Details

analyze2.0s (7.1%)

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)

sample153.0ms (0.5%)

Algorithm

1×

intervals

Results

37.0ms	256×	body	128	valid
33.0ms	256×	body	128	nan
22.0ms	156×	body	128	invalid

Compiler

Compiled 71 to 68 computations (4.2% saved)

simplify38.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (32.0ms)

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

25.4b

Counts

2 → 1

Compiler

Compiled 54 to 46 computations (14.8% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.2b	(.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))))
11.7b	(sqrt.f64 (/.f64 d h))
11.9b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
12.1b	(sqrt.f64 (/.f64 d l))

rewrite310.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

12.1b

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:

16.0ms	(.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))))
11.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
3.0ms	(sqrt.f64 (/.f64 d h))
3.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 4932 to 2296 computations (53.4% saved)

series1.6s (5.4%)

Error

17.5b

Counts

4 → 50

Calls

4 calls:

868.0ms	(.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))))
551.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
43.0ms	(sqrt.f64 (/.f64 d l))
37.0ms	(sqrt.f64 (/.f64 d h))

Compiler

Compiled 3752 to 2913 computations (22.4% saved)

simplify96.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4979	4371
1	4979	4371

prune284.0ms (1%)

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

10.4b

Counts

178 → 19

Compiler

Compiled 6104 to 2861 computations (53.1% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.2b	(/.f64 (.f64 M D) (.f64 d 2))
7.2b	(.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))))
11.9b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
12.1b	(sqrt.f64 (/.f64 d l))

rewrite282.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

9.2b

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:

21.0ms	(.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))
5.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 6223 to 2306 computations (62.9% saved)

series2.5s (8.7%)

Error

10.4b

Counts

4 → 51

Calls

4 calls:

1.7s	(.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))))
554.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
145.0ms	(/.f64 (.f64 M D) (.f64 d 2))
49.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 6088 to 4435 computations (27.2% saved)

simplify132.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4947	5747
1	4947	5747

prune332.0ms (1.2%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	167	10	177
Fresh	1	17	18
Picked	1	0	1
Done	0	0	0
Total	169	27	196

Error

9.2b

Counts

196 → 27

Compiler

Compiled 8351 to 3345 computations (59.9% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 l)
6.2b	(/.f64 (.f64 M D) (.f64 d 2))
7.2b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
11.9b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite301.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

7.5b

Rules

102×	`add-exp-log_binary64_1480`
55×	`prod-exp_binary64_1491`
46×	`add-cbrt-cube_binary64_1478`
24×	`pow1_binary64_1503`
23×	`cbrt-unprod_binary64_1475`
20×	`div-exp_binary64_1493`
18×	`associate-*r/_binary64_1384`
16×	`associate-r_binary64_1382`
14×	`pow-prod-down_binary64_1513`
13×	`add-cube-cbrt_binary64_1477` `add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
12×	`sqrt-div_binary64_1459`
10×	`pow-exp_binary64_1510` `times-frac_binary64_1448`
9×	`frac-times_binary64_1452`
6×	`cbrt-undiv_binary64_1476` `associate-*l/_binary64_1385`
4×	`add-log-exp_binary64_1481` `flip3--_binary64_1446` `flip--_binary64_1417`
3×	`cbrt-prod_binary64_1473`
2×	`pow-to-exp_binary64_1511` `associate-l_binary64_1383` `div-inv_binary64_1439` `*-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` `pow1/3_binary64_1524`

Counts

4 → 118

Calls

4 calls:

29.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.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))
1.0ms	(cbrt.f64 l)

Compiler

Compiled 7220 to 2249 computations (68.9% saved)

series3.0s (10.4%)

Error

8.0b

Counts

4 → 51

Calls

4 calls:

2.1s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
572.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
137.0ms	(/.f64 (.f64 M D) (.f64 d 2))
85.0ms	(cbrt.f64 l)

Compiler

Compiled 7346 to 4952 computations (32.6% saved)

simplify124.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4963	7097
1	4963	7097

prune323.0ms (1.1%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	164	5	169
Fresh	2	24	26
Picked	1	0	1
Done	0	0	0
Total	167	29	196

Error

8.0b

Counts

196 → 29

Compiler

Compiled 9643 to 3281 computations (66% saved)

localize34.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.7b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (*.f64 (cbrt.f64 h) (cbrt.f64 h)))
6.2b	(/.f64 (.f64 M D) (.f64 2 d))
7.2b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
8.4b	(.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))

rewrite508.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

7.5b

Rules

291×	`add-exp-log_binary64_1480`
189×	`prod-exp_binary64_1491`
70×	`add-cbrt-cube_binary64_1478`
51×	`cbrt-unprod_binary64_1475`
45×	`div-exp_binary64_1493`
36×	`pow1_binary64_1503`
30×	`pow-exp_binary64_1510`
26×	`associate-r_binary64_1382`
22×	`pow-prod-down_binary64_1513`
19×	`times-frac_binary64_1448`
18×	`add-cube-cbrt_binary64_1477` `add-sqr-sqrt_binary64_1464` `-un-lft-identity_binary64_1442` `associate-r/_binary64_1384`
12×	`sqrt-div_binary64_1459`
9×	`cbrt-undiv_binary64_1476` `cbrt-prod_binary64_1473` `frac-times_binary64_1452`
6×	`pow-to-exp_binary64_1511` `associate-*l/_binary64_1385`
4×	`add-log-exp_binary64_1481` `flip3--_binary64_1446` `flip--_binary64_1417`
3×	`associate-l_binary64_1383` `*-commutative_binary64_1373`
2×	`div-inv_binary64_1439` `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`

Counts

4 → 174

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 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
20.0ms	(.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
12.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (*.f64 (cbrt.f64 h) (cbrt.f64 h)))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 12018 to 3389 computations (71.8% saved)

series3.7s (12.9%)

Error

8.0b

Counts

4 → 60

Calls

4 calls:

2.1s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
705.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (*.f64 (cbrt.f64 h) (cbrt.f64 h)))
595.0ms	(.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
150.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 9080 to 5880 computations (35.2% saved)

simplify144.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

234 → 234

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4944	9202
1	4944	9202

prune404.0ms (1.4%)

Pruning

30 alts after pruning (29 fresh and 1 done)

	Pruned	Kept	Total
New	230	4	234
Fresh	3	25	28
Picked	0	1	1
Done	0	0	0
Total	233	30	263

Error

7.7b

Counts

263 → 30

Compiler

Compiled 12397 to 3369 computations (72.8% saved)

regimes3.3s (11.6%)

Accuracy

Total 5.7b remaining (41%)

Threshold costs 0b (0%)

Compiler

Compiled 48876 to 33983 computations (30.5% saved)

bsearch331.0ms (1.2%)

Steps

Iters	Range		Point
3	3.4772690407856903e-128	4.28417624472084e-128	3.7294275420154245e-128
9	-4.474377595079377e-299	-2.7020296975708577e-307	-2.7495816865703752e-307

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify24.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	300	240
1	300	240

Remove

(sort M D)

Compiler

Compiled 298 to 148 computations (50.3% saved)

end0.0ms (0%)

sample8.7s (30.2%)

Algorithm

1×

intervals

Results

1.2s	8000×	body	128	valid
1.1s	8153×	body	128	nan
710.0ms	4838×	body	128	invalid

Compiler

Compiled 7155 to 4948 computations (30.8% saved)

Details

analyze2.0s (7.1%)

sample153.0ms (0.5%)

simplify38.0ms (0.1%)

prune5.0ms (0%)

localize20.0ms (0.1%)

rewrite310.0ms (1.1%)

series1.6s (5.4%)

simplify96.0ms (0.3%)

prune284.0ms (1%)

localize25.0ms (0.1%)

rewrite282.0ms (1%)

series2.5s (8.7%)

simplify132.0ms (0.5%)

prune332.0ms (1.2%)

localize30.0ms (0.1%)

rewrite301.0ms (1%)

series3.0s (10.4%)

simplify124.0ms (0.4%)

prune323.0ms (1.1%)

localize34.0ms (0.1%)

rewrite508.0ms (1.8%)

series3.7s (12.9%)

simplify144.0ms (0.5%)

prune404.0ms (1.4%)

regimes3.3s (11.6%)

bsearch331.0ms (1.2%)

simplify24.0ms (0.1%)

end0.0ms (0%)

sample8.7s (30.2%)

Profiling