Details

analyze2.5s (20%)

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)

sample63.0ms (0.5%)

Algorithm

1×

intervals

Results

18.0ms	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)

localize13.0ms (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))

rewrite218.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

9.5b

Rules

67×	`add-exp-log_binary64_798`
38×	`add-sqr-sqrt_binary64_782`
27×	`prod-exp_binary64_809`
23×	`add-cbrt-cube_binary64_796`
19×	`div-exp_binary64_811` `associate-r_binary64_700`
17×	`add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
15×	`times-frac_binary64_766`
13×	`associate-l_binary64_701`
10×	`pow-exp_binary64_828` `unswap-sqr_binary64_728`
7×	`pow1_binary64_821` `cbrt-unprod_binary64_793` `unpow-prod-down_binary64_839` `sqrt-prod_binary64_776`
5×	`cbrt-undiv_binary64_794`
4×	`add-log-exp_binary64_799` `sqrt-div_binary64_777`
3×	`unpow2_binary64_825` `sqr-pow_binary64_732` `associate-*r/_binary64_702` `div-inv_binary64_757`
2×	`pow-to-exp_binary64_829` `*-commutative_binary64_691` `flip3--_binary64_764` `flip--_binary64_735`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l_binary64_705` `associate-/r_binary64_704` `pow-prod-down_binary64_831`

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 (12.6%)

Error

7.9b

Counts

4 → 71

Calls

4 calls:

556.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
523.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
310.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
135.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 4216 to 3713 computations (11.9% saved)

simplify86.0ms (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)

localize13.0ms (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))

rewrite191.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

5.3b

Rules

69×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
26×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793`
21×	`div-exp_binary64_811` `cbrt-undiv_binary64_794`
19×	`add-sqr-sqrt_binary64_782`
13×	`add-cube-cbrt_binary64_795` `-un-lft-identity_binary64_760` `times-frac_binary64_766` `associate-r*_binary64_700`
7×	`pow1_binary64_821`
5×	`associate-l_binary64_701`
4×	`add-log-exp_binary64_799` `div-inv_binary64_757`
3×	`sqrt-prod_binary64_776`
2×	`unswap-sqr_binary64_728` `sqrt-div_binary64_777` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l_binary64_705` `associate-/r_binary64_704`
1×	`pow-prod-down_binary64_831` `frac-times_binary64_770` `associate-l/_binary64_703` `associate-r/_binary64_702` `*-commutative_binary64_691` `pow1/2_binary64_840` `sqrt-pow1_binary64_778` `flip3--_binary64_764` `flip--_binary64_735` `rem-sqrt-square_binary64_773`

Counts

4 → 109

Calls

4 calls:

13.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))
8.0ms	(/.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)

series968.0ms (7.7%)

Error

5.3b

Counts

4 → 55

Calls

4 calls:

354.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))
313.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))
128.0ms	(/.f64 (.f64 M D) (.f64 2 d))
123.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 3647 to 2843 computations (22% saved)

simplify67.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5600	2854

prune195.0ms (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)

localize16.0ms (0.1%)

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)

rewrite147.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

4.4b

Rules

43×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
17×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793`
11×	`div-exp_binary64_811` `cbrt-undiv_binary64_794` `add-sqr-sqrt_binary64_782`
10×	`pow1_binary64_821` `add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
6×	`times-frac_binary64_766` `associate-/r*_binary64_704`
4×	`add-log-exp_binary64_799` `associate-*r/_binary64_702`
3×	`pow-prod-down_binary64_831` `associate-l_binary64_701` `sqrt-prod_binary64_776`
2×	`frac-2neg_binary64_771` `clear-num_binary64_759` `div-inv_binary64_757` `associate-/l*_binary64_705` `sqrt-div_binary64_777`
1×	`associate-/l/_binary64_707` `associate-r_binary64_700` `*-commutative_binary64_691` `pow1/2_binary64_840` `sqrt-pow1_binary64_778` `flip3--_binary64_764` `flip--_binary64_735` `rem-sqrt-square_binary64_773`

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 (8.1%)

Error

4.4b

Counts

4 → 58

Calls

4 calls:

352.0ms	(/.f64 (.f64 h (.f64 1/2 (/.f64 (*.f64 M D) d))) l)
310.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 h (.f64 1/2 (/.f64 (.f64 M D) d))) l))))
204.0ms	(.f64 h (.f64 1/2 (/.f64 (*.f64 M D) d)))
104.0ms	(/.f64 (*.f64 M D) d)

Compiler

Compiled 3863 to 3029 computations (21.6% saved)

simplify81.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4964	2534
1	4964	2534

prune166.0ms (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%)

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%)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

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%)

sample3.0s (24%)

Algorithm

1×

intervals

Results

596.0ms	8000×	body	128	valid
443.0ms	3238×	body	128	nan
100.0ms	1368×	body	128	invalid

Compiler

Compiled 1588 to 1394 computations (12.2% saved)

Details

analyze2.5s (20%)

sample63.0ms (0.5%)

simplify41.0ms (0.3%)

prune3.0ms (0%)

localize13.0ms (0.1%)

rewrite218.0ms (1.7%)

series1.6s (12.6%)

simplify86.0ms (0.7%)

prune215.0ms (1.7%)

localize13.0ms (0.1%)

rewrite191.0ms (1.5%)

series968.0ms (7.7%)

simplify67.0ms (0.5%)

prune195.0ms (1.5%)

localize16.0ms (0.1%)

rewrite147.0ms (1.2%)

series1.0s (8.1%)

simplify81.0ms (0.6%)

prune166.0ms (1.3%)

localize1.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0%)

prune1.0ms (0%)

regimes2.0s (15.5%)

bsearch0.0ms (0%)

simplify11.0ms (0.1%)

end0.0ms (0%)

sample3.0s (24%)

Profiling