Details

analyze2.1s (17.3%)

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)

sample51.0ms (0.4%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
7.0ms	93×	body	128	nan
3.0ms	38×	body	128	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify133.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (38.0ms)

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

13.3b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
2.6b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
3.0b	(/.f64 (.f64 M D) (.f64 2 d))
12.5b	(.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:

13.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
8.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
8.0ms	(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))

series1.6s (13.1%)

Counts

4 → 65

Calls

4 calls:

585.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
538.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
319.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
129.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 2952 to 2829 computations (4.2% saved)

simplify87.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5023	4119

prune239.0ms (2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	170	11	181
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	171	11	182

Error

3.5b

Counts

182 → 11

Compiler

Compiled 4477 to 2406 computations (46.3% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.6b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
3.0b	(/.f64 (.f64 M D) (.f64 2 d))
4.7b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
8.0b	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)

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))

series1.4s (11.3%)

Counts

4 → 55

Calls

4 calls:

548.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
367.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
321.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
121.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 2428 to 2380 computations (2% saved)

simplify59.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5109	3064

prune182.0ms (1.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	150	4	154
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	154	11	165

Error

2.7b

Counts

165 → 11

Compiler

Compiled 3655 to 2224 computations (39.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.0b	(/.f64 (.f64 M D) (.f64 2 d))
3.0b	(/.f64 (.f64 M D) (.f64 2 d))
6.6b	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
8.0b	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)

rewrite66.0ms (0.6%)

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 (.f64 M D) (.f64 2 d))
8.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series1.0s (8.4%)

Counts

4 → 45

Calls

4 calls:

537.0ms	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)
224.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
128.0ms	(/.f64 (.f64 M D) (.f64 2 d))
119.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 2100 to 1884 computations (10.3% saved)

simplify108.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5025	3667

prune251.0ms (2.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	197	1	198
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	198	11	209

Error

2.7b

Counts

209 → 11

Compiler

Compiled 5246 to 2955 computations (43.7% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.0b	(/.f64 (.f64 M D) (.f64 2 d))
3.0b	(/.f64 (.f64 M D) (.f64 2 d))
5.4b	(/.f64 (/.f64 (.f64 M D) (.f64 2 d)) l)
6.6b	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))

rewrite39.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
22×	`times-frac_binary64_1107`
21×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
18×	`add-sqr-sqrt_binary64_1123`
16×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
8×	`div-inv_binary64_1098`
7×	`associate-/l*_binary64_1046`
6×	`pow1_binary64_1162`
5×	`associate-r_binary64_1041` `associate-/r*_binary64_1045`
4×	`add-log-exp_binary64_1140`
3×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-l_binary64_1042`
1×	`-commutative_binary64_1032` `associate-/l/_binary64_1048` `associate-r/_binary64_1043` `pow-prod-down_binary64_1172` `unswap-sqr_binary64_1069`

Counts

4 → 115

Calls

4 calls:

8.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
8.0ms	(/.f64 (/.f64 (.f64 M D) (.f64 2 d)) l)
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series705.0ms (5.9%)

Counts

4 → 42

Calls

4 calls:

231.0ms	(/.f64 (/.f64 (.f64 M D) (.f64 2 d)) l)
230.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
124.0ms	(/.f64 (.f64 M D) (.f64 2 d))
120.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 2016 to 1704 computations (15.5% saved)

simplify78.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5000	2237

prune184.0ms (1.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	157	11	168

Error

2.7b

Counts

168 → 11

Compiler

Compiled 4288 to 2311 computations (46.1% saved)

regimes1.4s (11.9%)

Accuracy

Total 4.4b remaining (51.4%)

Threshold costs 0b (0%)

Compiler

Compiled 16364 to 13978 computations (14.6% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	89	36
1	89	36

end0.0ms (0%)

sample2.2s (18.5%)

Algorithm

1×

intervals

Results

596.0ms	8000×	body	128	valid
231.0ms	3122×	body	128	nan
98.0ms	1272×	body	128	invalid

Compiler

Compiled 1039 to 883 computations (15% saved)

Details

analyze2.1s (17.3%)

sample51.0ms (0.4%)

simplify133.0ms (1.1%)

prune3.0ms (0%)

localize14.0ms (0.1%)

rewrite46.0ms (0.4%)

series1.6s (13.1%)

simplify87.0ms (0.7%)

prune239.0ms (2%)

localize14.0ms (0.1%)

rewrite37.0ms (0.3%)

series1.4s (11.3%)

simplify59.0ms (0.5%)

prune182.0ms (1.5%)

localize14.0ms (0.1%)

rewrite66.0ms (0.6%)

series1.0s (8.4%)

simplify108.0ms (0.9%)

prune251.0ms (2.1%)

localize14.0ms (0.1%)

rewrite39.0ms (0.3%)

series705.0ms (5.9%)

simplify78.0ms (0.6%)

prune184.0ms (1.5%)

regimes1.4s (11.9%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.2s (18.5%)

Profiling