Details

analyze1.9s (6.3%)

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)

sample144.0ms (0.5%)

Algorithm

1×

intervals

Results

36.0ms	270×	body	128	nan
34.0ms	256×	body	128	valid
22.0ms	160×	body	128	invalid

Compiler

Compiled 71 to 68 computations (4.2% saved)

simplify35.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5205	41

prune5.0ms (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

28.9b

Counts

2 → 1

Compiler

Compiled 54 to 46 computations (14.8% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.1b	(.f64 (.f64 (sqrt.f64 (/.f64 d 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))))
11.8b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
12.5b	(sqrt.f64 (/.f64 d h))
13.7b	(sqrt.f64 (/.f64 d l))

rewrite290.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

11.7b

Rules

77×	`add-exp-log_binary64_1480`
41×	`prod-exp_binary64_1491`
32×	`add-sqr-sqrt_binary64_1464`
29×	`times-frac_binary64_1448`
26×	`add-cube-cbrt_binary64_1477` `sqrt-prod_binary64_1458` `*-un-lft-identity_binary64_1442`
21×	`add-cbrt-cube_binary64_1478`
16×	`div-exp_binary64_1493` `associate-r_binary64_1382`
14×	`sqrt-div_binary64_1459`
13×	`pow1_binary64_1503`
10×	`pow-exp_binary64_1510`
9×	`cbrt-unprod_binary64_1475` `frac-times_binary64_1452`
6×	`associate-r/_binary64_1384` `associate-l/_binary64_1385`
4×	`add-log-exp_binary64_1481` `rem-sqrt-square_binary64_1455` `pow-prod-down_binary64_1513` `flip3--_binary64_1446` `flip--_binary64_1417`
3×	`div-inv_binary64_1439`
2×	`pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `pow-to-exp_binary64_1511` `cbrt-undiv_binary64_1476` `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`

Counts

4 → 127

Calls

4 calls:

15.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 d 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))))
15.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
3.0ms	(sqrt.f64 (/.f64 d l))
3.0ms	(sqrt.f64 (/.f64 d h))

Compiler

Compiled 4932 to 2296 computations (53.4% saved)

series1.5s (5.1%)

Error

19.3b

Counts

4 → 50

Calls

4 calls:

852.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 d 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))))
544.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
42.0ms	(sqrt.f64 (/.f64 d h))
41.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 3752 to 2913 computations (22.4% saved)

simplify99.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4979	4371
1	4979	4371

prune284.0ms (0.9%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	158	19	177
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	159	19	178

Error

10.7b

Counts

178 → 19

Compiler

Compiled 6103 to 2862 computations (53.1% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.3b	(/.f64 (.f64 M D) (.f64 d 2))
6.1b	(.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))))
11.8b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
13.7b	(sqrt.f64 (/.f64 d l))

rewrite275.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

9.3b

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:

22.0ms	(.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)

series3.0s (10.1%)

Error

10.7b

Counts

4 → 55

Calls

4 calls:

2.2s	(.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))))
550.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
133.0ms	(/.f64 (.f64 M D) (.f64 d 2))
48.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 6576 to 4835 computations (26.5% saved)

simplify126.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4947	6103
1	4947	6103

prune317.0ms (1.1%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	170	11	181
Fresh	4	14	18
Picked	1	0	1
Done	0	0	0
Total	175	25	200

Error

9.9b

Counts

200 → 25

Compiler

Compiled 8507 to 3411 computations (59.9% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.5b	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
5.3b	(/.f64 (.f64 M D) (.f64 d 2))
6.1b	(.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))))
11.8b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite433.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

7.6b

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:

37.0ms	(.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))
6.0ms	(/.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)

series3.3s (11%)

Error

8.7b

Counts

4 → 55

Calls

4 calls:

2.3s	(.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))))
581.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
152.0ms	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
150.0ms	(/.f64 (.f64 M D) (.f64 d 2))

Compiler

Compiled 7567 to 5465 computations (27.8% saved)

simplify130.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

209 → 209

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4971	8682
1	4971	8682

prune498.0ms (1.7%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	204	5	209
Fresh	3	21	24
Picked	1	0	1
Done	0	0	0
Total	208	26	234

Error

8.2b

Counts

234 → 26

Compiler

Compiled 11875 to 4903 computations (58.7% saved)

localize32.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.6b	(.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)))
5.3b	(.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))) (/.f64 1 l))
5.3b	(/.f64 (.f64 M D) (.f64 2 d))
6.1b	(.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 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) (/.f64 1 l))))

rewrite544.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

7.3b

Rules

233×	`add-exp-log_binary64_1480`
148×	`prod-exp_binary64_1491`
60×	`add-cbrt-cube_binary64_1478`
42×	`div-exp_binary64_1493`
36×	`sqrt-div_binary64_1459`
32×	`cbrt-unprod_binary64_1475`
30×	`associate-*r/_binary64_1384`
29×	`pow1_binary64_1503` `frac-times_binary64_1452`
25×	`pow-exp_binary64_1510`
17×	`pow-prod-down_binary64_1513` `associate-r_binary64_1382`
16×	`associate-*l/_binary64_1385`
13×	`add-cube-cbrt_binary64_1477` `add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
10×	`times-frac_binary64_1448`
9×	`1-exp_binary64_1486` `rec-exp_binary64_1492`
8×	`flip3--_binary64_1446` `flip--_binary64_1417`
7×	`cbrt-undiv_binary64_1476`
5×	`associate-l_binary64_1383` `pow-to-exp_binary64_1511`
4×	`add-log-exp_binary64_1481`
3×	`*-commutative_binary64_1373`
2×	`sub-neg_binary64_1435` `distribute-rgt-in_binary64_1392` `cancel-sign-sub-inv_binary64_1408` `distribute-lft-in_binary64_1391` `div-inv_binary64_1439`
1×	`frac-2neg_binary64_1453` `clear-num_binary64_1441` `associate-/l_binary64_1387` `associate-/r_binary64_1386` `un-div-inv_binary64_1440`

Counts

4 → 166

Calls

4 calls:

39.0ms	(.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 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) (/.f64 1 l))))
14.0ms	(.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))) (/.f64 1 l))
8.0ms	(.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 10777 to 4805 computations (55.4% saved)

series3.4s (11.3%)

Error

8.2b

Counts

4 → 61

Calls

4 calls:

2.2s	(.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 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) (/.f64 1 l))))
538.0ms	(.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))) (/.f64 1 l))
371.0ms	(.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)))
136.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 8493 to 6064 computations (28.6% saved)

simplify133.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4953	9343
1	4953	9343

prune633.0ms (2.1%)

Pruning

30 alts after pruning (30 fresh and 0 done)

	Pruned	Kept	Total
New	221	6	227
Fresh	1	24	25
Picked	1	0	1
Done	0	0	0
Total	223	30	253

Error

8.0b

Counts

253 → 30

Compiler

Compiled 11765 to 4777 computations (59.4% saved)

regimes3.5s (11.7%)

Accuracy

Total 7.0b remaining (45%)

Threshold costs 0b (0%)

Compiler

Compiled 56569 to 41417 computations (26.8% saved)

bsearch0.0ms (0%)

simplify14.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	133	77
1	133	77

Removed

((sort M D))

Compiler

Compiled 96 to 70 computations (27.1% saved)

end0.0ms (0%)

sample9.3s (30.9%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
1.0s	8324×	body	128	nan
669.0ms	4805×	body	128	invalid

Compiler

Compiled 8153 to 5971 computations (26.8% saved)

Details

analyze1.9s (6.3%)

sample144.0ms (0.5%)

simplify35.0ms (0.1%)

prune5.0ms (0%)

localize18.0ms (0.1%)

rewrite290.0ms (1%)

series1.5s (5.1%)

simplify99.0ms (0.3%)

prune284.0ms (0.9%)

localize29.0ms (0.1%)

rewrite275.0ms (0.9%)

series3.0s (10.1%)

simplify126.0ms (0.4%)

prune317.0ms (1.1%)

localize30.0ms (0.1%)

rewrite433.0ms (1.4%)

series3.3s (11%)

simplify130.0ms (0.4%)

prune498.0ms (1.7%)

localize32.0ms (0.1%)

rewrite544.0ms (1.8%)

series3.4s (11.3%)

simplify133.0ms (0.4%)

prune633.0ms (2.1%)

regimes3.5s (11.7%)

bsearch0.0ms (0%)

simplify14.0ms (0%)

end0.0ms (0%)

sample9.3s (30.9%)

Profiling