Details

analyze1.6s (9.4%)

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)

sample130.0ms (0.8%)

Algorithm

1×

intervals

Results

38.0ms	301×	body	128	nan
35.0ms	256×	body	128	valid
26.0ms	163×	body	128	invalid

Compiler

Compiled 71 to 68 computations (4.2% saved)

simplify128.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5205	41

prune8.0ms (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: 25.9b

Counts

2 → 1

Compiler

Compiled 54 to 46 computations (14.8% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.0b	(.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))))
11.1b	(sqrt.f64 (/.f64 d h))
12.5b	(sqrt.f64 (/.f64 d l))
13.4b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite48.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`add-exp-log_binary64_1139`
41×	`prod-exp_binary64_1150`
32×	`add-sqr-sqrt_binary64_1123`
29×	`times-frac_binary64_1107`
26×	`*-un-lft-identity_binary64_1101` `sqrt-prod_binary64_1117` `add-cube-cbrt_binary64_1136`
21×	`add-cbrt-cube_binary64_1137`
16×	`associate-r_binary64_1041` `div-exp_binary64_1152`
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×	`rem-sqrt-square_binary64_1114` `add-log-exp_binary64_1140` `flip--_binary64_1076` `flip3--_binary64_1105` `pow-prod-down_binary64_1172`
3×	`div-inv_binary64_1098`
2×	`-commutative_binary64_1032` `sub-neg_binary64_1094` `sqrt-pow1_binary64_1119` `distribute-lft-in_binary64_1050` `cbrt-undiv_binary64_1135` `associate-l*_binary64_1042` `cancel-sign-sub-inv_binary64_1067` `pow-to-exp_binary64_1170` `distribute-rgt-in_binary64_1051` `pow1/2_binary64_1181`

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))

series1.5s (8.8%)

Counts

4 → 50

Calls

4 calls:

869.0ms	(.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))))
562.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
40.0ms	(sqrt.f64 (/.f64 d h))
35.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 2576 to 2255 computations (12.5% saved)

simplify95.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5007	4365

prune309.0ms (1.8%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	151	26	177
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	152	26	178

Merged error: 10.7b

Counts

178 → 26

Compiler

Compiled 6289 to 3034 computations (51.8% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

6.2b	(/.f64 (.f64 M D) (.f64 d 2))
7.0b	(.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))))
12.5b	(sqrt.f64 (/.f64 d l))
13.4b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite61.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

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×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
16×	`cbrt-unprod_binary64_1134` `pow1_binary64_1162` `associate-r_binary64_1041`
13×	`sqrt-prod_binary64_1117` `sqrt-div_binary64_1118`
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` `flip--_binary64_1076` `flip3--_binary64_1105`
3×	`div-inv_binary64_1098`
2×	`-commutative_binary64_1032` `rem-sqrt-square_binary64_1114` `sub-neg_binary64_1094` `distribute-lft-in_binary64_1050` `associate-l*_binary64_1042` `cancel-sign-sub-inv_binary64_1067` `pow-to-exp_binary64_1170` `distribute-rgt-in_binary64_1051`
1×	`frac-2neg_binary64_1112` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `associate-/l_binary64_1046` `associate-/r_binary64_1045` `pow1/2_binary64_1181`

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))

series2.5s (14.7%)

Counts

4 → 51

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))))
549.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
141.0ms	(/.f64 (.f64 M D) (.f64 d 2))
41.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 4131 to 3370 computations (18.4% saved)

simplify105.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5007	5758

prune309.0ms (1.8%)

Pruning

30 alts after pruning (30 fresh and 0 done)

	Pruned	Kept	Total
New	170	7	177
Fresh	2	23	25
Picked	1	0	1
Done	0	0	0
Total	173	30	203

Merged error: 9.9b

Counts

203 → 30

Compiler

Compiled 8305 to 3389 computations (59.2% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

12.5b	(sqrt.f64 (/.f64 d l))
12.5b	(sqrt.f64 (/.f64 d l))
12.5b	(sqrt.f64 (/.f64 d l))
13.4b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite38.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-exp-log_binary64_1139`
41×	`add-sqr-sqrt_binary64_1123`
39×	`sqrt-prod_binary64_1117` `times-frac_binary64_1107`
38×	`prod-exp_binary64_1150`
32×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
16×	`add-cbrt-cube_binary64_1137` `div-exp_binary64_1152`
13×	`associate-r_binary64_1041`
10×	`pow-exp_binary64_1169`
9×	`pow1_binary64_1162`
6×	`rem-sqrt-square_binary64_1114` `cbrt-unprod_binary64_1134`
4×	`add-log-exp_binary64_1140` `div-inv_binary64_1098`
3×	`sqrt-pow1_binary64_1119` `sqrt-div_binary64_1118` `pow1/2_binary64_1181`
2×	`cbrt-undiv_binary64_1135` `pow-to-exp_binary64_1170`
1×	`-commutative_binary64_1032` `associate-r/_binary64_1043` `pow-prod-down_binary64_1172` `associate-l_binary64_1042`

Counts

4 → 119

Calls

4 calls:

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 l))
3.0ms	(sqrt.f64 (/.f64 d l))

series717.0ms (4.2%)

Counts

4 → 33

Calls

4 calls:

575.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
49.0ms	(sqrt.f64 (/.f64 d l))
48.0ms	(sqrt.f64 (/.f64 d l))
46.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 3492 to 2310 computations (33.8% saved)

simplify62.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5010	2401

prune282.0ms (1.6%)

Pruning

32 alts after pruning (32 fresh and 0 done)

	Pruned	Kept	Total
New	148	4	152
Fresh	1	28	29
Picked	1	0	1
Done	0	0	0
Total	150	32	182

Merged error: 9.9b

Counts

182 → 32

Compiler

Compiled 9134 to 2963 computations (67.6% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

8.5b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h)
12.5b	(sqrt.f64 (/.f64 d l))
12.5b	(sqrt.f64 (/.f64 d l))
12.5b	(sqrt.f64 (/.f64 d l))

rewrite32.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`sqrt-prod_binary64_1117`
35×	`add-sqr-sqrt_binary64_1123`
34×	`add-exp-log_binary64_1139`
30×	`times-frac_binary64_1107`
26×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
19×	`prod-exp_binary64_1150`
9×	`pow1_binary64_1162` `add-cbrt-cube_binary64_1137`
6×	`rem-sqrt-square_binary64_1114`
5×	`pow-exp_binary64_1169`
4×	`add-log-exp_binary64_1140` `div-exp_binary64_1152`
3×	`cbrt-unprod_binary64_1134` `sqrt-pow1_binary64_1119` `div-inv_binary64_1098` `associate-r_binary64_1041` `sqrt-div_binary64_1118` `pow1/2_binary64_1181`
1×	`-commutative_binary64_1032` `pow-prod-down_binary64_1172` `associate-l*_binary64_1042` `pow-to-exp_binary64_1170`

Counts

4 → 98

Calls

4 calls:

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

series534.0ms (3.1%)

Counts

4 → 30

Calls

4 calls:

384.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h)
52.0ms	(sqrt.f64 (/.f64 d l))
50.0ms	(sqrt.f64 (/.f64 d l))
46.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 3186 to 2118 computations (33.5% saved)

simplify59.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5216	1707

prune204.0ms (1.2%)

Pruning

32 alts after pruning (31 fresh and 1 done)

	Pruned	Kept	Total
New	126	2	128
Fresh	2	29	31
Picked	0	1	1
Done	0	0	0
Total	128	32	160

Merged error: 9.9b

Counts

160 → 32

Compiler

Compiled 6769 to 1972 computations (70.9% saved)

regimes2.2s (12.9%)

Compiler: Compiled 23638 to 17933 computations (24.1% saved)

bsearch310.0ms (1.8%)

Steps

Iters	Range		Point
8	2.5311371237992697e+206	1.365161950417748e+209	3.9383585648083115e+207
9	-9.253022506217927e-305	6.012695935742612e-307	1.8341402207961e-310

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	130	141
1	130	141

end0.0ms (0%)

sample5.8s (33.6%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
1.0s	8456×	body	128	nan
670.0ms	4788×	body	128	invalid

Compiler

Compiled 3109 to 2348 computations (24.5% saved)

Details

analyze1.6s (9.4%)

sample130.0ms (0.8%)

simplify128.0ms (0.7%)

prune8.0ms (0%)

localize19.0ms (0.1%)

rewrite48.0ms (0.3%)

series1.5s (8.8%)

simplify95.0ms (0.6%)

prune309.0ms (1.8%)

localize26.0ms (0.2%)

rewrite61.0ms (0.4%)

series2.5s (14.7%)

simplify105.0ms (0.6%)

prune309.0ms (1.8%)

localize29.0ms (0.2%)

rewrite38.0ms (0.2%)

series717.0ms (4.2%)

simplify62.0ms (0.4%)

prune282.0ms (1.6%)

localize29.0ms (0.2%)

rewrite32.0ms (0.2%)

series534.0ms (3.1%)

simplify59.0ms (0.3%)

prune204.0ms (1.2%)

regimes2.2s (12.9%)

bsearch310.0ms (1.8%)

simplify5.0ms (0%)

end0.0ms (0%)

sample5.8s (33.6%)

Profiling