Details

analyze2.6s (20.6%)

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)

sample68.0ms (0.5%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
7.0ms	103×	body	128	nan
3.0ms	40×	body	128	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify41.0ms (0.3%)

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

17.3b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
3.7b	(/.f64 (.f64 M D) (.f64 2 d))
3.7b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
13.2b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite220.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

9.5b

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×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l_binary64_1046` `associate-/r_binary64_1045` `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)

series1.6s (12.5%)

Error

7.9b

Counts

4 → 71

Calls

4 calls:

547.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
547.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
306.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
121.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 4216 to 3713 computations (11.9% saved)

simplify88.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4982	4087
1	4982	4087

prune215.0ms (1.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	177	10	187
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	178	10	188

Error

6.0b

Counts

188 → 10

Compiler

Compiled 4355 to 2289 computations (47.4% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.7b	(/.f64 (.f64 M D) (.f64 2 d))
3.7b	(/.f64 (.f64 M D) (.f64 2 d))
3.7b	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))
11.6b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))

rewrite189.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

5.3b

Rules

69×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
26×	`prod-exp_binary64_1150` `cbrt-unprod_binary64_1134`
21×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
19×	`add-sqr-sqrt_binary64_1123`
13×	`add-cube-cbrt_binary64_1136` `-un-lft-identity_binary64_1101` `times-frac_binary64_1107` `associate-r*_binary64_1041`
7×	`pow1_binary64_1162`
5×	`associate-l_binary64_1042`
4×	`add-log-exp_binary64_1140` `div-inv_binary64_1098`
3×	`sqrt-prod_binary64_1117`
2×	`unswap-sqr_binary64_1069` `sqrt-div_binary64_1118` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l_binary64_1046` `associate-/r_binary64_1045`
1×	`pow-prod-down_binary64_1172` `frac-times_binary64_1111` `associate-l/_binary64_1044` `associate-r/_binary64_1043` `*-commutative_binary64_1032` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `flip3--_binary64_1105` `flip--_binary64_1076` `rem-sqrt-square_binary64_1114`

Counts

4 → 109

Calls

4 calls:

12.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h 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 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))

Compiler

Compiled 3773 to 1881 computations (50.1% saved)

series934.0ms (7.3%)

Error

5.3b

Counts

4 → 55

Calls

4 calls:

338.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))
303.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))
124.0ms	(/.f64 (.f64 M D) (.f64 2 d))
119.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 3647 to 2843 computations (22% saved)

simplify61.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5600	2854

prune187.0ms (1.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	159	5	164
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	161	13	174

Error

4.4b

Counts

174 → 13

Compiler

Compiled 4536 to 2189 computations (51.7% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.7b	(/.f64 (*.f64 M D) d)
3.7b	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 h (.f64 1/2 (/.f64 (.f64 M D) d))) l))))
5.8b	(.f64 h (.f64 1/2 (/.f64 (*.f64 M D) d)))
7.5b	(/.f64 (.f64 h (.f64 1/2 (/.f64 (*.f64 M D) d))) l)

rewrite156.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

4.4b

Rules

43×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
17×	`prod-exp_binary64_1150` `cbrt-unprod_binary64_1134`
11×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `add-sqr-sqrt_binary64_1123`
10×	`pow1_binary64_1162` `add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
6×	`times-frac_binary64_1107` `associate-/r*_binary64_1045`
4×	`add-log-exp_binary64_1140` `associate-*r/_binary64_1043`
3×	`pow-prod-down_binary64_1172` `associate-l_binary64_1042` `sqrt-prod_binary64_1117`
2×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098` `associate-/l*_binary64_1046` `sqrt-div_binary64_1118`
1×	`associate-/l/_binary64_1048` `associate-r_binary64_1041` `*-commutative_binary64_1032` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `flip3--_binary64_1105` `flip--_binary64_1076` `rem-sqrt-square_binary64_1114`

Counts

4 → 87

Calls

4 calls:

10.0ms	(/.f64 (.f64 h (.f64 1/2 (/.f64 (*.f64 M D) d))) l)
8.0ms	(.f64 h (.f64 1/2 (/.f64 (*.f64 M D) d)))
5.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 h (.f64 1/2 (/.f64 (.f64 M D) d))) l))))
5.0ms	(/.f64 (*.f64 M D) d)

Compiler

Compiled 2962 to 1484 computations (49.9% saved)

series1.0s (7.9%)

Error

4.4b

Counts

4 → 58

Calls

4 calls:

355.0ms	(/.f64 (.f64 h (.f64 1/2 (/.f64 (*.f64 M D) d))) l)
302.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 h (.f64 1/2 (/.f64 (.f64 M D) d))) l))))
207.0ms	(.f64 h (.f64 1/2 (/.f64 (*.f64 M D) d)))
101.0ms	(/.f64 (*.f64 M D) d)

Compiler

Compiled 3863 to 3029 computations (21.6% saved)

simplify83.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4964	2534
1	4964	2534

prune170.0ms (1.3%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	145	13	158

Error

4.4b

Counts

158 → 13

Compiler

Compiled 3986 to 1959 computations (50.9% saved)

localize1.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

4.4b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 4.4b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune1.0ms (0%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	10	10
Picked	1	1
Done	2	2
Total	13	13

Error

4.4b

Counts

13 → 13

Compiler

Compiled 0 to 0 computations (0% saved)

regimes2.0s (15.5%)

Accuracy

Total 4.5b remaining (51.8%)

Threshold costs 0b (0%)

Compiler

Compiled 26748 to 23389 computations (12.6% saved)

bsearch0.0ms (0%)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	82	36
1	82	36

Remove

(sort M D)

Compiler

Compiled 48 to 40 computations (16.7% saved)

end0.0ms (0%)

sample3.1s (23.9%)

Algorithm

1×

intervals

Results

623.0ms	8000×	body	128	valid
387.0ms	3238×	body	128	nan
108.0ms	1368×	body	128	invalid

Compiler

Compiled 1588 to 1394 computations (12.2% saved)

Details

analyze2.6s (20.6%)

sample68.0ms (0.5%)

simplify41.0ms (0.3%)

prune3.0ms (0%)

localize14.0ms (0.1%)

rewrite220.0ms (1.7%)

series1.6s (12.5%)

simplify88.0ms (0.7%)

prune215.0ms (1.7%)

localize14.0ms (0.1%)

rewrite189.0ms (1.5%)

series934.0ms (7.3%)

simplify61.0ms (0.5%)

prune187.0ms (1.5%)

localize20.0ms (0.2%)

rewrite156.0ms (1.2%)

series1.0s (7.9%)

simplify83.0ms (0.6%)

prune170.0ms (1.3%)

localize1.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0.1%)

prune1.0ms (0%)

regimes2.0s (15.5%)

bsearch0.0ms (0%)

simplify10.0ms (0.1%)

end0.0ms (0%)

sample3.1s (23.9%)

Profiling