Details

analyze2.6s (16.6%)

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)

sample62.0ms (0.4%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
7.0ms	102×	body	128	nan
4.0ms	49×	body	128	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify48.0ms (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

14.1b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
4.9b	(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))
9.8b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite223.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

7.5b

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×	`frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l_binary64_705` `associate-/r_binary64_704` `pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `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)

series1.4s (9.1%)

Error

6.1b

Counts

4 → 58

Calls

4 calls:

544.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
480.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
225.0ms	(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 3414 to 3065 computations (10.2% saved)

simplify70.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5425	3754

prune217.0ms (1.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	165	9	174
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	166	9	175

Error

3.2b

Counts

175 → 9

Compiler

Compiled 4041 to 2167 computations (46.4% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.0b	(.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))
4.9b	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))))
5.4b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
7.0b	(/.f64 (.f64 M D) (.f64 2 d))

rewrite450.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

3.0b

Rules

165×	`add-exp-log_binary64_798`
91×	`prod-exp_binary64_809`
40×	`div-exp_binary64_811`
30×	`add-cbrt-cube_binary64_796`
25×	`pow-exp_binary64_828`
23×	`associate-r_binary64_700`
22×	`add-sqr-sqrt_binary64_782`
15×	`add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
11×	`cbrt-unprod_binary64_793` `times-frac_binary64_766`
8×	`1-exp_binary64_804` `rec-exp_binary64_810`
7×	`pow1_binary64_821`
6×	`cbrt-undiv_binary64_794` `unpow-prod-down_binary64_839`
5×	`pow-to-exp_binary64_829`
4×	`add-log-exp_binary64_799` `unswap-sqr_binary64_728` `associate-l_binary64_701`
3×	`div-inv_binary64_757` `sqrt-prod_binary64_776`
2×	`unpow2_binary64_825` `sqr-pow_binary64_732` `*-commutative_binary64_691` `sqrt-div_binary64_777`
1×	`frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l_binary64_705` `associate-/r_binary64_704` `pow1/2_binary64_840` `sqrt-pow1_binary64_778` `flip3--_binary64_764` `flip--_binary64_735` `rem-sqrt-square_binary64_773` `pow-prod-down_binary64_831` `un-div-inv_binary64_758` `associate-*r/_binary64_702`

Counts

4 → 130

Calls

4 calls:

220.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
12.0ms	(.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
5.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))))

Compiler

Compiled 3800 to 2447 computations (35.6% saved)

series1.3s (7.9%)

Error

3.0b

Counts

4 → 51

Calls

4 calls:

520.0ms	(.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))
341.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
219.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))))
123.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 3217 to 2929 computations (9% saved)

simplify86.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5011	3445

prune229.0ms (1.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	176	5	181
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	178	12	190

Error

2.8b

Counts

190 → 12

Compiler

Compiled 4252 to 2728 computations (35.8% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.0b	(/.f64 (.f64 M D) (.f64 d 2))
7.0b	(/.f64 (.f64 M D) (.f64 d 2))
16.5b	(cbrt.f64 (/.f64 (.f64 M D) (.f64 d 2)))
16.5b	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))

rewrite156.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

2.8b

Rules

28×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
10×	`cbrt-prod_binary64_791`
8×	`prod-exp_binary64_809` `div-exp_binary64_811` `cbrt-undiv_binary64_794` `cbrt-unprod_binary64_793`
6×	`add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782` `*-un-lft-identity_binary64_760`
4×	`pow1_binary64_821` `add-log-exp_binary64_799` `times-frac_binary64_766` `div-inv_binary64_757`
2×	`pow1/3_binary64_842` `cbrt-div_binary64_792` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l_binary64_705` `associate-/r_binary64_704`

Counts

4 → 70

Calls

4 calls:

6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
5.0ms	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))
4.0ms	(cbrt.f64 (/.f64 (.f64 M D) (.f64 d 2)))

Compiler

Compiled 3146 to 1908 computations (39.4% saved)

series1.1s (6.8%)

Error

2.8b

Counts

4 → 36

Calls

4 calls:

391.0ms	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))
378.0ms	(cbrt.f64 (/.f64 (.f64 M D) (.f64 d 2)))
127.0ms	(/.f64 (.f64 M D) (.f64 d 2))
126.0ms	(/.f64 (.f64 M D) (.f64 d 2))

Compiler

Compiled 4446 to 3325 computations (25.2% saved)

simplify82.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4977	1428
1	4977	1428

prune194.0ms (1.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	106	12	118

Error

2.8b

Counts

118 → 12

Compiler

Compiled 4532 to 2808 computations (38% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.9b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) l)))
5.4b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2))
7.0b	(/.f64 (.f64 M D) (.f64 d 2))
7.4b	(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) l))) 3))

rewrite238.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

2.7b

Rules

37×	`add-exp-log_binary64_798`
29×	`add-sqr-sqrt_binary64_782`
24×	`cbrt-prod_binary64_791`
22×	`*-un-lft-identity_binary64_760`
18×	`add-cbrt-cube_binary64_796` `sqrt-prod_binary64_776`
15×	`unpow-prod-down_binary64_839` `prod-exp_binary64_809`
13×	`add-cube-cbrt_binary64_795`
10×	`associate-r_binary64_700`
9×	`cube-prod_binary64_788`
8×	`div-exp_binary64_811`
6×	`difference-of-squares_binary64_729`
5×	`pow1_binary64_821` `cbrt-unprod_binary64_793` `pow-exp_binary64_828`
4×	`add-log-exp_binary64_799` `sqrt-div_binary64_777` `cbrt-undiv_binary64_794` `unswap-sqr_binary64_728`
3×	`distribute-lft-out--_binary64_712` `sqr-pow_binary64_732` `associate-l_binary64_701`
2×	`flip3--_binary64_764` `cube-div_binary64_789` `cbrt-div_binary64_792` `flip--_binary64_735` `times-frac_binary64_766` `div-inv_binary64_757` `unpow2_binary64_825`
1×	`pow1/3_binary64_842` `unpow3_binary64_826` `cube-mult_binary64_790` `rem-cbrt-cube_binary64_784` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l_binary64_705` `associate-/r_binary64_704` `pow-to-exp_binary64_829` `*-commutative_binary64_691` `pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773`

Counts

4 → 107

Calls

4 calls:

9.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) l))) 3))
8.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2))
7.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) l)))
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))

Compiler

Compiled 3716 to 2509 computations (32.5% saved)

series964.0ms (6.1%)

Error

2.8b

Counts

4 → 51

Calls

4 calls:

345.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2))
228.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) l))) 3))
221.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) l)))
121.0ms	(/.f64 (.f64 M D) (.f64 d 2))

Compiler

Compiled 3248 to 2987 computations (8% saved)

simplify76.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5018	3481

prune202.0ms (1.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	154	4	158
Fresh	3	6	9
Picked	1	0	1
Done	1	1	2
Total	159	11	170

Error

2.0b

Counts

170 → 11

Compiler

Compiled 3868 to 2479 computations (35.9% saved)

regimes2.7s (16.8%)

Accuracy

Total 6.2b remaining (66.1%)

Threshold costs 0b (0%)

Compiler

Compiled 28772 to 25815 computations (10.3% saved)

bsearch4.0ms (0%)

Compiler: Compiled 13 to 14 computations (-7.7% saved)

simplify16.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	183	142
1	183	142

Compiler

Compiled 188 to 126 computations (33% saved)

end0.0ms (0%)

sample3.4s (21.3%)

Algorithm

1×

intervals

Results

618.0ms	8000×	body	128	valid
255.0ms	3224×	body	128	nan
97.0ms	1262×	body	128	invalid

Compiler

Compiled 1726 to 1533 computations (11.2% saved)

Details

analyze2.6s (16.6%)

sample62.0ms (0.4%)

simplify48.0ms (0.3%)

prune3.0ms (0%)

localize15.0ms (0.1%)

rewrite223.0ms (1.4%)

series1.4s (9.1%)

simplify70.0ms (0.4%)

prune217.0ms (1.4%)

localize16.0ms (0.1%)

rewrite450.0ms (2.8%)

series1.3s (7.9%)

simplify86.0ms (0.5%)

prune229.0ms (1.4%)

localize23.0ms (0.1%)

rewrite156.0ms (1%)

series1.1s (6.8%)

simplify82.0ms (0.5%)

prune194.0ms (1.2%)

localize18.0ms (0.1%)

rewrite238.0ms (1.5%)

series964.0ms (6.1%)

simplify76.0ms (0.5%)

prune202.0ms (1.3%)

regimes2.7s (16.8%)

bsearch4.0ms (0%)

simplify16.0ms (0.1%)

end0.0ms (0%)

sample3.4s (21.3%)

Profiling