Details

analyze2.3s (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)

sample163.0ms (0.5%)

Algorithm

1×

intervals

Results

40.0ms	263×	body	128	nan
39.0ms	256×	body	128	valid
26.0ms	169×	body	128	invalid

Compiler

Compiled 71 to 68 computations (4.2% saved)

simplify46.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5205	41

prune9.0ms (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

27.0b

Counts

2 → 1

Compiler

Compiled 54 to 46 computations (14.8% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.7b	(.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))))
10.2b	(sqrt.f64 (/.f64 d h))
15.0b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
16.0b	(sqrt.f64 (/.f64 d l))

rewrite641.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

14.0b

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:

17.0ms	(.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))
6.0ms	(sqrt.f64 (/.f64 d l))
3.0ms	(sqrt.f64 (/.f64 d h))

Compiler

Compiled 4932 to 2296 computations (53.4% saved)

series1.9s (5.3%)

Error

17.5b

Counts

4 → 50

Calls

4 calls:

1.1s	(.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))
52.0ms	(sqrt.f64 (/.f64 d l))
43.0ms	(sqrt.f64 (/.f64 d h))

Compiler

Compiled 3752 to 2913 computations (22.4% saved)

simplify103.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4979	4371
1	4979	4371

prune322.0ms (0.9%)

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

10.8b

Counts

178 → 21

Compiler

Compiled 6159 to 2904 computations (52.8% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.1b	(/.f64 (.f64 M D) (.f64 d 2))
5.7b	(.f64 (.f64 (sqrt.f64 (/.f64 d 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))))
10.2b	(sqrt.f64 (/.f64 d h))
15.0b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite379.0ms (1.1%)

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:

23.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 d 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))))
18.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
8.0ms	(/.f64 (.f64 M D) (.f64 d 2))
3.0ms	(sqrt.f64 (/.f64 d h))

Compiler

Compiled 6223 to 2306 computations (62.9% saved)

series3.8s (10.7%)

Error

8.5b

Counts

4 → 55

Calls

4 calls:

2.8s	(.f64 (.f64 (sqrt.f64 (/.f64 d 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))))
677.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
173.0ms	(/.f64 (.f64 M D) (.f64 d 2))
64.0ms	(sqrt.f64 (/.f64 d h))

Compiler

Compiled 6480 to 4729 computations (27% saved)

simplify128.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4953	6056
1	4953	6056

prune359.0ms (1%)

Pruning

25 alts after pruning (24 fresh and 1 done)

	Pruned	Kept	Total
New	176	5	181
Fresh	1	19	20
Picked	0	1	1
Done	0	0	0
Total	177	25	202

Error

7.7b

Counts

202 → 25

Compiler

Compiled 8291 to 3267 computations (60.6% saved)

localize32.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.4b	(sqrt.f64 (/.f64 (cbrt.f64 d) h))
4.1b	(/.f64 (.f64 M D) (.f64 d 2))
5.7b	(.f64 (.f64 (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) 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))))
15.0b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite392.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

6.0b

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:

32.0ms	(.f64 (.f64 (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) 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))
4.0ms	(sqrt.f64 (/.f64 (cbrt.f64 d) h))

Compiler

Compiled 7884 to 2640 computations (66.5% saved)

series4.1s (11.5%)

Error

7.7b

Counts

4 → 55

Calls

4 calls:

3.0s	(.f64 (.f64 (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) 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))))
672.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
163.0ms	(/.f64 (.f64 M D) (.f64 d 2))
161.0ms	(sqrt.f64 (/.f64 (cbrt.f64 d) h))

Compiler

Compiled 7407 to 5263 computations (28.9% saved)

simplify133.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4957	7292
1	4957	7292

prune422.0ms (1.2%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	191	6	197
Fresh	3	20	23
Picked	1	0	1
Done	1	0	1
Total	196	26	222

Error

7.0b

Counts

222 → 26

Compiler

Compiled 10197 to 3694 computations (63.8% saved)

localize49.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.1b	(/.f64 (.f64 M D) (.f64 2 d))
5.7b	(.f64 (.f64 (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) h))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.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 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
6.4b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (*.f64 (cbrt.f64 h) (cbrt.f64 h)))
7.9b	(.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))

rewrite585.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

6.0b

Rules

291×	`add-exp-log_binary64_1139`
189×	`prod-exp_binary64_1150`
70×	`add-cbrt-cube_binary64_1137`
51×	`cbrt-unprod_binary64_1134`
45×	`div-exp_binary64_1152`
36×	`pow1_binary64_1162`
30×	`pow-exp_binary64_1169`
26×	`associate-r_binary64_1041`
22×	`pow-prod-down_binary64_1172`
19×	`times-frac_binary64_1107`
18×	`add-cube-cbrt_binary64_1136` `add-sqr-sqrt_binary64_1123` `-un-lft-identity_binary64_1101` `associate-r/_binary64_1043`
12×	`sqrt-div_binary64_1118`
9×	`cbrt-undiv_binary64_1135` `cbrt-prod_binary64_1132` `frac-times_binary64_1111`
6×	`pow-to-exp_binary64_1170` `associate-*l/_binary64_1044`
4×	`add-log-exp_binary64_1140` `flip3--_binary64_1105` `flip--_binary64_1076`
3×	`associate-l_binary64_1042` `*-commutative_binary64_1032`
2×	`div-inv_binary64_1098` `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`

Counts

4 → 174

Calls

4 calls:

28.0ms	(.f64 (.f64 (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) h))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.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 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
27.0ms	(.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
17.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (*.f64 (cbrt.f64 h) (cbrt.f64 h)))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 11246 to 3389 computations (69.9% saved)

series5.0s (14%)

Error

7.0b

Counts

4 → 61

Calls

4 calls:

3.0s	(.f64 (.f64 (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) h))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.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 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
835.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (*.f64 (cbrt.f64 h) (cbrt.f64 h)))
776.0ms	(.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
180.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 8620 to 5960 computations (30.9% saved)

simplify157.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4986	8884
1	4986	8884

prune434.0ms (1.2%)

Pruning

27 alts after pruning (26 fresh and 1 done)

	Pruned	Kept	Total
New	234	1	235
Fresh	0	25	25
Picked	0	1	1
Done	0	0	0
Total	234	27	261

Error

6.6b

Counts

261 → 27

Compiler

Compiled 11527 to 3437 computations (70.2% saved)

regimes3.5s (9.9%)

Accuracy

Total 5.3b remaining (39%)

Threshold costs 0b (0%)

Compiler

Compiled 42555 to 30826 computations (27.6% saved)

bsearch13.0ms (0%)

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	121	190
1	121	190

Remove

(sort M D)

Compiler

Compiled 238 to 136 computations (42.9% saved)

end0.0ms (0%)

sample10.5s (29.5%)

Algorithm

1×

intervals

Results

1.5s	8000×	body	128	valid
1.4s	8488×	body	128	nan
881.0ms	4781×	body	128	invalid

Compiler

Compiled 6222 to 4491 computations (27.8% saved)

Details

analyze2.3s (6.6%)

sample163.0ms (0.5%)

simplify46.0ms (0.1%)

prune9.0ms (0%)

localize19.0ms (0.1%)

rewrite641.0ms (1.8%)

series1.9s (5.3%)

simplify103.0ms (0.3%)

prune322.0ms (0.9%)

localize23.0ms (0.1%)

rewrite379.0ms (1.1%)

series3.8s (10.7%)

simplify128.0ms (0.4%)

prune359.0ms (1%)

localize32.0ms (0.1%)

rewrite392.0ms (1.1%)

series4.1s (11.5%)

simplify133.0ms (0.4%)

prune422.0ms (1.2%)

localize49.0ms (0.1%)

rewrite585.0ms (1.6%)

series5.0s (14%)

simplify157.0ms (0.4%)

prune434.0ms (1.2%)

regimes3.5s (9.9%)

bsearch13.0ms (0%)

simplify22.0ms (0.1%)

end0.0ms (0%)

sample10.5s (29.5%)

Profiling