Details

analyze2.0s (15.6%)

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

18.0ms	256×	body	128	valid
7.0ms	102×	body	128	nan
4.0ms	53×	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 (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

14.6b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
3.3b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
4.0b	(/.f64 (.f64 M D) (.f64 2 d))
11.4b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite42.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

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

series1.5s (11.6%)

Counts

4 → 67

Calls

4 calls:

558.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
518.0ms	(.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))))
126.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 2856 to 2765 computations (3.2% saved)

simplify87.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4998	3984
1	4998	3984

prune239.0ms (1.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	170	13	183
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	171	13	184

Error

4.7b

Counts

184 → 13

Compiler

Compiled 4321 to 2289 computations (47% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.3b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
4.0b	(/.f64 (.f64 M D) (.f64 2 d))
4.5b	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
4.8b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))

rewrite40.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-exp-log_binary64_798`
26×	`prod-exp_binary64_809`
23×	`add-cbrt-cube_binary64_796`
20×	`div-exp_binary64_811` `add-sqr-sqrt_binary64_782`
13×	`*-un-lft-identity_binary64_760`
10×	`add-cube-cbrt_binary64_795` `pow-exp_binary64_828` `associate-r_binary64_700`
6×	`cbrt-undiv_binary64_794` `sqrt-prod_binary64_776` `cbrt-unprod_binary64_793` `unpow-prod-down_binary64_839`
5×	`pow1_binary64_821` `times-frac_binary64_766`
4×	`unswap-sqr_binary64_728` `associate-/r*_binary64_704` `add-log-exp_binary64_799`
3×	`div-inv_binary64_757` `associate-l_binary64_701`
2×	`frac-2neg_binary64_771` `unpow2_binary64_825` `difference-of-squares_binary64_729` `sqrt-div_binary64_777` `associate-/l*_binary64_705` `pow-to-exp_binary64_829` `sqr-pow_binary64_732` `clear-num_binary64_759`
1×	`rem-sqrt-square_binary64_773` `sqrt-pow1_binary64_778` `distribute-lft-out--_binary64_712` `pow1/2_binary64_840` `*-commutative_binary64_691` `flip--_binary64_735` `flip3--_binary64_764`

Counts

4 → 99

Calls

4 calls:

10.0ms	(.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 (10.5%)

Counts

4 → 58

Calls

4 calls:

567.0ms	(/.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))
312.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
119.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 2465 to 2422 computations (1.7% saved)

simplify59.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5149	3033

prune194.0ms (1.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	152	5	157
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	156	14	170

Error

3.7b

Counts

170 → 14

Compiler

Compiled 3642 to 2247 computations (38.3% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.0b	(/.f64 (.f64 M D) (.f64 2 d))
4.0b	(/.f64 (.f64 M D) (.f64 2 d))
4.5b	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)
5.9b	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))

rewrite69.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

251×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
116×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793`
87×	`cbrt-undiv_binary64_794` `div-exp_binary64_811`
10×	`add-sqr-sqrt_binary64_782`
8×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
6×	`pow1_binary64_821` `times-frac_binary64_766`
5×	`associate-/r_binary64_704` `associate-r*_binary64_700`
4×	`add-log-exp_binary64_799` `div-inv_binary64_757` `associate-*r/_binary64_702`
3×	`frac-2neg_binary64_771` `associate-/l/_binary64_707` `associate-/l_binary64_705` `associate-l*_binary64_701` `clear-num_binary64_759`
1×	`unswap-sqr_binary64_728` `associate-l/_binary64_703` `frac-times_binary64_770` `pow-prod-down_binary64_831` `-commutative_binary64_691`

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))

series1.0s (8%)

Counts

4 → 45

Calls

4 calls:

541.0ms	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)
238.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
131.0ms	(/.f64 (.f64 M D) (.f64 2 d))
130.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 2100 to 1884 computations (10.3% saved)

simplify113.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5025	3667

prune256.0ms (2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	196	2	198
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	198	14	212

Error

3.7b

Counts

212 → 14

Compiler

Compiled 5240 to 2967 computations (43.4% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.0b	(/.f64 (.f64 M D) (.f64 2 d))
4.2b	(/.f64 (.f64 2 d) (.f64 M D))
4.5b	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 1 (/.f64 (.f64 2 d) (.f64 M D)))) l)
5.9b	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))

rewrite99.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

718×	`add-exp-log_binary64_798`
329×	`prod-exp_binary64_809`
312×	`add-cbrt-cube_binary64_796`
305×	`div-exp_binary64_811`
131×	`cbrt-unprod_binary64_793`
127×	`cbrt-undiv_binary64_794`
30×	`rec-exp_binary64_810` `1-exp_binary64_804`
10×	`add-sqr-sqrt_binary64_782`
8×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
6×	`pow1_binary64_821` `times-frac_binary64_766`
5×	`associate-/r_binary64_704` `associate-r*_binary64_700`
4×	`associate-/l/_binary64_707` `add-log-exp_binary64_799` `div-inv_binary64_757` `associate-*r/_binary64_702`
3×	`frac-2neg_binary64_771` `associate-/l_binary64_705` `associate-l*_binary64_701` `clear-num_binary64_759`
1×	`unswap-sqr_binary64_728` `associate-l/_binary64_703` `frac-times_binary64_770` `pow-prod-down_binary64_831` `un-div-inv_binary64_758` `-commutative_binary64_691`

Counts

4 → 226

Calls

4 calls:

25.0ms	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 1 (/.f64 (.f64 2 d) (.f64 M 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 2 d) (.f64 M D))

series1.1s (8.1%)

Counts

4 → 45

Calls

4 calls:

557.0ms	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 1 (/.f64 (.f64 2 d) (.f64 M D)))) l)
232.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
138.0ms	(/.f64 (.f64 2 d) (.f64 M D))
125.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 2220 to 2004 computations (9.7% saved)

simplify140.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

271 → 271

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4964	5806
1	4964	5806

prune312.0ms (2.4%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	271	0	271
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	271	14	285

Error

3.7b

Counts

285 → 14

Compiler

Compiled 7058 to 3277 computations (53.6% saved)

regimes1.7s (13.1%)

Accuracy

Total 5.0b remaining (56.3%)

Threshold costs 0b (0%)

Compiler

Compiled 19994 to 17178 computations (14.1% saved)

bsearch2.0ms (0%)

Compiler: Compiled 7 to 10 computations (-42.9% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	157	78
1	157	78

end0.0ms (0%)

sample2.4s (18.5%)

Algorithm

1×

intervals

Results

606.0ms	8000×	body	128	valid
230.0ms	3176×	body	128	nan
98.0ms	1346×	body	128	invalid

Compiler

Compiled 1249 to 1063 computations (14.9% saved)

Details

analyze2.0s (15.6%)

sample47.0ms (0.4%)

simplify132.0ms (1%)

prune3.0ms (0%)

localize16.0ms (0.1%)

rewrite42.0ms (0.3%)

series1.5s (11.6%)

simplify87.0ms (0.7%)

prune239.0ms (1.8%)

localize13.0ms (0.1%)

rewrite40.0ms (0.3%)

series1.4s (10.5%)

simplify59.0ms (0.5%)

prune194.0ms (1.5%)

localize14.0ms (0.1%)

rewrite69.0ms (0.5%)

series1.0s (8%)

simplify113.0ms (0.9%)

prune256.0ms (2%)

localize16.0ms (0.1%)

rewrite99.0ms (0.8%)

series1.1s (8.1%)

simplify140.0ms (1.1%)

prune312.0ms (2.4%)

regimes1.7s (13.1%)

bsearch2.0ms (0%)

simplify5.0ms (0%)

end0.0ms (0%)

sample2.4s (18.5%)

Profiling