Details

analyze2.5s (14.9%)

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

18.0ms	256×	body	128	valid
12.0ms	106×	body	128	nan
2.0ms	28×	body	128	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify41.0ms (0.2%)

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

13.4b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
3.8b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
3.9b	(/.f64 (.f64 M D) (.f64 2 d))
11.5b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite219.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

8.3b

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:

12.0ms	(.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 (9.7%)

Error

7.6b

Counts

4 → 71

Calls

4 calls:

544.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
542.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
322.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
130.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 4216 to 3713 computations (11.9% saved)

simplify85.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4982	4087
1	4982	4087

prune218.0ms (1.3%)

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

5.2b

Counts

188 → 10

Compiler

Compiled 4325 to 2262 computations (47.7% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.7b	(.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h)))
3.8b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
3.9b	(/.f64 (.f64 M D) (.f64 2 d))
5.6b	(.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))

rewrite273.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

4.9b

Rules

210×	`add-exp-log_binary64_798`
121×	`prod-exp_binary64_809`
43×	`div-exp_binary64_811`
33×	`add-cbrt-cube_binary64_796`
30×	`pow-exp_binary64_828`
23×	`add-sqr-sqrt_binary64_782` `associate-r_binary64_700`
20×	`add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760` `times-frac_binary64_766`
19×	`cbrt-unprod_binary64_793`
11×	`associate-l_binary64_701`
9×	`cbrt-prod_binary64_791`
7×	`pow1_binary64_821` `cbrt-undiv_binary64_794`
6×	`pow-to-exp_binary64_829` `unpow-prod-down_binary64_839`
4×	`add-log-exp_binary64_799` `unswap-sqr_binary64_728`
3×	`div-inv_binary64_757` `sqrt-prod_binary64_776`
2×	`pow-prod-down_binary64_831` `*-commutative_binary64_691` `sqrt-div_binary64_777` `unpow2_binary64_825` `sqr-pow_binary64_732`
1×	`associate-r/_binary64_702` `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` `pow2_binary64_841`

Counts

4 → 145

Calls

4 calls:

21.0ms	(.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
12.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h)))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
5.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))

Compiler

Compiled 5167 to 2359 computations (54.3% saved)

series1.8s (10.9%)

Error

5.2b

Counts

4 → 58

Calls

4 calls:

694.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h)))
581.0ms	(.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
335.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
132.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 4030 to 3473 computations (13.8% saved)

simplify97.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4993	4433
1	4993	4433

prune234.0ms (1.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	202	1	203
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	203	10	213

Error

5.1b

Counts

213 → 10

Compiler

Compiled 5302 to 2587 computations (51.2% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l)))))
3.8b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))))
3.9b	(/.f64 (.f64 M D) (.f64 2 d))
5.6b	(.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))

rewrite241.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

4.4b

Rules

82×	`add-exp-log_binary64_798`
45×	`add-sqr-sqrt_binary64_782`
39×	`prod-exp_binary64_809`
28×	`associate-r_binary64_700`
25×	`times-frac_binary64_766`
22×	`add-cbrt-cube_binary64_796` `add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
20×	`div-exp_binary64_811`
12×	`pow-exp_binary64_828` `cbrt-prod_binary64_791`
11×	`unswap-sqr_binary64_728`
9×	`associate-l_binary64_701`
7×	`pow1_binary64_821` `cbrt-unprod_binary64_793` `sqrt-prod_binary64_776`
5×	`cbrt-undiv_binary64_794`
4×	`add-log-exp_binary64_799` `unpow2_binary64_825` `sqr-pow_binary64_732` `sqrt-div_binary64_777`
3×	`associate-*r/_binary64_702`
2×	`pow-to-exp_binary64_829` `div-inv_binary64_757` `*-commutative_binary64_691` `flip3--_binary64_764` `flip--_binary64_735`
1×	`unpow-prod-down_binary64_839` `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 → 124

Calls

4 calls:

13.0ms	(.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))
11.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l)))))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
5.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))))

Compiler

Compiled 4389 to 2234 computations (49.1% saved)

series1.7s (10%)

Error

5.1b

Counts

4 → 71

Calls

4 calls:

574.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l)))))
571.0ms	(.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))
325.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))))
132.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 4379 to 3813 computations (12.9% saved)

simplify95.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4999	5157
1	4999	5157

prune229.0ms (1.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	192	3	195
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	193	12	205

Error

4.4b

Counts

205 → 12

Compiler

Compiled 5302 to 2577 computations (51.4% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (cbrt.f64 h) (pow.f64 (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (cbrt.f64 h)) 2)) l))))
3.8b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (cbrt.f64 h) (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) 2)) l)))
3.9b	(/.f64 (.f64 M D) (.f64 2 d))
4.7b	(/.f64 (.f64 (cbrt.f64 h) (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) 2)) l)

rewrite193.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

4.4b

Rules

56×	`add-exp-log_binary64_798`
22×	`prod-exp_binary64_809` `add-cbrt-cube_binary64_796`
21×	`add-sqr-sqrt_binary64_782`
17×	`div-exp_binary64_811`
16×	`*-un-lft-identity_binary64_760`
13×	`sqrt-prod_binary64_776`
10×	`add-cube-cbrt_binary64_795`
9×	`associate-r_binary64_700`
7×	`pow1_binary64_821`
6×	`pow-exp_binary64_828` `cbrt-undiv_binary64_794` `cbrt-unprod_binary64_793`
4×	`add-log-exp_binary64_799` `times-frac_binary64_766` `associate-/r*_binary64_704` `sqrt-div_binary64_777` `difference-of-squares_binary64_729`
3×	`associate-l_binary64_701`
2×	`frac-2neg_binary64_771` `clear-num_binary64_759` `div-inv_binary64_757` `associate-/l_binary64_705` `flip3--_binary64_764` `flip--_binary64_735` `distribute-lft-out--_binary64_712` `unswap-sqr_binary64_728` `associate-r/_binary64_702`
1×	`pow-to-exp_binary64_829` `pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `pow-prod-down_binary64_831` `*-commutative_binary64_691`

Counts

4 → 94

Calls

4 calls:

11.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (cbrt.f64 h) (pow.f64 (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (cbrt.f64 h)) 2)) l))))
9.0ms	(/.f64 (.f64 (cbrt.f64 h) (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) 2)) l)
7.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (cbrt.f64 h) (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) 2)) l)))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 3359 to 1898 computations (43.5% saved)

series1.7s (10%)

Error

4.4b

Counts

4 → 71

Calls

4 calls:

582.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (cbrt.f64 h) (pow.f64 (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (cbrt.f64 h)) 2)) l))))
555.0ms	(/.f64 (.f64 (cbrt.f64 h) (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) 2)) l)
325.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (cbrt.f64 h) (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) 2)) l)))
130.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 4379 to 3821 computations (12.7% saved)

simplify80.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5047	4180

prune176.0ms (1.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	164	1	165
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	166	11	177

Error

4.4b

Counts

177 → 11

Compiler

Compiled 4106 to 2034 computations (50.5% saved)

regimes2.1s (12.7%)

Accuracy

Total 5.9b remaining (59.3%)

Threshold costs 0b (0%)

Compiler

Compiled 27522 to 23999 computations (12.8% saved)

bsearch4.0ms (0%)

Compiler: Compiled 15 to 16 computations (-6.7% saved)

simplify18.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	219	164
1	219	164

Removed

()

Compiler

Compiled 216 to 136 computations (37% saved)

end0.0ms (0%)

sample2.9s (17.8%)

Algorithm

1×

intervals

Results

594.0ms	8000×	body	128	valid
233.0ms	3104×	body	128	nan
93.0ms	1329×	body	128	invalid

Compiler

Compiled 1721 to 1476 computations (14.2% saved)

Details

analyze2.5s (14.9%)

sample62.0ms (0.4%)

simplify41.0ms (0.2%)

prune3.0ms (0%)

localize13.0ms (0.1%)

rewrite219.0ms (1.3%)

series1.6s (9.7%)

simplify85.0ms (0.5%)

prune218.0ms (1.3%)

localize17.0ms (0.1%)

rewrite273.0ms (1.7%)

series1.8s (10.9%)

simplify97.0ms (0.6%)

prune234.0ms (1.4%)

localize16.0ms (0.1%)

rewrite241.0ms (1.5%)

series1.7s (10%)

simplify95.0ms (0.6%)

prune229.0ms (1.4%)

localize16.0ms (0.1%)

rewrite193.0ms (1.2%)

series1.7s (10%)

simplify80.0ms (0.5%)

prune176.0ms (1.1%)

regimes2.1s (12.7%)

bsearch4.0ms (0%)

simplify18.0ms (0.1%)

end0.0ms (0%)

sample2.9s (17.8%)

Profiling