Details

analyze2.0s (6.6%)

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)

sample160.0ms (0.5%)

Algorithm

1×

intervals

Results

44.0ms	318×	body	128	nan
36.0ms	256×	body	128	valid
21.0ms	151×	body	128	invalid

Compiler

Compiled 71 to 68 computations (4.2% saved)

simplify37.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (31.0ms)

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

27.8b

Counts

2 → 1

Compiler

Compiled 54 to 46 computations (14.8% saved)

localize19.0ms (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))))
11.0b	(sqrt.f64 (/.f64 d h))
11.8b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
13.4b	(sqrt.f64 (/.f64 d l))

rewrite310.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

13.6b

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` `sqrt-prod_binary64_1117` `*-un-lft-identity_binary64_1101`
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×	`add-log-exp_binary64_1140` `rem-sqrt-square_binary64_1114` `pow-prod-down_binary64_1172` `flip3--_binary64_1105` `flip--_binary64_1076`
3×	`div-inv_binary64_1098`
2×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `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`

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))))
11.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
7.0ms	(sqrt.f64 (/.f64 d l))
3.0ms	(sqrt.f64 (/.f64 d h))

Compiler

Compiled 4932 to 2296 computations (53.4% saved)

series1.5s (5%)

Error

21.1b

Counts

4 → 50

Calls

4 calls:

850.0ms	(.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))))
539.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
42.0ms	(sqrt.f64 (/.f64 d h))
42.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 3752 to 2913 computations (22.4% saved)

simplify92.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4979	4371
1	4979	4371

prune284.0ms (0.9%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	154	23	177
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	155	23	178

Error

12.1b

Counts

178 → 23

Compiler

Compiled 6275 to 2982 computations (52.5% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.9b	(/.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))))
11.8b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
13.4b	(sqrt.f64 (/.f64 d l))

rewrite290.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

10.4b

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×	`times-frac_binary64_1107` `div-exp_binary64_1152`
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×	`rem-sqrt-square_binary64_1114` `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 → 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)

series3.1s (10%)

Error

12.0b

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))))
561.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
130.0ms	(/.f64 (.f64 M D) (.f64 d 2))
44.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 6576 to 4835 computations (26.5% saved)

simplify128.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4947	6103
1	4947	6103

prune316.0ms (1%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	170	11	181
Fresh	9	13	22
Picked	1	0	1
Done	0	0	0
Total	180	24	204

Error

11.3b

Counts

204 → 24

Compiler

Compiled 8493 to 3387 computations (60.1% saved)

localize33.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 d)
4.9b	(/.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))))
11.8b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite292.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

8.5b

Rules

102×	`add-exp-log_binary64_1139`
55×	`prod-exp_binary64_1150`
46×	`add-cbrt-cube_binary64_1137`
24×	`pow1_binary64_1162`
23×	`cbrt-unprod_binary64_1134`
20×	`div-exp_binary64_1152`
18×	`associate-*r/_binary64_1043`
16×	`associate-r_binary64_1041`
14×	`pow-prod-down_binary64_1172`
13×	`add-cube-cbrt_binary64_1136` `add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101`
12×	`sqrt-div_binary64_1118`
10×	`pow-exp_binary64_1169` `times-frac_binary64_1107`
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×	`cbrt-prod_binary64_1132`
2×	`pow-to-exp_binary64_1170` `associate-l_binary64_1042` `div-inv_binary64_1098` `*-commutative_binary64_1032` `sub-neg_binary64_1094` `distribute-rgt-in_binary64_1051` `cancel-sign-sub-inv_binary64_1067` `distribute-lft-in_binary64_1050`
1×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l_binary64_1046` `associate-/r_binary64_1045` `pow1/3_binary64_1183`

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 d)

Compiler

Compiled 7220 to 2251 computations (68.8% saved)

series3.5s (11.3%)

Error

9.8b

Counts

4 → 54

Calls

4 calls:

2.6s	(.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))
141.0ms	(/.f64 (.f64 M D) (.f64 d 2))
76.0ms	(cbrt.f64 d)

Compiler

Compiled 7748 to 5252 computations (32.2% saved)

simplify123.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5105	7370

prune325.0ms (1.1%)

Pruning

30 alts after pruning (30 fresh and 0 done)

	Pruned	Kept	Total
New	164	8	172
Fresh	1	22	23
Picked	1	0	1
Done	0	0	0
Total	166	30	196

Error

9.5b

Counts

196 → 30

Compiler

Compiled 10028 to 3428 computations (65.8% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.9b	(/.f64 (.f64 M D) (.f64 2 d))
5.4b	(.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)))
5.5b	(/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) l)
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 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) l)))

rewrite360.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

8.9b

Rules

104×	`add-exp-log_binary64_1139`
55×	`prod-exp_binary64_1150`
48×	`add-cbrt-cube_binary64_1137`
24×	`pow1_binary64_1162`
23×	`cbrt-unprod_binary64_1134`
21×	`div-exp_binary64_1152`
17×	`associate-*r/_binary64_1043`
15×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101`
14×	`pow-prod-down_binary64_1172` `cancel-sign-sub-inv_binary64_1067`
12×	`add-cube-cbrt_binary64_1136` `sqrt-div_binary64_1118`
10×	`times-frac_binary64_1107` `pow-exp_binary64_1169`
9×	`frac-times_binary64_1111`
8×	`distribute-rgt-in_binary64_1051` `distribute-lft-in_binary64_1050`
7×	`associate-r_binary64_1041` `cbrt-undiv_binary64_1135`
6×	`associate-*l/_binary64_1044`
4×	`add-log-exp_binary64_1140` `flip3--_binary64_1105` `flip--_binary64_1076` `div-inv_binary64_1098` `associate-l_binary64_1042` `associate-/r*_binary64_1045`
2×	`sub-neg_binary64_1094` `difference-of-squares_binary64_1070` `-commutative_binary64_1032` `pow-to-exp_binary64_1170` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l_binary64_1046`
1×	`distribute-lft-out--_binary64_1053`

Counts

4 → 130

Calls

4 calls:

35.0ms	(.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 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) l)))
9.0ms	(/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) 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 8304 to 2673 computations (67.8% saved)

series3.8s (12.3%)

Error

9.5b

Counts

4 → 63

Calls

4 calls:

2.6s	(.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 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) l)))
542.0ms	(/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) l)
374.0ms	(.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)))
131.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 9011 to 5944 computations (34% saved)

simplify131.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4963	9314
1	4963	9314

prune343.0ms (1.1%)

Pruning

30 alts after pruning (30 fresh and 0 done)

	Pruned	Kept	Total
New	189	4	193
Fresh	3	26	29
Picked	1	0	1
Done	0	0	0
Total	193	30	223

Error

9.5b

Counts

223 → 30

Compiler

Compiled 10063 to 2870 computations (71.5% saved)

regimes3.5s (11.5%)

Accuracy

Total 5.8b remaining (42.3%)

Threshold costs 0b (0%)

Compiler

Compiled 54399 to 38232 computations (29.7% saved)

bsearch568.0ms (1.9%)

Steps

Iters	Range		Point
10	2.322707900397446e-209	1.905942803787666e-199	8.900337576947394e-206
9	-188501944740174.5	-95662316.03274614	-97032929.86049314

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify20.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	176	233
1	176	233

Remove

(sort M D)

Compiler

Compiled 288 to 134 computations (53.5% saved)

end0.0ms (0%)

sample9.4s (30.6%)

Algorithm

1×

intervals

Results

1.2s	8000×	body	128	valid
1.1s	8061×	body	128	nan
692.0ms	4783×	body	128	invalid

Compiler

Compiled 7939 to 5548 computations (30.1% saved)

Details

analyze2.0s (6.6%)

sample160.0ms (0.5%)

simplify37.0ms (0.1%)

prune5.0ms (0%)

localize19.0ms (0.1%)

rewrite310.0ms (1%)

series1.5s (5%)

simplify92.0ms (0.3%)

prune284.0ms (0.9%)

localize25.0ms (0.1%)

rewrite290.0ms (0.9%)

series3.1s (10%)

simplify128.0ms (0.4%)

prune316.0ms (1%)

localize33.0ms (0.1%)

rewrite292.0ms (1%)

series3.5s (11.3%)

simplify123.0ms (0.4%)

prune325.0ms (1.1%)

localize29.0ms (0.1%)

rewrite360.0ms (1.2%)

series3.8s (12.3%)

simplify131.0ms (0.4%)

prune343.0ms (1.1%)

regimes3.5s (11.5%)

bsearch568.0ms (1.9%)

simplify20.0ms (0.1%)

end0.0ms (0%)

sample9.4s (30.6%)

Profiling