Details

analyze2.4s (25.2%)

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

Compiler

Compiled 19 to 19 computations (0% saved)

sample55.0ms (0.6%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	128	valid
8.0ms	102×	body	128	nan
4.0ms	53×	body	128	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify42.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	6100	27

prune4.0ms (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 (0.2%)

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))

rewrite44.0ms (0.5%)

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:

16.0ms	(.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))))

series555.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

281.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
164.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
85.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
25.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify75.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5147	2845

prune193.0ms (2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	119	9	128
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	9	129

Error

7.1b

Counts

129 → 9

Compiler

Compiled 3361 to 1961 computations (41.7% saved)

localize16.0ms (0.2%)

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))

rewrite36.0ms (0.4%)

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:

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))

series536.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

317.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
101.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
95.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
22.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify51.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5069	2178

prune147.0ms (1.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	107	4	111
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	111	9	120

Error

6.6b

Counts

120 → 9

Compiler

Compiled 2749 to 1765 computations (35.8% saved)

localize16.0ms (0.2%)

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)))

rewrite64.0ms (0.7%)

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 (.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))

series198.0ms (2%)

Counts

4 → 12

Calls

4 calls:

113.0ms	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)
39.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
23.0ms	(/.f64 (.f64 M D) (.f64 2 d))
23.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify102.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5025	3130

prune225.0ms (2.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	163	2	165
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	166	8	174

Error

6.6b

Counts

174 → 8

Compiler

Compiled 4367 to 2555 computations (41.5% saved)

localize19.0ms (0.2%)

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)))

rewrite89.0ms (0.9%)

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)
8.0ms	(.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))

series200.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

113.0ms	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 1 (/.f64 (.f64 2 d) (.f64 M D)))) l)
43.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
22.0ms	(/.f64 (.f64 M D) (.f64 2 d))
22.0ms	(/.f64 (.f64 2 d) (.f64 M D))

simplify136.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4964	5269
1	4964	5269

prune290.0ms (3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	237	1	238
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	238	8	246

Error

6.6b

Counts

246 → 8

Compiler

Compiled 6248 to 2908 computations (53.5% saved)

regimes1.5s (15.1%)

Accuracy

Total 2.3b remaining (25.1%)

Threshold costs 0b (0%)

Compiler

Compiled 18238 to 15647 computations (14.2% saved)

bsearch0.0ms (0%)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	140	39
1	140	39

Compiler

Compiled 52 to 44 computations (15.4% saved)

end0.0ms (0%)

sample2.7s (27.6%)

Algorithm

1×

intervals

Results

672.0ms	8000×	body	128	valid
253.0ms	3176×	body	128	nan
111.0ms	1346×	body	128	invalid

Compiler

Compiled 1104 to 943 computations (14.6% saved)

Details

analyze2.4s (25.2%)

sample55.0ms (0.6%)

simplify42.0ms (0.4%)

prune4.0ms (0%)

localize16.0ms (0.2%)

rewrite44.0ms (0.5%)

series555.0ms (5.7%)

simplify75.0ms (0.8%)

prune193.0ms (2%)

localize16.0ms (0.2%)

rewrite36.0ms (0.4%)

series536.0ms (5.5%)

simplify51.0ms (0.5%)

prune147.0ms (1.5%)

localize16.0ms (0.2%)

rewrite64.0ms (0.7%)

series198.0ms (2%)

simplify102.0ms (1.1%)

prune225.0ms (2.3%)

localize19.0ms (0.2%)

rewrite89.0ms (0.9%)

series200.0ms (2.1%)

simplify136.0ms (1.4%)

prune290.0ms (3%)

regimes1.5s (15.1%)

bsearch0.0ms (0%)

simplify8.0ms (0.1%)

end0.0ms (0%)

sample2.7s (27.6%)

Profiling