Details

analyze2.3s (17.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
5.1%	94.6%	0.3%	13
7%	92.7%	0.3%	14

Compiler

Compiled 19 to 19 computations (0% saved)

sample47.0ms (0.4%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
7.0ms	98×	body	128	nan
3.0ms	42×	body	128	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify132.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	6100	27

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

11.6b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
3.1b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
4.5b	(/.f64 (.f64 M D) (.f64 2 d))
10.0b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite46.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-exp-log_binary64_1139`
38×	`add-sqr-sqrt_binary64_1123`
27×	`prod-exp_binary64_1150`
23×	`add-cbrt-cube_binary64_1137`
19×	`associate-r_binary64_1041` `div-exp_binary64_1152`
17×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
15×	`times-frac_binary64_1107`
13×	`associate-l_binary64_1042`
10×	`pow-exp_binary64_1169` `unswap-sqr_binary64_1069`
7×	`cbrt-unprod_binary64_1134` `unpow-prod-down_binary64_1180` `pow1_binary64_1162` `sqrt-prod_binary64_1117`
5×	`cbrt-undiv_binary64_1135`
4×	`add-log-exp_binary64_1140` `sqrt-div_binary64_1118`
3×	`associate-*r/_binary64_1043` `div-inv_binary64_1098` `sqr-pow_binary64_1073` `unpow2_binary64_1166`
2×	`*-commutative_binary64_1032` `flip--_binary64_1076` `flip3--_binary64_1105` `pow-to-exp_binary64_1170`
1×	`rem-sqrt-square_binary64_1114` `frac-2neg_binary64_1112` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `associate-/l_binary64_1046` `pow-prod-down_binary64_1172` `associate-/r_binary64_1045` `pow1/2_binary64_1181`

Counts

4 → 116

Calls

4 calls:

12.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
9.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
4.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))

series1.4s (11.2%)

Counts

4 → 67

Calls

4 calls:

516.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
487.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
300.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
120.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 2856 to 2765 computations (3.2% saved)

simplify86.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4998	3984
1	4998	3984

prune233.0ms (1.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	171	12	183
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	172	12	184

Error

2.8b

Counts

184 → 12

Compiler

Compiled 4290 to 2262 computations (47.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.1b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
4.5b	(/.f64 (.f64 M D) (.f64 2 d))
5.0b	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
5.0b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))

rewrite37.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-exp-log_binary64_1139`
26×	`prod-exp_binary64_1150`
23×	`add-cbrt-cube_binary64_1137`
20×	`add-sqr-sqrt_binary64_1123` `div-exp_binary64_1152`
13×	`*-un-lft-identity_binary64_1101`
10×	`pow-exp_binary64_1169` `add-cube-cbrt_binary64_1136` `associate-r_binary64_1041`
6×	`cbrt-unprod_binary64_1134` `unpow-prod-down_binary64_1180` `sqrt-prod_binary64_1117` `cbrt-undiv_binary64_1135`
5×	`pow1_binary64_1162` `times-frac_binary64_1107`
4×	`add-log-exp_binary64_1140` `unswap-sqr_binary64_1069` `associate-/r*_binary64_1045`
3×	`div-inv_binary64_1098` `associate-l_binary64_1042`
2×	`difference-of-squares_binary64_1070` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l*_binary64_1046` `sqrt-div_binary64_1118` `sqr-pow_binary64_1073` `pow-to-exp_binary64_1170` `unpow2_binary64_1166`
1×	`*-commutative_binary64_1032` `rem-sqrt-square_binary64_1114` `sqrt-pow1_binary64_1119` `distribute-lft-out--_binary64_1053` `flip--_binary64_1076` `flip3--_binary64_1105` `pow1/2_binary64_1181`

Counts

4 → 99

Calls

4 calls:

8.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
7.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
7.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series1.3s (10.6%)

Counts

4 → 58

Calls

4 calls:

534.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
375.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
300.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
130.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 2465 to 2422 computations (1.7% saved)

simplify57.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5149	3033

prune179.0ms (1.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	153	4	157
Fresh	3	8	11
Picked	0	1	1
Done	0	0	0
Total	156	13	169

Error

2.3b

Counts

169 → 13

Compiler

Compiled 3594 to 2201 computations (38.8% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.5b	(/.f64 (.f64 M D) (.f64 2 d))
4.5b	(/.f64 (.f64 M D) (.f64 2 d))
5.0b	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)
5.5b	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))

rewrite63.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

251×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
116×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150`
87×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
10×	`add-sqr-sqrt_binary64_1123`
8×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
6×	`pow1_binary64_1162` `times-frac_binary64_1107`
5×	`associate-r_binary64_1041` `associate-/r*_binary64_1045`
4×	`add-log-exp_binary64_1140` `associate-*r/_binary64_1043` `div-inv_binary64_1098`
3×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l/_binary64_1048` `associate-/l_binary64_1046` `associate-l*_binary64_1042`
1×	`-commutative_binary64_1032` `frac-times_binary64_1111` `pow-prod-down_binary64_1172` `unswap-sqr_binary64_1069` `associate-l/_binary64_1044`

Counts

4 → 153

Calls

4 calls:

18.0ms	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)
9.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series980.0ms (7.7%)

Counts

4 → 45

Calls

4 calls:

528.0ms	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)
212.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
122.0ms	(/.f64 (.f64 M D) (.f64 2 d))
118.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 2100 to 1884 computations (10.3% saved)

simplify114.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5025	3667

prune253.0ms (2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	197	1	198
Fresh	1	10	11
Picked	0	1	1
Done	1	0	1
Total	199	12	211

Error

2.1b

Counts

211 → 12

Compiler

Compiled 5175 to 2908 computations (43.8% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.4b	(/.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (.f64 (cbrt.f64 l) (cbrt.f64 l)))
4.5b	(/.f64 (.f64 M D) (.f64 2 d))
4.5b	(/.f64 (.f64 M D) (.f64 2 d))
5.5b	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))

rewrite51.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`add-exp-log_binary64_1139`
90×	`add-cbrt-cube_binary64_1137`
41×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150`
32×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
8×	`add-sqr-sqrt_binary64_1123`
6×	`*-un-lft-identity_binary64_1101` `pow1_binary64_1162` `add-cube-cbrt_binary64_1136`
5×	`associate-r_binary64_1041`
4×	`add-log-exp_binary64_1140` `div-inv_binary64_1098` `times-frac_binary64_1107`
3×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l_binary64_1046` `associate-l_binary64_1042` `associate-/r_binary64_1045`
2×	`associate-*r/_binary64_1043`
1×	`*-commutative_binary64_1032` `associate-/l/_binary64_1048` `pow-prod-down_binary64_1172` `unswap-sqr_binary64_1069`

Counts

4 → 109

Calls

4 calls:

13.0ms	(/.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (.f64 (cbrt.f64 l) (cbrt.f64 l)))
9.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series1.3s (10.3%)

Counts

4 → 45

Calls

4 calls:

842.0ms	(/.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (.f64 (cbrt.f64 l) (cbrt.f64 l)))
213.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
132.0ms	(/.f64 (.f64 M D) (.f64 2 d))
120.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 2860 to 2284 computations (20.1% saved)

simplify95.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4974	2472
1	4974	2472

prune208.0ms (1.6%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	154	12	166

Error

2.1b

Counts

166 → 12

Compiler

Compiled 5128 to 2432 computations (52.6% saved)

regimes1.3s (10.6%)

Accuracy

Total 4.2b remaining (52.4%)

Threshold costs 0b (0%)

Compiler

Compiled 17215 to 15219 computations (11.6% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	99	48
1	99	48

end0.0ms (0%)

sample2.3s (18.5%)

Algorithm

1×

intervals

Results

613.0ms	8000×	body	128	valid
235.0ms	3063×	body	128	nan
99.0ms	1319×	body	128	invalid

Compiler

Compiled 1111 to 973 computations (12.4% saved)

Details

analyze2.3s (17.9%)

sample47.0ms (0.4%)

simplify132.0ms (1%)

prune3.0ms (0%)

localize14.0ms (0.1%)

rewrite46.0ms (0.4%)

series1.4s (11.2%)

simplify86.0ms (0.7%)

prune233.0ms (1.8%)

localize13.0ms (0.1%)

rewrite37.0ms (0.3%)

series1.3s (10.6%)

simplify57.0ms (0.5%)

prune179.0ms (1.4%)

localize16.0ms (0.1%)

rewrite63.0ms (0.5%)

series980.0ms (7.7%)

simplify114.0ms (0.9%)

prune253.0ms (2%)

localize18.0ms (0.1%)

rewrite51.0ms (0.4%)

series1.3s (10.3%)

simplify95.0ms (0.8%)

prune208.0ms (1.6%)

regimes1.3s (10.6%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.3s (18.5%)

Profiling