Details

analyze2.0s (6.7%)

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)

sample156.0ms (0.5%)

Algorithm

1×

intervals

Results

41.0ms	256×	body	128	valid
35.0ms	277×	body	128	nan
23.0ms	167×	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

23.6b

Counts

2 → 1

Compiler

Compiled 54 to 46 computations (14.8% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.9b	(.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))))
9.1b	(sqrt.f64 (/.f64 d l))
9.1b	(sqrt.f64 (/.f64 d h))
13.8b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite306.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

8.9b

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)

series1.5s (5.1%)

Error

17.1b

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))))
545.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
45.0ms	(sqrt.f64 (/.f64 d h))
42.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 3752 to 2913 computations (22.4% saved)

simplify93.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4979	4371
1	4979	4371

prune282.0ms (0.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	161	16	177
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	162	16	178

Error

10.1b

Counts

178 → 16

Compiler

Compiled 6067 to 2811 computations (53.7% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.5b	(/.f64 (.f64 M D) (.f64 d 2))
4.9b	(.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))))
9.1b	(sqrt.f64 (/.f64 d l))
13.8b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite295.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

7.3b

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:

26.0ms	(.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)

series2.4s (8.2%)

Error

10.1b

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))))
574.0ms	(.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 6088 to 4435 computations (27.2% saved)

simplify127.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4947	5747
1	4947	5747

prune303.0ms (1%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	170	7	177
Fresh	3	12	15
Picked	1	0	1
Done	0	0	0
Total	174	19	193

Error

9.5b

Counts

193 → 19

Compiler

Compiled 8095 to 3143 computations (61.2% saved)

localize35.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.7b	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
4.5b	(/.f64 (.f64 M D) (.f64 d 2))
4.9b	(.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))))
13.8b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite464.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

6.3b

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))))
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 d (cbrt.f64 l)))

Compiler

Compiled 9641 to 3786 computations (60.7% saved)

series2.6s (8.7%)

Error

9.0b

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))))
549.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
142.0ms	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
133.0ms	(/.f64 (.f64 M D) (.f64 d 2))

Compiler

Compiled 7079 to 5065 computations (28.5% saved)

simplify126.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4971	8326
1	4971	8326

prune453.0ms (1.5%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	198	7	205
Fresh	3	15	18
Picked	1	0	1
Done	0	0	0
Total	202	22	224

Error

8.7b

Counts

224 → 22

Compiler

Compiled 11555 to 4700 computations (59.3% saved)

localize39.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.5b	(/.f64 (.f64 M D) (.f64 2 d))
4.9b	(.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 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l)))))
6.3b	(/.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))
7.4b	(.f64 (/.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (*.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l)))

rewrite659.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

6.2b

Rules

291×	`add-exp-log_binary64_1139`
141×	`prod-exp_binary64_1150`
93×	`div-exp_binary64_1152`
70×	`add-cbrt-cube_binary64_1137`
39×	`cbrt-unprod_binary64_1134`
36×	`sqrt-div_binary64_1118`
30×	`pow-exp_binary64_1169` `frac-times_binary64_1111` `associate-*r/_binary64_1043`
27×	`add-sqr-sqrt_binary64_1123`
25×	`associate-r_binary64_1041`
24×	`pow1_binary64_1162`
23×	`times-frac_binary64_1107`
21×	`cbrt-undiv_binary64_1135`
19×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
17×	`associate-*l/_binary64_1044`
14×	`pow-prod-down_binary64_1172`
10×	`cbrt-prod_binary64_1132`
8×	`flip3--_binary64_1105` `flip--_binary64_1076`
6×	`pow-to-exp_binary64_1170` `associate-l_binary64_1042`
4×	`add-log-exp_binary64_1140` `div-inv_binary64_1098`
3×	`unswap-sqr_binary64_1069`
2×	`-commutative_binary64_1032` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l_binary64_1046` `associate-/r*_binary64_1045` `sub-neg_binary64_1094` `distribute-rgt-in_binary64_1051` `cancel-sign-sub-inv_binary64_1067` `distribute-lft-in_binary64_1050`

Counts

4 → 194

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 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l)))))
25.0ms	(.f64 (/.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (*.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l)))
11.0ms	(/.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 13957 to 5004 computations (64.1% saved)

series3.3s (11.1%)

Error

8.7b

Counts

4 → 57

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 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l)))))
793.0ms	(/.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))
591.0ms	(.f64 (/.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (*.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l)))
149.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 8422 to 5827 computations (30.8% saved)

simplify145.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

251 → 251

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4980	10617
1	4980	10617

prune578.0ms (1.9%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	246	5	251
Fresh	1	20	21
Picked	1	0	1
Done	0	0	0
Total	248	25	273

Error

8.3b

Counts

273 → 25

Compiler

Compiled 13862 to 5081 computations (63.3% saved)

regimes3.8s (12.7%)

Accuracy

Total 4.2b remaining (33.9%)

Threshold costs 0b (0%)

Compiler

Compiled 59397 to 42348 computations (28.7% saved)

bsearch16.0ms (0.1%)

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

simplify29.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	153	343
1	153	343

Remove

(sort M D)

Compiler

Compiled 430 to 226 computations (47.4% saved)

end0.0ms (0%)

sample10.0s (33.4%)

Algorithm

1×

intervals

Results

1.2s	8000×	body	128	valid
1.1s	8415×	body	128	nan
683.0ms	4823×	body	128	invalid

Compiler

Compiled 8724 to 6182 computations (29.1% saved)

Details

analyze2.0s (6.7%)

sample156.0ms (0.5%)

simplify37.0ms (0.1%)

prune5.0ms (0%)

localize25.0ms (0.1%)

rewrite306.0ms (1%)

series1.5s (5.1%)

simplify93.0ms (0.3%)

prune282.0ms (0.9%)

localize27.0ms (0.1%)

rewrite295.0ms (1%)

series2.4s (8.2%)

simplify127.0ms (0.4%)

prune303.0ms (1%)

localize35.0ms (0.1%)

rewrite464.0ms (1.6%)

series2.6s (8.7%)

simplify126.0ms (0.4%)

prune453.0ms (1.5%)

localize39.0ms (0.1%)

rewrite659.0ms (2.2%)

series3.3s (11.1%)

simplify145.0ms (0.5%)

prune578.0ms (1.9%)

regimes3.8s (12.7%)

bsearch16.0ms (0.1%)

simplify29.0ms (0.1%)

end0.0ms (0%)

sample10.0s (33.4%)

Profiling