Details

analyze2.4s (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)

sample166.0ms (0.5%)

Algorithm

1×

intervals

Results

39.0ms	256×	body	128	valid
37.0ms	270×	body	128	nan
26.0ms	168×	body	128	invalid

Compiler

Compiled 71 to 68 computations (4.2% saved)

simplify40.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (35.0ms)

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)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

8.0b	(.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))))
9.5b	(sqrt.f64 (/.f64 d h))
12.6b	(sqrt.f64 (/.f64 d l))
13.7b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite350.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

16.6b

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` `*-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:

22.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
18.0ms	(.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))))
6.0ms	(sqrt.f64 (/.f64 d l))
5.0ms	(sqrt.f64 (/.f64 d h))

Compiler

Compiled 4932 to 2296 computations (53.4% saved)

series1.9s (5.7%)

Error

20.9b

Counts

4 → 50

Calls

4 calls:

1.0s	(.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))))
666.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
50.0ms	(sqrt.f64 (/.f64 d l))
41.0ms	(sqrt.f64 (/.f64 d h))

Compiler

Compiled 3752 to 2913 computations (22.4% saved)

simplify109.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4979	4371
1	4979	4371

prune330.0ms (1%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	155	22	177
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	156	22	178

Error

14.2b

Counts

178 → 22

Compiler

Compiled 6262 to 2958 computations (52.8% saved)

localize35.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.5b	(/.f64 (.f64 M D) (.f64 d 2))
8.0b	(.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))))
12.6b	(sqrt.f64 (/.f64 d l))
13.7b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite346.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

12.3b

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:

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))))
20.0ms	(.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)

series3.0s (9%)

Error

14.2b

Counts

4 → 51

Calls

4 calls:

2.0s	(.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))))
657.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
165.0ms	(/.f64 (.f64 M D) (.f64 d 2))
46.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 6088 to 4435 computations (27.2% saved)

simplify156.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4947	5747
1	4947	5747

prune374.0ms (1.1%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	169	8	177
Fresh	4	17	21
Picked	1	0	1
Done	0	0	0
Total	174	25	199

Error

13.6b

Counts

199 → 25

Compiler

Compiled 8257 to 3269 computations (60.4% saved)

localize32.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.5b	(sqrt.f64 (/.f64 (cbrt.f64 d) l))
5.5b	(/.f64 (.f64 M D) (.f64 d 2))
8.0b	(.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))))
13.7b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite412.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

12.1b

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×	`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 → 142

Calls

4 calls:

48.0ms	(.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))))
12.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
11.0ms	(/.f64 (.f64 M D) (.f64 d 2))
8.0ms	(sqrt.f64 (/.f64 (cbrt.f64 d) l))

Compiler

Compiled 7884 to 2640 computations (66.5% saved)

series3.2s (9.9%)

Error

13.3b

Counts

4 → 51

Calls

4 calls:

2.1s	(.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))))
679.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
197.0ms	(/.f64 (.f64 M D) (.f64 d 2))
172.0ms	(sqrt.f64 (/.f64 (cbrt.f64 d) l))

Compiler

Compiled 6949 to 4919 computations (29.2% saved)

simplify151.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4965	6948
1	4965	6948

prune442.0ms (1.3%)

Pruning

27 alts after pruning (26 fresh and 1 done)

	Pruned	Kept	Total
New	191	2	193
Fresh	0	24	24
Picked	0	1	1
Done	0	0	0
Total	191	27	218

Error

13.3b

Counts

218 → 27

Compiler

Compiled 9959 to 3618 computations (63.7% saved)

localize31.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.9b	(/.f64 M (/.f64 d (/.f64 D 2)))
8.0b	(.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 M (/.f64 d (/.f64 D 2))) 2)) (/.f64 h l))))
12.6b	(sqrt.f64 (/.f64 d l))
13.7b	(.f64 (.f64 1/2 (pow.f64 (/.f64 M (/.f64 d (/.f64 D 2))) 2)) (/.f64 h l))

rewrite913.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

11.6b

Rules

415×	`times-frac_binary64_1107`
207×	`add-sqr-sqrt_binary64_1123`
204×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
79×	`add-exp-log_binary64_1139`
44×	`associate-/r*_binary64_1045`
34×	`add-cbrt-cube_binary64_1137`
32×	`prod-exp_binary64_1150`
25×	`div-exp_binary64_1152`
19×	`div-inv_binary64_1098`
16×	`pow1_binary64_1162` `associate-r_binary64_1041`
13×	`sqrt-div_binary64_1118` `sqrt-prod_binary64_1117`
12×	`cbrt-unprod_binary64_1134` `associate-*r/_binary64_1043`
9×	`frac-times_binary64_1111`
8×	`pow-exp_binary64_1169` `cbrt-undiv_binary64_1135`
7×	`pow-prod-down_binary64_1172`
6×	`associate-*l/_binary64_1044`
5×	`associate-/r/_binary64_1047`
4×	`add-log-exp_binary64_1140` `flip3--_binary64_1105` `flip--_binary64_1076`
3×	`associate-/l*_binary64_1046`
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`

Counts

4 → 299

Calls

4 calls:

71.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 M (/.f64 d (/.f64 D 2))) 2)) (/.f64 h l))
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 M (/.f64 d (/.f64 D 2))) 2)) (/.f64 h l))))
14.0ms	(/.f64 M (/.f64 d (/.f64 D 2)))
3.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 14974 to 5837 computations (61% saved)

series2.9s (8.8%)

Error

13.3b

Counts

4 → 51

Calls

4 calls:

1.9s	(.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 M (/.f64 d (/.f64 D 2))) 2)) (/.f64 h l))))
650.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 M (/.f64 d (/.f64 D 2))) 2)) (/.f64 h l))
195.0ms	(/.f64 M (/.f64 d (/.f64 D 2)))
48.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 6088 to 4441 computations (27.1% saved)

simplify190.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

350 → 350

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4963	10428
1	4963	10428

prune861.0ms (2.6%)

Pruning

27 alts after pruning (26 fresh and 1 done)

	Pruned	Kept	Total
New	348	2	350
Fresh	1	24	25
Picked	1	0	1
Done	0	1	1
Total	350	27	377

Error

13.0b

Counts

377 → 27

Compiler

Compiled 15785 to 5770 computations (63.4% saved)

regimes3.8s (11.7%)

Accuracy

Total 5.5b remaining (38.8%)

Threshold costs 0b (0%)

Compiler

Compiled 46657 to 34907 computations (25.2% saved)

bsearch13.0ms (0%)

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

simplify32.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	168	302
1	168	302

Remove

(sort M D)

Compiler

Compiled 382 to 212 computations (44.5% saved)

end0.0ms (0%)

sample10.6s (32.4%)

Algorithm

1×

intervals

Results

1.4s	8000×	body	128	valid
1.3s	8505×	body	128	nan
829.0ms	4762×	body	128	invalid

Compiler

Compiled 6880 to 5112 computations (25.7% saved)

Details

analyze2.4s (7.2%)

sample166.0ms (0.5%)

simplify40.0ms (0.1%)

prune5.0ms (0%)

localize30.0ms (0.1%)

rewrite350.0ms (1.1%)

series1.9s (5.7%)

simplify109.0ms (0.3%)

prune330.0ms (1%)

localize35.0ms (0.1%)

rewrite346.0ms (1.1%)

series3.0s (9%)

simplify156.0ms (0.5%)

prune374.0ms (1.1%)

localize32.0ms (0.1%)

rewrite412.0ms (1.3%)

series3.2s (9.9%)

simplify151.0ms (0.5%)

prune442.0ms (1.3%)

localize31.0ms (0.1%)

rewrite913.0ms (2.8%)

series2.9s (8.8%)

simplify190.0ms (0.6%)

prune861.0ms (2.6%)

regimes3.8s (11.7%)

bsearch13.0ms (0%)

simplify32.0ms (0.1%)

end0.0ms (0%)

sample10.6s (32.4%)

Profiling