Details

analyze2.1s (4%)

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)

sample147.0ms (0.3%)

Algorithm

1×

intervals

Results

37.0ms	256×	body	128	valid
33.0ms	258×	body	128	nan
19.0ms	134×	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

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

26.7b

Counts

2 → 1

Compiler

Compiled 54 to 46 computations (14.8% saved)

localize21.0ms (0%)

Local error

Found 4 expressions with local error:

7.1b	(/.f64 (.f64 M D) (.f64 d 2))
11.1b	(sqrt.f64 (/.f64 d h))
13.2b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
13.2b	(sqrt.f64 (/.f64 d l))

rewrite378.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

12.4b

Rules

84×	`add-exp-log_binary64_1139`
42×	`prod-exp_binary64_1150`
31×	`add-sqr-sqrt_binary64_1123`
30×	`times-frac_binary64_1107`
28×	`add-cbrt-cube_binary64_1137`
26×	`sqrt-prod_binary64_1117`
25×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
20×	`div-exp_binary64_1152`
13×	`associate-r_binary64_1041`
10×	`pow-exp_binary64_1169` `cbrt-unprod_binary64_1134`
8×	`pow1_binary64_1162`
6×	`cbrt-undiv_binary64_1135`
4×	`add-log-exp_binary64_1140` `div-inv_binary64_1098` `rem-sqrt-square_binary64_1114`
2×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `sqrt-div_binary64_1118` `pow-to-exp_binary64_1170`
1×	`pow-prod-down_binary64_1172` `associate-r/_binary64_1043` `associate-l_binary64_1042` `-commutative_binary64_1032` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l_binary64_1046` `associate-/r_binary64_1045`

Counts

4 → 115

Calls

4 calls:

12.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
9.0ms	(sqrt.f64 (/.f64 d l))
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
3.0ms	(sqrt.f64 (/.f64 d h))

Compiler

Compiled 3820 to 1753 computations (54.1% saved)

series1.2s (2.3%)

Error

25.7b

Counts

4 → 36

Calls

4 calls:

865.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
177.0ms	(/.f64 (.f64 M D) (.f64 d 2))
59.0ms	(sqrt.f64 (/.f64 d h))
58.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 2196 to 1866 computations (15% saved)

simplify67.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5039	2413

prune274.0ms (0.5%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	130	21	151
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	131	21	152

Error

13.1b

Counts

152 → 21

Compiler

Compiled 3233 to 1697 computations (47.5% saved)

localize31.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.6b	(.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))))
7.1b	(/.f64 (.f64 M D) (.f64 d 2))
13.2b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
13.2b	(sqrt.f64 (/.f64 d l))

rewrite495.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

11.1b

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:

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))))
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 5947 to 2215 computations (62.8% saved)

series5.2s (10%)

Error

13.1b

Counts

4 → 55

Calls

4 calls:

4.0s	(.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))))
891.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
208.0ms	(/.f64 (.f64 M D) (.f64 d 2))
68.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 4809 to 3911 computations (18.7% saved)

simplify134.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4947	6103
1	4947	6103

prune333.0ms (0.6%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	172	9	181
Fresh	3	17	20
Picked	1	0	1
Done	0	0	0
Total	176	26	202

Error

13.0b

Counts

202 → 26

Compiler

Compiled 4844 to 2177 computations (55.1% saved)

localize39.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.8b	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
5.6b	(.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))))
7.1b	(/.f64 (.f64 M D) (.f64 d 2))
13.2b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite955.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

10.0b

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:

36.0ms	(.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 9198 to 3624 computations (60.6% saved)

series5.4s (10.5%)

Error

12.5b

Counts

4 → 55

Calls

4 calls:

4.0s	(.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))))
935.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
238.0ms	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
221.0ms	(/.f64 (.f64 M D) (.f64 d 2))

Compiler

Compiled 5588 to 4406 computations (21.2% saved)

simplify132.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

209 → 209

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4971	8682
1	4971	8682

prune490.0ms (0.9%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	201	8	209
Fresh	8	17	25
Picked	1	0	1
Done	0	0	0
Total	210	25	235

Error

12.0b

Counts

235 → 25

Compiler

Compiled 7357 to 3211 computations (56.4% saved)

localize47.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.8b	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
5.6b	(.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 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
7.1b	(/.f64 (.f64 M D) (.f64 2 d))
8.1b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l))))

rewrite977.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

10.2b

Rules

248×	`add-exp-log_binary64_1139`
144×	`prod-exp_binary64_1150`
59×	`add-cbrt-cube_binary64_1137`
56×	`div-exp_binary64_1152`
40×	`cbrt-unprod_binary64_1134`
37×	`sqrt-div_binary64_1118`
30×	`associate-*r/_binary64_1043`
29×	`frac-times_binary64_1111`
25×	`pow1_binary64_1162` `pow-exp_binary64_1169`
24×	`add-sqr-sqrt_binary64_1123`
22×	`times-frac_binary64_1107` `sqrt-prod_binary64_1117`
19×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
16×	`associate-*l/_binary64_1044`
14×	`pow-prod-down_binary64_1172`
12×	`cbrt-undiv_binary64_1135`
10×	`cbrt-prod_binary64_1132`
8×	`associate-r_binary64_1041` `flip3--_binary64_1105` `flip--_binary64_1076`
5×	`pow-to-exp_binary64_1170`
4×	`add-log-exp_binary64_1140`
3×	`div-inv_binary64_1098` `rem-sqrt-square_binary64_1114`
2×	`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 → 176

Calls

4 calls:

41.0ms	(.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 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
18.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l))))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
6.0ms	(sqrt.f64 (/.f64 d (cbrt.f64 l)))

Compiler

Compiled 13566 to 4294 computations (68.3% saved)

series6.6s (12.8%)

Error

11.7b

Counts

4 → 55

Calls

4 calls:

4.0s	(.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 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
2.0s	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l))))
242.0ms	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
225.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 6908 to 5036 computations (27.1% saved)

simplify142.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

231 → 231

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4963	9822
1	4963	9822

prune422.0ms (0.8%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	224	7	231
Fresh	2	22	24
Picked	1	0	1
Done	0	0	0
Total	227	29	256

Error

11.4b

Counts

256 → 29

Compiler

Compiled 7055 to 2459 computations (65.1% saved)

regimes21.1s (40.9%)

Accuracy

Total 3.8b remaining (27.5%)

Threshold costs 0b (0%)

Compiler

Compiled 282959 to 186561 computations (34.1% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	119	117
1	119	117

end16.0ms (0%)

Remove: (sort M D)
Compiler: Compiled 213 to 126 computations (40.8% saved)

sample4.9s (9.5%)

Algorithm

1×

intervals

Results

1.2s	8000×	body	128	valid
1.1s	8180×	body	128	nan
710.0ms	4816×	body	128	invalid

Compiler

Compiled 1454 to 1013 computations (30.3% saved)

Details

analyze2.1s (4%)

sample147.0ms (0.3%)

simplify38.0ms (0.1%)

prune6.0ms (0%)

localize21.0ms (0%)

rewrite378.0ms (0.7%)

series1.2s (2.3%)

simplify67.0ms (0.1%)

prune274.0ms (0.5%)

localize31.0ms (0.1%)

rewrite495.0ms (1%)

series5.2s (10%)

simplify134.0ms (0.3%)

prune333.0ms (0.6%)

localize39.0ms (0.1%)

rewrite955.0ms (1.8%)

series5.4s (10.5%)

simplify132.0ms (0.3%)

prune490.0ms (0.9%)

localize47.0ms (0.1%)

rewrite977.0ms (1.9%)

series6.6s (12.8%)

simplify142.0ms (0.3%)

prune422.0ms (0.8%)

regimes21.1s (40.9%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end16.0ms (0%)

sample4.9s (9.5%)

Profiling