Details

analyze3.6s (8.8%)

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)

sample281.0ms (0.7%)

Algorithm

1×

intervals

Results

89.0ms	256×	body	128	valid
81.0ms	277×	body	128	nan
57.0ms	157×	body	128	invalid

Compiler

Compiled 71 to 68 computations (4.2% saved)

simplify330.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (53.0ms)

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

Merged error: 27.7b

Counts

2 → 1

Compiler

Compiled 54 to 46 computations (14.8% saved)

localize44.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.8b	(.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))))
12.6b	(sqrt.f64 (/.f64 d h))
13.0b	(sqrt.f64 (/.f64 d l))
13.6b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite100.0ms (0.2%)

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:

31.0ms	(.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))))
22.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
6.0ms	(sqrt.f64 (/.f64 d h))
6.0ms	(sqrt.f64 (/.f64 d l))

series1.6s (3.8%)

Counts

4 → 12

Calls

4 calls:

968.0ms	(.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))))
317.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
146.0ms	(sqrt.f64 (/.f64 d l))
139.0ms	(sqrt.f64 (/.f64 d h))

simplify159.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4954	3595
1	4954	3595

prune371.0ms (0.9%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	120	19	139
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	121	19	140

Merged error: 13.6b

Counts

140 → 19

Compiler

Compiled 5336 to 2646 computations (50.4% saved)

localize48.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.7b	(/.f64 (.f64 M D) (.f64 d 2))
6.8b	(.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))))
13.0b	(sqrt.f64 (/.f64 d l))
13.6b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite136.0ms (0.3%)

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:

51.0ms	(.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))))
24.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
13.0ms	(/.f64 (.f64 M D) (.f64 d 2))
6.0ms	(sqrt.f64 (/.f64 d l))

series4.0s (9.6%)

Counts

4 → 12

Calls

4 calls:

3.5s	(.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))))
322.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
144.0ms	(sqrt.f64 (/.f64 d l))
49.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify146.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4960	4485
1	4960	4485

prune410.0ms (1%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	132	6	138
Fresh	2	16	18
Picked	1	0	1
Done	0	0	0
Total	135	22	157

Merged error: 11.7b

Counts

157 → 22

Compiler

Compiled 6796 to 2734 computations (59.8% saved)

localize72.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.0b	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
4.7b	(/.f64 (.f64 M D) (.f64 d 2))
6.8b	(.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))))
13.6b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite185.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

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×	`*-un-lft-identity_binary64_1101` `pow1_binary64_1162` `add-cube-cbrt_binary64_1136`
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×	`flip--_binary64_1076` `flip3--_binary64_1105`
6×	`cbrt-undiv_binary64_1135`
4×	`add-log-exp_binary64_1140`
3×	`rem-sqrt-square_binary64_1114` `div-inv_binary64_1098`
2×	`-commutative_binary64_1032` `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 → 154

Calls

4 calls:

73.0ms	(.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))))
23.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
13.0ms	(/.f64 (.f64 M D) (.f64 d 2))
9.0ms	(sqrt.f64 (/.f64 d (cbrt.f64 l)))

series5.0s (12.2%)

Counts

4 → 12

Calls

4 calls:

4.3s	(.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))))
323.0ms	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
288.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
80.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify217.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	4992	7171
1	4992	7171

prune687.0ms (1.7%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	159	7	166
Fresh	4	17	21
Picked	1	0	1
Done	0	0	0
Total	164	24	188

Merged error: 9.5b

Counts

188 → 24

Compiler

Compiled 10178 to 4255 computations (58.2% saved)

localize72.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.0b	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
4.7b	(/.f64 (.f64 M D) (.f64 d 2))
6.4b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l))))
6.8b	(.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 d 2)) 2)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))

rewrite237.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

248×	`add-exp-log_binary64_1139`
144×	`prod-exp_binary64_1150`
59×	`add-cbrt-cube_binary64_1137`
56×	`div-exp_binary64_1152`
40×	`cbrt-unprod_binary64_1134`
37×	`sqrt-div_binary64_1118`
30×	`associate-*r/_binary64_1043`
29×	`frac-times_binary64_1111`
25×	`pow-exp_binary64_1169` `pow1_binary64_1162`
24×	`add-sqr-sqrt_binary64_1123`
22×	`sqrt-prod_binary64_1117` `times-frac_binary64_1107`
19×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
16×	`associate-*l/_binary64_1044`
14×	`pow-prod-down_binary64_1172`
12×	`cbrt-undiv_binary64_1135`
10×	`cbrt-prod_binary64_1132`
8×	`flip--_binary64_1076` `flip3--_binary64_1105` `associate-r_binary64_1041`
5×	`pow-to-exp_binary64_1170`
4×	`add-log-exp_binary64_1140`
3×	`rem-sqrt-square_binary64_1114` `div-inv_binary64_1098`
2×	`-commutative_binary64_1032` `sub-neg_binary64_1094` `distribute-lft-in_binary64_1050` `associate-l*_binary64_1042` `cancel-sign-sub-inv_binary64_1067` `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 → 176

Calls

4 calls:

85.0ms	(.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 d 2)) 2)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
38.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l))))
13.0ms	(/.f64 (.f64 M D) (.f64 d 2))
9.0ms	(sqrt.f64 (/.f64 d (cbrt.f64 l)))

series5.3s (13%)

Counts

4 → 12

Calls

4 calls:

4.3s	(.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 d 2)) 2)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
641.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l))))
327.0ms	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
85.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify235.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4979	8375
1	4979	8375

prune812.0ms (2%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	182	6	188
Fresh	2	21	23
Picked	1	0	1
Done	0	0	0
Total	185	27	212

Merged error: 8.5b

Counts

212 → 27

Compiler

Compiled 12034 to 4227 computations (64.9% saved)

regimes3.3s (8%)

Compiler: Compiled 28850 to 19844 computations (31.2% saved)

bsearch0.0ms (0%)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	121	107
1	121	107

end0.0ms (0%)

sample13.8s (33.5%)

Algorithm

1×

intervals

Results

2.8s	8000×	body	128	valid
2.4s	8648×	body	128	nan
1.8s	4967×	body	128	invalid

Compiler

Compiled 4195 to 2878 computations (31.4% saved)

Details

analyze3.6s (8.8%)

sample281.0ms (0.7%)

simplify330.0ms (0.8%)

prune9.0ms (0%)

localize44.0ms (0.1%)

rewrite100.0ms (0.2%)

series1.6s (3.8%)

simplify159.0ms (0.4%)

prune371.0ms (0.9%)

localize48.0ms (0.1%)

rewrite136.0ms (0.3%)

series4.0s (9.6%)

simplify146.0ms (0.4%)

prune410.0ms (1%)

localize72.0ms (0.2%)

rewrite185.0ms (0.4%)

series5.0s (12.2%)

simplify217.0ms (0.5%)

prune687.0ms (1.7%)

localize72.0ms (0.2%)

rewrite237.0ms (0.6%)

series5.3s (13%)

simplify235.0ms (0.6%)

prune812.0ms (2%)

regimes3.3s (8%)

bsearch0.0ms (0%)

simplify8.0ms (0%)

end0.0ms (0%)

sample13.8s (33.5%)

Profiling