Details

analyze2.1s (13.6%)

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)

sample46.0ms (0.3%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
6.0ms	92×	body	128	nan
3.0ms	37×	body	128	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify129.0ms (0.8%)

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

12.6b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize13.0ms (0.1%)

Local error

Found 8 expressions with local error:

5.4b	(/.f64 (.f64 M D) (.f64 2 d))
4.0b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
0.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
0.2b	(pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)
0.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
4.0b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
5.4b	(/.f64 (.f64 M D) (.f64 2 d))
9.4b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite40.0ms (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

8 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))))
0.0ms	(pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)

series1.5s (9.7%)

Counts

4 → 61

Calls

4 calls:

549.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
539.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
283.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
118.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 2740 to 2650 computations (3.3% saved)

simplify83.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5054	3992

prune296.0ms (1.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	163	14	177
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	164	14	178

Error

3.1b

Counts

178 → 14

Compiler

Compiled 4333 to 2334 computations (46.1% saved)

localize14.0ms (0.1%)

Local error

Found 8 expressions with local error:

5.4b	(/.f64 (.f64 M D) (.f64 2 d))
4.0b	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))
1.2b	(.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))
0.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))))))
4.0b	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))
5.4b	(/.f64 (.f64 M D) (.f64 2 d))
5.4b	(/.f64 (.f64 M D) (.f64 2 d))
9.1b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))

rewrite41.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

8 calls:

12.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
5.0ms	(/.f64 (.f64 M D) (.f64 2 d))
5.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))
0.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))))))

series874.0ms (5.7%)

Counts

4 → 50

Calls

4 calls:

336.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))
290.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))
126.0ms	(/.f64 (.f64 M D) (.f64 2 d))
122.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 2396 to 2129 computations (11.1% saved)

simplify80.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5005	2799

prune226.0ms (1.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	153	6	159
Fresh	7	6	13
Picked	1	0	1
Done	0	0	0
Total	161	12	173

Error

2.2b

Counts

173 → 12

Compiler

Compiled 4496 to 2271 computations (49.5% saved)

localize14.0ms (0.1%)

Local error

Found 8 expressions with local error:

4.0b	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h) l))))
3.5b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)
1.2b	(.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h) l))
0.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h) l)))))
4.0b	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h) l))))
5.4b	(/.f64 (.f64 M D) (.f64 2 d))
5.4b	(/.f64 (.f64 M D) (.f64 2 d))
7.7b	(/.f64 (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h) l)

rewrite38.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
18×	`cbrt-undiv_binary64_794` `div-exp_binary64_811`
17×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793`
8×	`add-sqr-sqrt_binary64_782`
7×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
5×	`associate-/r*_binary64_704` `pow1_binary64_821` `times-frac_binary64_766`
4×	`add-log-exp_binary64_799`
3×	`frac-2neg_binary64_771` `sqrt-prod_binary64_776` `div-inv_binary64_757` `associate-/l*_binary64_705` `clear-num_binary64_759`
2×	`sqrt-div_binary64_777`
1×	`rem-sqrt-square_binary64_773` `associate-*l/_binary64_703` `associate-/l/_binary64_707` `sqrt-pow1_binary64_778` `pow1/2_binary64_840` `flip--_binary64_735` `flip3--_binary64_764`

Counts

4 → 87

Calls

8 calls:

12.0ms	(/.f64 (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h) l)
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
5.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h) l))))
0.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h) l)))))

series867.0ms (5.6%)

Counts

4 → 50

Calls

4 calls:

341.0ms	(/.f64 (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h) l)
295.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h) l))))
117.0ms	(/.f64 (.f64 M D) (.f64 2 d))
113.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 2396 to 2129 computations (11.1% saved)

simplify70.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4991	2381
1	4991	2381

prune168.0ms (1.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	137	12	149

Error

2.2b

Counts

149 → 12

Compiler

Compiled 3815 to 2027 computations (46.9% saved)

localize13.0ms (0.1%)

Local error

Found 8 expressions with local error:

4.0b	(sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (/.f64 h l))))
0.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (/.f64 h l)))))
0.2b	(/.f64 2 (/.f64 D d))
0.2b	(pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2)
0.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (/.f64 h l)))))
4.0b	(sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (/.f64 h l))))
5.9b	(/.f64 M (/.f64 2 (/.f64 D d)))
9.4b	(*.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (/.f64 h l))

rewrite159.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

754×	`times-frac_binary64_766`
399×	`add-sqr-sqrt_binary64_782`
351×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
145×	`associate-l_binary64_701` `unpow-prod-down_binary64_839`
55×	`add-exp-log_binary64_798`
44×	`associate-/r*_binary64_704`
31×	`div-inv_binary64_757`
24×	`div-exp_binary64_811`
20×	`add-cbrt-cube_binary64_796`
19×	`associate-r_binary64_700`
16×	`unswap-sqr_binary64_728`
13×	`prod-exp_binary64_809`
9×	`associate-/r/_binary64_706`
8×	`pow-exp_binary64_828`
7×	`cbrt-undiv_binary64_794` `sqrt-prod_binary64_776` `pow1_binary64_821`
4×	`add-log-exp_binary64_799` `sqrt-div_binary64_777`
3×	`unpow2_binary64_825` `associate-/l_binary64_705` `associate-r/_binary64_702` `sqr-pow_binary64_732` `cbrt-unprod_binary64_793`
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` `pow1/2_binary64_840` `clear-num_binary64_759` `pow-prod-down_binary64_831`

Counts

4 → 427

Calls

8 calls:

67.0ms	(*.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (/.f64 h l))
13.0ms	(/.f64 M (/.f64 2 (/.f64 D d)))
8.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (/.f64 h l)))))
4.0ms	(sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (/.f64 h l))))
0.0ms	(pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2)

series1.5s (9.7%)

Counts

4 → 61

Calls

4 calls:

552.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (/.f64 h l)))))
534.0ms	(*.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (/.f64 h l))
287.0ms	(sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (/.f64 h l))))
114.0ms	(/.f64 M (/.f64 2 (/.f64 D d)))

Compiler

Compiled 2740 to 2650 computations (3.3% saved)

simplify154.0ms (1%)

Algorithm

1×	egg-herbie

Counts

488 → 488

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4999	11958
1	4999	11958

prune800.0ms (5.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	485	3	488
Fresh	0	10	10
Picked	1	0	1
Done	0	1	1
Total	486	14	500

Error

1.7b

Counts

500 → 14

Compiler

Compiled 14207 to 7511 computations (47.1% saved)

simplify43.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	1416	1916
1	1416	1916

regimes1.8s (11.8%)

Compiler: Compiled 17599 to 15048 computations (14.5% saved)

bsearch2.0ms (0%)

Compiler: Compiled 3 to 7 computations (-133.3% saved)

regimes511.0ms (3.3%)

Compiler: Compiled 3314 to 3302 computations (0.4% saved)

bsearch1.0ms (0%)

Compiler: Compiled 3 to 7 computations (-133.3% saved)

regimes338.0ms (2.2%)

Compiler: Compiled 2197 to 2290 computations (-4.2% saved)

bsearch1.0ms (0%)

Compiler: Compiled 3 to 7 computations (-133.3% saved)

regimes340.0ms (2.2%)

Compiler: Compiled 1803 to 1853 computations (-2.8% saved)

bsearch1.0ms (0%)

Compiler: Compiled 3 to 7 computations (-133.3% saved)

regimes176.0ms (1.1%)

Compiler: Compiled 1229 to 1297 computations (-5.5% saved)

bsearch62.0ms (0.4%)

Steps

Iters	Range		Point
2	2.8191180629205917e+137	3.1652798997754564e+137	2.8623882925274497e+137
10	8.155176704072439e-172	2.2478709908930268e-156	2.1017646892466287e-156

Compiler

Compiled 1 to 6 computations (-500% saved)

regimes154.0ms (1%)

Compiler: Compiled 1075 to 1171 computations (-8.9% saved)

bsearch0.0ms (0%)

regimes54.0ms (0.4%)

Accuracy

Total 5.4b remaining (64.8%)

Threshold costs 0b (0%)

Compiler

Compiled 30 to 198 computations (-560% saved)

bsearch10.0ms (0.1%)

Compiler: Compiled 248 to 180 computations (27.4% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	331	368
1	331	368

end0.0ms (0%)

sample2.6s (17.2%)

Algorithm

1×

intervals

Results

603.0ms	8000×	body	128	valid
228.0ms	3109×	body	128	nan
95.0ms	1326×	body	128	invalid

Compiler

Compiled 1525 to 1272 computations (16.6% saved)

Pareto

0.04593547214257949

Details

analyze2.1s (13.6%)

sample46.0ms (0.3%)

simplify129.0ms (0.8%)

prune3.0ms (0%)

localize13.0ms (0.1%)

rewrite40.0ms (0.3%)

series1.5s (9.7%)

simplify83.0ms (0.5%)

prune296.0ms (1.9%)

localize14.0ms (0.1%)

rewrite41.0ms (0.3%)

series874.0ms (5.7%)

simplify80.0ms (0.5%)

prune226.0ms (1.5%)

localize14.0ms (0.1%)

rewrite38.0ms (0.2%)

series867.0ms (5.6%)

simplify70.0ms (0.5%)

prune168.0ms (1.1%)

localize13.0ms (0.1%)

rewrite159.0ms (1%)

series1.5s (9.7%)

simplify154.0ms (1%)

prune800.0ms (5.2%)

simplify43.0ms (0.3%)

regimes1.8s (11.8%)

bsearch2.0ms (0%)

regimes511.0ms (3.3%)

bsearch1.0ms (0%)

regimes338.0ms (2.2%)

bsearch1.0ms (0%)

regimes340.0ms (2.2%)

bsearch1.0ms (0%)

regimes176.0ms (1.1%)

bsearch62.0ms (0.4%)

regimes154.0ms (1%)

bsearch0.0ms (0%)

regimes54.0ms (0.4%)

bsearch10.0ms (0.1%)

simplify10.0ms (0.1%)

end0.0ms (0%)

sample2.6s (17.2%)

Profiling