Details

analyze2.0s (7.5%)

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)

sample138.0ms (0.5%)

Algorithm

1×

intervals

Results

37.0ms	256×	body	128	valid
28.0ms	221×	body	128	nan
19.0ms	135×	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 (31.0ms)

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

28.7b

Counts

2 → 1

Compiler

Compiled 54 to 46 computations (14.8% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

8.1b	(.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))))
10.8b	(sqrt.f64 (/.f64 d h))
13.7b	(sqrt.f64 (/.f64 d l))
14.7b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite311.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

14.9b

Rules

77×	`add-exp-log_binary64_1139`
41×	`prod-exp_binary64_1150`
32×	`add-sqr-sqrt_binary64_1123`
29×	`times-frac_binary64_1107`
26×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101` `sqrt-prod_binary64_1117`
21×	`add-cbrt-cube_binary64_1137`
16×	`div-exp_binary64_1152` `associate-r_binary64_1041`
14×	`sqrt-div_binary64_1118`
13×	`pow1_binary64_1162`
10×	`pow-exp_binary64_1169`
9×	`cbrt-unprod_binary64_1134` `frac-times_binary64_1111`
6×	`associate-r/_binary64_1043` `associate-l/_binary64_1044`
4×	`pow-prod-down_binary64_1172` `add-log-exp_binary64_1140` `rem-sqrt-square_binary64_1114` `flip3--_binary64_1105` `flip--_binary64_1076`
3×	`div-inv_binary64_1098`
2×	`pow-to-exp_binary64_1170` `cbrt-undiv_binary64_1135` `associate-l_binary64_1042` `*-commutative_binary64_1032` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `sub-neg_binary64_1094` `distribute-rgt-in_binary64_1051` `cancel-sign-sub-inv_binary64_1067` `distribute-lft-in_binary64_1050`

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 l))
3.0ms	(sqrt.f64 (/.f64 d h))

Compiler

Compiled 4932 to 2296 computations (53.4% saved)

series1.6s (5.8%)

Error

16.7b

Counts

4 → 50

Calls

4 calls:

880.0ms	(.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))))
553.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
42.0ms	(sqrt.f64 (/.f64 d h))
36.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 3752 to 2913 computations (22.4% saved)

simplify89.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4979	4371
1	4979	4371

prune280.0ms (1%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	156	21	177
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	157	21	178

Error

10.2b

Counts

178 → 21

Compiler

Compiled 6212 to 2934 computations (52.8% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.4b	(/.f64 (.f64 M D) (.f64 d 2))
8.1b	(.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))))
13.7b	(sqrt.f64 (/.f64 d l))
14.7b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite278.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

9.9b

Rules

93×	`add-exp-log_binary64_1139`
48×	`prod-exp_binary64_1150`
37×	`add-cbrt-cube_binary64_1137`
22×	`add-sqr-sqrt_binary64_1123`
20×	`div-exp_binary64_1152` `times-frac_binary64_1107`
19×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
16×	`pow1_binary64_1162` `cbrt-unprod_binary64_1134` `associate-r_binary64_1041`
13×	`sqrt-div_binary64_1118` `sqrt-prod_binary64_1117`
12×	`associate-*r/_binary64_1043`
10×	`pow-exp_binary64_1169`
9×	`frac-times_binary64_1111`
7×	`pow-prod-down_binary64_1172`
6×	`cbrt-undiv_binary64_1135` `associate-*l/_binary64_1044`
4×	`add-log-exp_binary64_1140` `flip3--_binary64_1105` `flip--_binary64_1076`
3×	`div-inv_binary64_1098`
2×	`pow-to-exp_binary64_1170` `associate-l_binary64_1042` `*-commutative_binary64_1032` `rem-sqrt-square_binary64_1114` `sub-neg_binary64_1094` `distribute-rgt-in_binary64_1051` `cancel-sign-sub-inv_binary64_1067` `distribute-lft-in_binary64_1050`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l_binary64_1046` `associate-/r_binary64_1045`

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))
9.0ms	(/.f64 (.f64 M D) (.f64 d 2))
3.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 6223 to 2306 computations (62.9% saved)

series2.4s (9%)

Error

10.2b

Counts

4 → 51

Calls

4 calls:

1.6s	(.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))))
548.0ms	(.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))
45.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 6088 to 4435 computations (27.2% saved)

simplify123.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4947	5747
1	4947	5747

prune315.0ms (1.2%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	167	10	177
Fresh	3	17	20
Picked	1	0	1
Done	0	0	0
Total	171	27	198

Error

9.9b

Counts

198 → 27

Compiler

Compiled 8388 to 3370 computations (59.8% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.4b	(/.f64 (.f64 M D) (.f64 d 2))
5.0b	(sqrt.f64 (/.f64 (cbrt.f64 d) l))
8.1b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
14.7b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite330.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

9.2b

Rules

102×	`add-exp-log_binary64_1139`
55×	`prod-exp_binary64_1150`
46×	`add-cbrt-cube_binary64_1137`
30×	`add-sqr-sqrt_binary64_1123` `times-frac_binary64_1107`
25×	`pow1_binary64_1162` `add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
23×	`cbrt-unprod_binary64_1134`
22×	`sqrt-prod_binary64_1117`
20×	`div-exp_binary64_1152`
18×	`associate-*r/_binary64_1043`
16×	`associate-r_binary64_1041`
14×	`pow-prod-down_binary64_1172`
13×	`sqrt-div_binary64_1118`
10×	`pow-exp_binary64_1169` `cbrt-prod_binary64_1132`
9×	`frac-times_binary64_1111`
6×	`cbrt-undiv_binary64_1135` `associate-*l/_binary64_1044`
4×	`add-log-exp_binary64_1140` `flip3--_binary64_1105` `flip--_binary64_1076`
3×	`div-inv_binary64_1098` `rem-sqrt-square_binary64_1114`
2×	`pow-to-exp_binary64_1170` `associate-l_binary64_1042` `*-commutative_binary64_1032` `sub-neg_binary64_1094` `distribute-rgt-in_binary64_1051` `cancel-sign-sub-inv_binary64_1067` `distribute-lft-in_binary64_1050`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l_binary64_1046` `associate-/r_binary64_1045`

Counts

4 → 142

Calls

4 calls:

25.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
13.0ms	(.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 (cbrt.f64 d) l))

Compiler

Compiled 7884 to 2640 computations (66.5% saved)

series2.7s (9.9%)

Error

9.2b

Counts

4 → 51

Calls

4 calls:

1.8s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
532.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
155.0ms	(sqrt.f64 (/.f64 (cbrt.f64 d) l))
135.0ms	(/.f64 (.f64 M D) (.f64 d 2))

Compiler

Compiled 6949 to 4919 computations (29.2% saved)

simplify133.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4965	6948
1	4965	6948

prune380.0ms (1.4%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	188	5	193
Fresh	2	24	26
Picked	1	0	1
Done	0	0	0
Total	191	29	220

Error

9.2b

Counts

220 → 29

Compiler

Compiled 10276 to 3794 computations (63.1% saved)

localize34.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.0b	(sqrt.f64 (/.f64 (cbrt.f64 d) l))
5.0b	(sqrt.f64 (/.f64 (cbrt.f64 d) l))
8.1b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 d)) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) l))) (cbrt.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (cbrt.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) l)))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
14.7b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite635.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

9.1b

Rules

114×	`add-exp-log_binary64_1139`
108×	`associate-*r/_binary64_1043`
98×	`sqrt-div_binary64_1118`
81×	`frac-times_binary64_1111`
72×	`cbrt-div_binary64_1133`
71×	`prod-exp_binary64_1150`
50×	`pow1_binary64_1162` `add-cbrt-cube_binary64_1137`
49×	`times-frac_binary64_1107`
48×	`add-sqr-sqrt_binary64_1123` `associate-*l/_binary64_1044`
44×	`sqrt-prod_binary64_1117`
39×	`cbrt-unprod_binary64_1134`
38×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
34×	`pow-prod-down_binary64_1172`
20×	`cbrt-prod_binary64_1132`
16×	`div-exp_binary64_1152` `associate-r_binary64_1041` `flip3--_binary64_1105` `flip--_binary64_1076`
10×	`pow-exp_binary64_1169`
6×	`rem-sqrt-square_binary64_1114`
4×	`add-log-exp_binary64_1140`
3×	`div-inv_binary64_1098`
2×	`pow-to-exp_binary64_1170` `cbrt-undiv_binary64_1135` `associate-l_binary64_1042` `*-commutative_binary64_1032` `sub-neg_binary64_1094` `distribute-rgt-in_binary64_1051` `cancel-sign-sub-inv_binary64_1067` `distribute-lft-in_binary64_1050` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119`

Counts

4 → 204

Calls

4 calls:

49.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 d)) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) l))) (cbrt.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (cbrt.f64 (sqrt.f64 (/.f64 (cbrt.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))
4.0ms	(sqrt.f64 (/.f64 (cbrt.f64 d) l))
4.0ms	(sqrt.f64 (/.f64 (cbrt.f64 d) l))

Compiler

Compiled 15561 to 4430 computations (71.5% saved)

series2.7s (10.1%)

Error

9.1b

Counts

4 → 48

Calls

4 calls:

1.8s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 d)) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) l))) (cbrt.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (cbrt.f64 (sqrt.f64 (/.f64 (cbrt.f64 d) l)))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
570.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
151.0ms	(sqrt.f64 (/.f64 (cbrt.f64 d) l))
149.0ms	(sqrt.f64 (/.f64 (cbrt.f64 d) l))

Compiler

Compiled 7883 to 5106 computations (35.2% saved)

simplify153.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

252 → 252

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4948	12217
1	4948	12217

prune552.0ms (2%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	248	4	252
Fresh	3	25	28
Picked	1	0	1
Done	0	0	0
Total	252	29	281

Error

9.1b

Counts

281 → 29

Compiler

Compiled 15068 to 4392 computations (70.9% saved)

regimes2.9s (10.8%)

Accuracy

Total 7.1b remaining (44%)

Threshold costs 0b (0%)

Compiler

Compiled 43920 to 31176 computations (29% saved)

bsearch512.0ms (1.9%)

Steps

Iters	Range		Point
9	3.037055053079952e-162	8.136137254216543e-157	1.592068893566198e-159
9	-1.5840642498661027e-258	-2.8001222409748333e-265	-2.854379532887666e-265

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify20.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	203	193
1	203	193

Remove

(sort M D)

Compiler

Compiled 242 to 140 computations (42.1% saved)

end0.0ms (0%)

sample8.3s (30.7%)

Algorithm

1×

intervals

Results

1.3s	8000×	body	128	valid
1.1s	8270×	body	128	nan
678.0ms	4769×	body	128	invalid

Compiler

Compiled 6419 to 4543 computations (29.2% saved)

Details

analyze2.0s (7.5%)

sample138.0ms (0.5%)

simplify36.0ms (0.1%)

prune6.0ms (0%)

localize24.0ms (0.1%)

rewrite311.0ms (1.1%)

series1.6s (5.8%)

simplify89.0ms (0.3%)

prune280.0ms (1%)

localize25.0ms (0.1%)

rewrite278.0ms (1%)

series2.4s (9%)

simplify123.0ms (0.5%)

prune315.0ms (1.2%)

localize27.0ms (0.1%)

rewrite330.0ms (1.2%)

series2.7s (9.9%)

simplify133.0ms (0.5%)

prune380.0ms (1.4%)

localize34.0ms (0.1%)

rewrite635.0ms (2.3%)

series2.7s (10.1%)

simplify153.0ms (0.6%)

prune552.0ms (2%)

regimes2.9s (10.8%)

bsearch512.0ms (1.9%)

simplify20.0ms (0.1%)

end0.0ms (0%)

sample8.3s (30.7%)

Profiling