Details

analyze2.0s (7.2%)

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)

sample159.0ms (0.6%)

Algorithm

1×

intervals

Results

37.0ms	294×	body	128	nan
36.0ms	256×	body	128	valid
23.0ms	161×	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 (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

28.9b

Counts

2 → 1

Compiler

Compiled 54 to 46 computations (14.8% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.5b	(.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))))
10.0b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
12.0b	(sqrt.f64 (/.f64 d h))
13.9b	(sqrt.f64 (/.f64 d l))

rewrite299.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

12.5b

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:

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))))
16.0ms	(.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 (5.4%)

Error

20.2b

Counts

4 → 50

Calls

4 calls:

839.0ms	(.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))))
541.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
43.0ms	(sqrt.f64 (/.f64 d h))
41.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 3752 to 2913 computations (22.4% saved)

simplify91.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4979	4371
1	4979	4371

prune289.0ms (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 6152 to 2905 computations (52.8% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.8b	(/.f64 (.f64 M D) (.f64 d 2))
6.5b	(.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))))
10.0b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
13.9b	(sqrt.f64 (/.f64 d l))

rewrite284.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

8.5b

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:

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))))
12.0ms	(.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)

series2.5s (8.7%)

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))))
545.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
144.0ms	(/.f64 (.f64 M D) (.f64 d 2))
44.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 6088 to 4435 computations (27.2% saved)

simplify131.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4947	5747
1	4947	5747

prune303.0ms (1.1%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	167	10	177
Fresh	5	15	20
Picked	1	0	1
Done	0	0	0
Total	173	25	198

Error

8.9b

Counts

198 → 25

Compiler

Compiled 8248 to 3277 computations (60.3% saved)

localize33.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.1b	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
3.8b	(/.f64 (.f64 M D) (.f64 d 2))
6.5b	(.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))))
10.0b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite454.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

7.8b

Rules

102×	`add-exp-log_binary64_1139`
55×	`prod-exp_binary64_1150`
46×	`add-cbrt-cube_binary64_1137`
37×	`sqrt-div_binary64_1118`
30×	`add-sqr-sqrt_binary64_1123` `associate-*r/_binary64_1043` `times-frac_binary64_1107`
29×	`frac-times_binary64_1111`
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`
16×	`associate-r_binary64_1041` `associate-*l/_binary64_1044`
14×	`pow-prod-down_binary64_1172`
10×	`pow-exp_binary64_1169` `cbrt-prod_binary64_1132`
8×	`flip3--_binary64_1105` `flip--_binary64_1076`
6×	`cbrt-undiv_binary64_1135`
4×	`add-log-exp_binary64_1140`
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×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l_binary64_1046` `associate-/r_binary64_1045` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119`

Counts

4 → 154

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 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 (cbrt.f64 l)))

Compiler

Compiled 9641 to 3786 computations (60.7% saved)

series2.6s (9.3%)

Error

8.7b

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)))) (.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))))
544.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
145.0ms	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
142.0ms	(/.f64 (.f64 M D) (.f64 d 2))

Compiler

Compiled 7079 to 5065 computations (28.5% saved)

simplify123.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4971	8326
1	4971	8326

prune512.0ms (1.8%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	199	6	205
Fresh	2	22	24
Picked	1	0	1
Done	0	0	0
Total	202	28	230

Error

8.4b

Counts

230 → 28

Compiler

Compiled 11757 to 4860 computations (58.7% saved)

localize37.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (cbrt.f64 l))
3.8b	(/.f64 (.f64 M D) (.f64 d 2))
6.5b	(.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)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 (cbrt.f64 l)))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 (cbrt.f64 l))))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
10.0b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite446.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

7.8b

Rules

113×	`add-exp-log_binary64_1139`
64×	`prod-exp_binary64_1150`
57×	`add-cbrt-cube_binary64_1137`
42×	`associate-*r/_binary64_1043`
36×	`sqrt-div_binary64_1118`
35×	`pow1_binary64_1162`
32×	`cbrt-unprod_binary64_1134`
29×	`frac-times_binary64_1111`
23×	`pow-prod-down_binary64_1172`
20×	`div-exp_binary64_1152`
16×	`associate-r_binary64_1041` `associate-*l/_binary64_1044`
14×	`add-cube-cbrt_binary64_1136` `add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101`
10×	`pow-exp_binary64_1169` `times-frac_binary64_1107`
9×	`cbrt-prod_binary64_1132`
8×	`flip3--_binary64_1105` `flip--_binary64_1076`
6×	`cbrt-undiv_binary64_1135`
4×	`add-log-exp_binary64_1140`
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 → 139

Calls

4 calls:

46.0ms	(.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)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 (cbrt.f64 l)))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 (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))
2.0ms	(cbrt.f64 (cbrt.f64 l))

Compiler

Compiled 10577 to 3580 computations (66.2% saved)

series3.6s (12.8%)

Error

8.4b

Counts

4 → 49

Calls

4 calls:

2.7s	(.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)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 (cbrt.f64 l)))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 (cbrt.f64 l))))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
579.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
151.0ms	(/.f64 (.f64 M D) (.f64 d 2))
105.0ms	(cbrt.f64 (cbrt.f64 l))

Compiler

Compiled 8534 to 5882 computations (31.1% saved)

simplify136.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4929	10040
1	4929	10040

prune430.0ms (1.5%)

Pruning

32 alts after pruning (32 fresh and 0 done)

	Pruned	Kept	Total
New	183	5	188
Fresh	0	27	27
Picked	1	0	1
Done	0	0	0
Total	184	32	216

Error

8.4b

Counts

216 → 32

Compiler

Compiled 11744 to 4019 computations (65.8% saved)

regimes3.3s (11.8%)

Accuracy

Total 4.5b remaining (34.9%)

Threshold costs 0b (0%)

Compiler

Compiled 46608 to 34011 computations (27% saved)

bsearch16.0ms (0.1%)

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

simplify22.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	184	241
1	184	241

Remove

(sort M D)

Compiler

Compiled 298 to 160 computations (46.3% saved)

end0.0ms (0%)

sample8.7s (30.9%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
1.1s	8276×	body	128	nan
676.0ms	4732×	body	128	invalid

Compiler

Compiled 6831 to 4958 computations (27.4% saved)

Details

analyze2.0s (7.2%)

sample159.0ms (0.6%)

simplify37.0ms (0.1%)

prune5.0ms (0%)

localize19.0ms (0.1%)

rewrite299.0ms (1.1%)

series1.5s (5.4%)

simplify91.0ms (0.3%)

prune289.0ms (1%)

localize27.0ms (0.1%)

rewrite284.0ms (1%)

series2.5s (8.7%)

simplify131.0ms (0.5%)

prune303.0ms (1.1%)

localize33.0ms (0.1%)

rewrite454.0ms (1.6%)

series2.6s (9.3%)

simplify123.0ms (0.4%)

prune512.0ms (1.8%)

localize37.0ms (0.1%)

rewrite446.0ms (1.6%)

series3.6s (12.8%)

simplify136.0ms (0.5%)

prune430.0ms (1.5%)

regimes3.3s (11.8%)

bsearch16.0ms (0.1%)

simplify22.0ms (0.1%)

end0.0ms (0%)

sample8.7s (30.9%)

Profiling