Details

analyze2.8s (20.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5015	432
0	6	6
1	6	6

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

Symmetry

(sort M D)

Compiler

Compiled 19 to 19 computations (0% saved)

sample66.0ms (0.5%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
7.0ms	107×	body	128	nan
3.0ms	41×	body	128	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify43.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

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

17.1b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
5.4b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
7.0b	(/.f64 (.f64 M D) (.f64 2 d))
11.5b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite228.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

11.0b

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

Counts

4 → 116

Calls

4 calls:

11.0ms	(.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)))))
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))))

Compiler

Compiled 3444 to 1962 computations (43% saved)

series1.3s (9.7%)

Error

10.7b

Counts

4 → 57

Calls

4 calls:

524.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
441.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
216.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
115.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 3306 to 2982 computations (9.8% saved)

simplify66.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5385	3695

prune201.0ms (1.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	164	9	173
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	165	9	174

Error

7.5b

Counts

174 → 9

Compiler

Compiled 4012 to 2163 computations (46.1% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.0b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
5.4b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
7.0b	(/.f64 (.f64 M D) (.f64 2 d))
8.4b	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)

rewrite170.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

7.0b

Rules

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

Counts

4 → 99

Calls

4 calls:

10.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
8.0ms	(/.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))

Compiler

Compiled 2731 to 1689 computations (38.2% saved)

series1.3s (9.1%)

Error

7.5b

Counts

4 → 51

Calls

4 calls:

530.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
350.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
220.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
120.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 3091 to 2803 computations (9.3% saved)

simplify58.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4987	2858
1	4987	2858

prune181.0ms (1.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	147	3	150
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	148	11	159

Error

6.5b

Counts

159 → 11

Compiler

Compiled 3432 to 2109 computations (38.5% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.4b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)))
7.0b	(/.f64 (.f64 M D) (.f64 2 d))
7.0b	(/.f64 (.f64 M D) (.f64 2 d))
8.4b	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)

rewrite305.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

6.3b

Rules

233×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
107×	`prod-exp_binary64_1150` `cbrt-unprod_binary64_1134`
83×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
11×	`add-sqr-sqrt_binary64_1123`
10×	`*-un-lft-identity_binary64_1101`
7×	`add-cube-cbrt_binary64_1136`
6×	`sqrt-prod_binary64_1117`
5×	`pow1_binary64_1162` `times-frac_binary64_1107` `associate-/r*_binary64_1045`
4×	`add-log-exp_binary64_1140`
3×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098` `associate-r/_binary64_1043` `associate-/l/_binary64_1048` `associate-/l_binary64_1046`
2×	`sqrt-div_binary64_1118` `difference-of-squares_binary64_1070`
1×	`frac-times_binary64_1111` `associate-*l/_binary64_1044` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `flip3--_binary64_1105` `flip--_binary64_1076` `distribute-lft-out--_binary64_1053` `rem-sqrt-square_binary64_1114`

Counts

4 → 142

Calls

4 calls:

18.0ms	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)
8.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.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))

Compiler

Compiled 5730 to 2829 computations (50.6% saved)

series1.1s (7.7%)

Error

6.5b

Counts

4 → 48

Calls

4 calls:

551.0ms	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)
231.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)))
127.0ms	(/.f64 (.f64 M D) (.f64 2 d))
119.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 3109 to 2605 computations (16.2% saved)

simplify116.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4970	4018
1	4970	4018

prune225.0ms (1.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	189	1	190
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	191	10	201

Error

6.3b

Counts

201 → 10

Compiler

Compiled 4847 to 2636 computations (45.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.0b	(/.f64 (/.f64 (.f64 M D) (.f64 2 d)) l)
5.4b	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (/.f64 (.f64 M D) (.f64 2 d)) l))))
7.0b	(/.f64 (.f64 M D) (.f64 2 d))
7.0b	(/.f64 (.f64 M D) (.f64 2 d))

rewrite168.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

6.3b

Rules

46×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
21×	`times-frac_binary64_1107`
17×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
16×	`add-sqr-sqrt_binary64_1123`
15×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
12×	`prod-exp_binary64_1150` `cbrt-unprod_binary64_1134`
7×	`div-inv_binary64_1098` `associate-/l*_binary64_1046`
5×	`pow1_binary64_1162` `associate-/r*_binary64_1045`
4×	`add-log-exp_binary64_1140`
3×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `sqrt-prod_binary64_1117`
2×	`sqrt-div_binary64_1118`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `flip3--_binary64_1105` `flip--_binary64_1076` `rem-sqrt-square_binary64_1114` `associate-/l/_binary64_1048`

Counts

4 → 101

Calls

4 calls:

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

Compiler

Compiled 3446 to 1878 computations (45.5% saved)

series716.0ms (5.1%)

Error

6.3b

Counts

4 → 45

Calls

4 calls:

224.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (/.f64 (.f64 M D) (.f64 2 d)) l))))
214.0ms	(/.f64 (/.f64 (.f64 M D) (.f64 2 d)) l)
119.0ms	(/.f64 (.f64 M D) (.f64 2 d))
117.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 2983 to 2319 computations (22.3% saved)

simplify72.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4991	2447
1	4991	2447

prune163.0ms (1.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	146	10	156

Error

6.3b

Counts

156 → 10

Compiler

Compiled 3890 to 2029 computations (47.8% saved)

regimes1.8s (13%)

Accuracy

Total 4.3b remaining (49.9%)

Threshold costs 0b (0%)

Compiler

Compiled 23504 to 20905 computations (11.1% saved)

bsearch0.0ms (0%)

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	99	48
1	99	48

Remove

(sort M D)

Compiler

Compiled 62 to 46 computations (25.8% saved)

end0.0ms (0%)

sample2.8s (20%)

Algorithm

1×

intervals

Results

610.0ms	8000×	body	128	valid
219.0ms	2965×	body	128	nan
98.0ms	1327×	body	128	invalid

Compiler

Compiled 1507 to 1334 computations (11.5% saved)

Details

analyze2.8s (20.1%)

sample66.0ms (0.5%)

simplify43.0ms (0.3%)

prune3.0ms (0%)

localize13.0ms (0.1%)

rewrite228.0ms (1.6%)

series1.3s (9.7%)

simplify66.0ms (0.5%)

prune201.0ms (1.4%)

localize13.0ms (0.1%)

rewrite170.0ms (1.2%)

series1.3s (9.1%)

simplify58.0ms (0.4%)

prune181.0ms (1.3%)

localize14.0ms (0.1%)

rewrite305.0ms (2.2%)

series1.1s (7.7%)

simplify116.0ms (0.8%)

prune225.0ms (1.6%)

localize13.0ms (0.1%)

rewrite168.0ms (1.2%)

series716.0ms (5.1%)

simplify72.0ms (0.5%)

prune163.0ms (1.2%)

regimes1.8s (13%)

bsearch0.0ms (0%)

simplify12.0ms (0.1%)

end0.0ms (0%)

sample2.8s (20%)

Profiling