Details

analyze2.0s (10.8%)

Algorithm

1×

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

Compiler

Compiled 36 to 32 computations (11.1% saved)

sample152.0ms (0.8%)

Algorithm

1×

intervals

Results

49.0ms	256×	body	128	valid
41.0ms	265×	body	128	nan
30.0ms	152×	body	128	invalid

Compiler

Compiled 71 to 68 computations (4.2% saved)

simplify195.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (30.0ms)

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

Merged error: 24.5b

Counts

2 → 1

Compiler

Compiled 54 to 46 computations (14.8% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.1b	(.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))))
10.8b	(sqrt.f64 (/.f64 d h))
12.2b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
12.4b	(sqrt.f64 (/.f64 d l))

rewrite56.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`add-exp-log_binary64_801`
41×	`prod-exp_binary64_812`
32×	`add-sqr-sqrt_binary64_785`
29×	`times-frac_binary64_769`
26×	`*-un-lft-identity_binary64_763` `sqrt-prod_binary64_779` `add-cube-cbrt_binary64_798`
21×	`add-cbrt-cube_binary64_799`
16×	`associate-r_binary64_703` `div-exp_binary64_814`
14×	`sqrt-div_binary64_780`
13×	`pow1_binary64_824`
10×	`pow-exp_binary64_831`
9×	`frac-times_binary64_773` `cbrt-unprod_binary64_796`
6×	`associate-r/_binary64_705` `associate-l/_binary64_706`
4×	`rem-sqrt-square_binary64_776` `pow-prod-down_binary64_834` `flip3--_binary64_767` `add-log-exp_binary64_802` `flip--_binary64_738`
3×	`div-inv_binary64_760`
2×	`cbrt-undiv_binary64_797` `pow1/2_binary64_843` `distribute-lft-in_binary64_712` `cancel-sign-sub-inv_binary64_729` `sqrt-pow1_binary64_781` `-commutative_binary64_694` `distribute-rgt-in_binary64_713` `pow-to-exp_binary64_832` `associate-l*_binary64_704` `sub-neg_binary64_756`

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))))
15.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
4.0ms	(sqrt.f64 (/.f64 d l))
3.0ms	(sqrt.f64 (/.f64 d h))

series840.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

544.0ms	(.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))))
147.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
78.0ms	(sqrt.f64 (/.f64 d l))
71.0ms	(sqrt.f64 (/.f64 d h))

simplify84.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4954	3595
1	4954	3595

prune286.0ms (1.6%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	115	24	139
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	116	24	140

Merged error: 11.6b

Counts

140 → 24

Compiler

Compiled 5503 to 2776 computations (49.6% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.6b	(/.f64 (.f64 M D) (.f64 d 2))
5.1b	(.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))))
12.2b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
12.4b	(sqrt.f64 (/.f64 d l))

rewrite69.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

93×	`add-exp-log_binary64_801`
48×	`prod-exp_binary64_812`
37×	`add-cbrt-cube_binary64_799`
22×	`add-sqr-sqrt_binary64_785`
20×	`div-exp_binary64_814` `times-frac_binary64_769`
19×	`*-un-lft-identity_binary64_763` `add-cube-cbrt_binary64_798`
16×	`associate-r_binary64_703` `pow1_binary64_824` `cbrt-unprod_binary64_796`
13×	`sqrt-prod_binary64_779` `sqrt-div_binary64_780`
12×	`associate-*r/_binary64_705`
10×	`pow-exp_binary64_831`
9×	`frac-times_binary64_773`
7×	`pow-prod-down_binary64_834`
6×	`cbrt-undiv_binary64_797` `associate-*l/_binary64_706`
4×	`flip3--_binary64_767` `add-log-exp_binary64_802` `flip--_binary64_738`
3×	`div-inv_binary64_760`
2×	`distribute-lft-in_binary64_712` `cancel-sign-sub-inv_binary64_729` `-commutative_binary64_694` `distribute-rgt-in_binary64_713` `pow-to-exp_binary64_832` `rem-sqrt-square_binary64_776` `associate-l*_binary64_704` `sub-neg_binary64_756`
1×	`frac-2neg_binary64_774` `pow1/2_binary64_843` `sqrt-pow1_binary64_781` `associate-/r_binary64_707` `clear-num_binary64_762` `associate-/l_binary64_708`

Counts

4 → 126

Calls

4 calls:

28.0ms	(.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))

series2.1s (11.5%)

Counts

4 → 12

Calls

4 calls:

1.8s	(.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))))
165.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
77.0ms	(sqrt.f64 (/.f64 d l))
44.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify99.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4960	4485
1	4960	4485

prune264.0ms (1.4%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	131	7	138
Fresh	4	19	23
Picked	1	0	1
Done	0	0	0
Total	136	26	162

Merged error: 9.9b

Counts

162 → 26

Compiler

Compiled 6910 to 2824 computations (59.1% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 d)
4.6b	(/.f64 (.f64 M D) (.f64 d 2))
5.1b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 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))))
12.2b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite79.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`add-exp-log_binary64_801`
55×	`prod-exp_binary64_812`
46×	`add-cbrt-cube_binary64_799`
24×	`pow1_binary64_824`
23×	`cbrt-unprod_binary64_796`
20×	`div-exp_binary64_814`
18×	`associate-*r/_binary64_705`
16×	`associate-r_binary64_703`
14×	`pow-prod-down_binary64_834`
13×	`*-un-lft-identity_binary64_763` `add-cube-cbrt_binary64_798` `add-sqr-sqrt_binary64_785`
12×	`sqrt-div_binary64_780`
10×	`pow-exp_binary64_831` `times-frac_binary64_769`
9×	`frac-times_binary64_773`
6×	`cbrt-undiv_binary64_797` `associate-*l/_binary64_706`
4×	`flip3--_binary64_767` `add-log-exp_binary64_802` `flip--_binary64_738`
3×	`cbrt-prod_binary64_794`
2×	`distribute-lft-in_binary64_712` `cancel-sign-sub-inv_binary64_729` `-commutative_binary64_694` `div-inv_binary64_760` `distribute-rgt-in_binary64_713` `pow-to-exp_binary64_832` `associate-l*_binary64_704` `sub-neg_binary64_756`
1×	`frac-2neg_binary64_774` `associate-/r_binary64_707` `clear-num_binary64_762` `pow1/3_binary64_845` `associate-/l_binary64_708`

Counts

4 → 118

Calls

4 calls:

31.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.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))))
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))
1.0ms	(cbrt.f64 d)

series2.5s (13.6%)

Counts

4 → 12

Calls

4 calls:

2.2s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 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))))
158.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
146.0ms	(cbrt.f64 d)
42.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify104.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4995	5248
1	4995	5248

prune270.0ms (1.5%)

Pruning

30 alts after pruning (30 fresh and 0 done)

	Pruned	Kept	Total
New	124	6	130
Fresh	1	24	25
Picked	1	0	1
Done	0	0	0
Total	126	30	156

Merged error: 7.7b

Counts

156 → 30

Compiler

Compiled 7864 to 2830 computations (64% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.5b	(.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) h) (/.f64 1 l))
4.6b	(/.f64 (.f64 M D) (.f64 d 2))
5.1b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 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 d 2)) 2)) h) (/.f64 1 l))))
6.3b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h)

rewrite97.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

233×	`add-exp-log_binary64_801`
148×	`prod-exp_binary64_812`
60×	`add-cbrt-cube_binary64_799`
42×	`div-exp_binary64_814`
32×	`cbrt-unprod_binary64_796`
29×	`pow1_binary64_824`
25×	`pow-exp_binary64_831`
19×	`associate-r_binary64_703`
18×	`associate-*r/_binary64_705`
17×	`pow-prod-down_binary64_834`
13×	`*-un-lft-identity_binary64_763` `add-cube-cbrt_binary64_798` `add-sqr-sqrt_binary64_785`
12×	`sqrt-div_binary64_780`
10×	`times-frac_binary64_769`
9×	`frac-times_binary64_773` `1-exp_binary64_807` `rec-exp_binary64_813`
7×	`cbrt-undiv_binary64_797`
6×	`associate-*l/_binary64_706`
5×	`pow-to-exp_binary64_832`
4×	`flip3--_binary64_767` `add-log-exp_binary64_802` `flip--_binary64_738`
3×	`-commutative_binary64_694` `associate-l*_binary64_704`
2×	`distribute-lft-in_binary64_712` `cancel-sign-sub-inv_binary64_729` `div-inv_binary64_760` `distribute-rgt-in_binary64_713` `sub-neg_binary64_756`
1×	`frac-2neg_binary64_774` `associate-/r_binary64_707` `clear-num_binary64_762` `associate-/l_binary64_708` `un-div-inv_binary64_761`

Counts

4 → 154

Calls

4 calls:

34.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.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 d 2)) 2)) h) (/.f64 1 l))))
15.0ms	(.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) h) (/.f64 1 l))
9.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h)
7.0ms	(/.f64 (.f64 M D) (.f64 d 2))

series2.4s (13.3%)

Counts

4 → 12

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 (/.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 d 2)) 2)) h) (/.f64 1 l))))
157.0ms	(.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) h) (/.f64 1 l))
146.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h)
42.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify126.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4926	6272
1	4926	6272

prune310.0ms (1.7%)

Pruning

32 alts after pruning (31 fresh and 1 done)

	Pruned	Kept	Total
New	163	3	166
Fresh	1	28	29
Picked	0	1	1
Done	0	0	0
Total	164	32	196

Merged error: 7.6b

Counts

196 → 32

Compiler

Compiled 8652 to 2784 computations (67.8% saved)

regimes538.0ms (2.9%)

Compiler: Compiled 7858 to 5558 computations (29.3% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	91	229
1	91	229

end0.0ms (0%)

sample5.6s (30.6%)

Algorithm

1×

intervals

Results

1.6s	8000×	body	128	valid
1.3s	8488×	body	128	nan
960.0ms	4793×	body	128	invalid

Compiler

Compiled 1483 to 1012 computations (31.8% saved)

Details

analyze2.0s (10.8%)

sample152.0ms (0.8%)

simplify195.0ms (1.1%)

prune5.0ms (0%)

localize19.0ms (0.1%)

rewrite56.0ms (0.3%)

series840.0ms (4.6%)

simplify84.0ms (0.5%)

prune286.0ms (1.6%)

localize26.0ms (0.1%)

rewrite69.0ms (0.4%)

series2.1s (11.5%)

simplify99.0ms (0.5%)

prune264.0ms (1.4%)

localize33.0ms (0.2%)

rewrite79.0ms (0.4%)

series2.5s (13.6%)

simplify104.0ms (0.6%)

prune270.0ms (1.5%)

localize32.0ms (0.2%)

rewrite97.0ms (0.5%)

series2.4s (13.3%)

simplify126.0ms (0.7%)

prune310.0ms (1.7%)

regimes538.0ms (2.9%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample5.6s (30.6%)

Profiling