Details

analyze1.7s (9.9%)

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)

sample124.0ms (0.7%)

Algorithm

1×

intervals

Results

37.0ms	264×	body	128	nan
36.0ms	256×	body	128	valid
22.0ms	152×	body	128	invalid

Compiler

Compiled 71 to 68 computations (4.2% saved)

simplify119.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5205	41

prune6.0ms (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: 31.7b

Counts

2 → 1

Compiler

Compiled 54 to 46 computations (14.8% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.9b	(.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))))
12.9b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
13.0b	(sqrt.f64 (/.f64 d h))
15.1b	(sqrt.f64 (/.f64 d l))

rewrite50.0ms (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:

15.0ms	(.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))))
14.0ms	(.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))

series473.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

303.0ms	(.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))))
93.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
39.0ms	(sqrt.f64 (/.f64 d l))
38.0ms	(sqrt.f64 (/.f64 d h))

simplify83.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5007	3595

prune264.0ms (1.6%)

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: 15.2b

Counts

140 → 19

Compiler

Compiled 5328 to 2633 computations (50.6% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.4b	(/.f64 (.f64 M D) (.f64 d 2))
7.9b	(.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))))
12.9b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
15.1b	(sqrt.f64 (/.f64 d l))

rewrite58.0ms (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:

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

series1.2s (7.4%)

Counts

4 → 12

Calls

4 calls:

1.1s	(.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))))
91.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
45.0ms	(sqrt.f64 (/.f64 d l))
22.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify95.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5089	4485

prune238.0ms (1.4%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	131	7	138
Fresh	3	15	18
Picked	1	0	1
Done	0	0	0
Total	135	22	157

Merged error: 13.6b

Counts

157 → 22

Compiler

Compiled 6771 to 2711 computations (60% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.2b	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
4.4b	(/.f64 (.f64 M D) (.f64 d 2))
7.9b	(.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))))
12.9b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite85.0ms (0.5%)

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:

37.0ms	(.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))))
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 d (cbrt.f64 l)))

series1.7s (10.3%)

Counts

4 → 12

Calls

4 calls:

1.5s	(.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))))
104.0ms	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
91.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
24.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify115.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4974	7171
1	4974	7171

prune370.0ms (2.2%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	161	5	166
Fresh	3	18	21
Picked	1	0	1
Done	0	0	0
Total	165	23	188

Merged error: 11.2b

Counts

188 → 23

Compiler

Compiled 10006 to 4162 computations (58.4% saved)

localize40.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.5b	(cbrt.f64 (/.f64 d (cbrt.f64 l)))
4.4b	(/.f64 (.f64 M D) (.f64 d 2))
7.9b	(.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)))) (.f64 (fabs.f64 (cbrt.f64 (/.f64 d (cbrt.f64 l)))) (sqrt.f64 (cbrt.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))))
12.9b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite93.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

113×	`add-exp-log_binary64_1139`
64×	`prod-exp_binary64_1150`
57×	`add-cbrt-cube_binary64_1137`
42×	`associate-*r/_binary64_1043`
36×	`sqrt-div_binary64_1118`
35×	`pow1_binary64_1162`
32×	`cbrt-unprod_binary64_1134`
31×	`cbrt-prod_binary64_1132`
29×	`frac-times_binary64_1111`
28×	`times-frac_binary64_1107`
25×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
23×	`pow-prod-down_binary64_1172`
20×	`div-exp_binary64_1152`
16×	`associate-r_binary64_1041` `associate-*l/_binary64_1044`
13×	`cbrt-div_binary64_1133`
10×	`pow-exp_binary64_1169`
8×	`flip--_binary64_1076` `flip3--_binary64_1105`
6×	`cbrt-undiv_binary64_1135`
4×	`add-log-exp_binary64_1140`
3×	`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×	`pow1/3_binary64_1183` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l_binary64_1046` `associate-/r_binary64_1045`

Counts

4 → 156

Calls

4 calls:

43.0ms	(.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)))) (.f64 (fabs.f64 (cbrt.f64 (/.f64 d (cbrt.f64 l)))) (sqrt.f64 (cbrt.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))))
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	(cbrt.f64 (/.f64 d (cbrt.f64 l)))

series2.2s (13.3%)

Counts

4 → 12

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)))) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (.f64 (fabs.f64 (cbrt.f64 (/.f64 d (cbrt.f64 l)))) (sqrt.f64 (cbrt.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))))
101.0ms	(cbrt.f64 (/.f64 d (cbrt.f64 l)))
96.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
22.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify123.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4951	8423
1	4951	8423

prune364.0ms (2.2%)

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	167	1	168
Fresh	0	22	22
Picked	0	1	1
Done	0	0	0
Total	167	24	191

Merged error: 11.2b

Counts

191 → 24

Compiler

Compiled 10561 to 3623 computations (65.7% saved)

regimes1.5s (8.8%)

Compiler: Compiled 18910 to 14139 computations (25.2% saved)

bsearch6.0ms (0%)

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

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	116	199
1	116	199

end0.0ms (0%)

sample5.6s (33.6%)

Algorithm

1×

intervals

Results

1.2s	8000×	body	128	valid
1.1s	8329×	body	128	nan
690.0ms	4745×	body	128	invalid

Compiler

Compiled 2835 to 2096 computations (26.1% saved)

Details

analyze1.7s (9.9%)

sample124.0ms (0.7%)

simplify119.0ms (0.7%)

prune6.0ms (0%)

localize18.0ms (0.1%)

rewrite50.0ms (0.3%)

series473.0ms (2.8%)

simplify83.0ms (0.5%)

prune264.0ms (1.6%)

localize28.0ms (0.2%)

rewrite58.0ms (0.3%)

series1.2s (7.4%)

simplify95.0ms (0.6%)

prune238.0ms (1.4%)

localize32.0ms (0.2%)

rewrite85.0ms (0.5%)

series1.7s (10.3%)

simplify115.0ms (0.7%)

prune370.0ms (2.2%)

localize40.0ms (0.2%)

rewrite93.0ms (0.6%)

series2.2s (13.3%)

simplify123.0ms (0.7%)

prune364.0ms (2.2%)

regimes1.5s (8.8%)

bsearch6.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample5.6s (33.6%)

Profiling