.0ms (1.8%)

localize37.0ms (0.1%)

rewrite287.0ms (0.9%)

series2.7s (8.4%)

simplify71.0ms (0.2%)

prune333.0ms (1%)

regimes4.2s (12.9%)

bsearch16.0ms (0.1%)

simplify29.0ms (0.1%)

end0.0ms (0%)

sample9.0s (27.9%)

Profiling