Details

analyze2.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample19.0ms (0.6%)

Algorithm

1×

intervals

Results

6.0ms	63×	body	1024	valid
4.0ms	138×	body	128	valid
2.0ms	32×	body	512	valid
1.0ms	18×	body	256	valid
1.0ms	5×	body	2048	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify100.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune2.0ms (0.1%)

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

29.2b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

1.9b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
1.9b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`sqrt-prod_binary64_14075` `add-sqr-sqrt_binary64_14081`
10×	`*-un-lft-identity_binary64_14059`
6×	`cancel-sign-sub-inv_binary64_14025`
4×	`difference-of-squares_binary64_14028`
3×	`add-log-exp_binary64_14098` `add-cube-cbrt_binary64_14094` `distribute-lft-out--_binary64_14011`
1×	`add-cbrt-cube_binary64_14095` `flip--_binary64_14034` `distribute-lft-out_binary64_14010` `pow1_binary64_14120` `diff-log_binary64_14151` `sub-neg_binary64_14052` `flip3--_binary64_14063` `add-exp-log_binary64_14097`

Counts

1 → 24

Calls

2 calls:

9.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series30.0ms (0.9%)

Counts

1 → 3

Calls

1 calls:

30.0ms

(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 88 to 74 computations (15.9% saved)

simplify62.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5280	397

prune48.0ms (1.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	25	2	27
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	2	28

Error

0.1b

Counts

28 → 2

Compiler

Compiled 335 to 218 computations (34.9% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
0.0b	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.0b	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

rewrite23.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`*-un-lft-identity_binary64_14059`
20×	`sqrt-prod_binary64_14075` `distribute-lft-out_binary64_14010`
18×	`times-frac_binary64_14065`
13×	`add-cube-cbrt_binary64_14094` `add-sqr-sqrt_binary64_14081`
6×	`associate-/r*_binary64_14003` `add-exp-log_binary64_14097`
4×	`add-log-exp_binary64_14098` `add-cbrt-cube_binary64_14095`
3×	`pow1_binary64_14120` `associate-/l*_binary64_14004`
2×	`flip-+_binary64_14033` `div-exp_binary64_14110` `associate-/r/_binary64_14005` `flip3-+_binary64_14062`
1×	`frac-2neg_binary64_14070` `sum-log_binary64_14150` `pow-flip_binary64_14133` `div-inv_binary64_14056` `clear-num_binary64_14058` `cbrt-undiv_binary64_14093` `rec-exp_binary64_14109` `+-commutative_binary64_13989` `inv-pow_binary64_14144` `1-exp_binary64_14103`

Counts

2 → 59

Calls

4 calls:

11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

series31.0ms (0.9%)

Counts

2 → 6

Calls

2 calls:

16.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
14.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 84 to 84 computations (0% saved)

simplify109.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4780	1037
1	4780	1037

prune90.0ms (2.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	60	5	65
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	60	7	67

Error

0.0b

Counts

67 → 7

Compiler

Compiled 1014 to 741 computations (26.9% saved)

localize11.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.1b	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.1b	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.1b	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.3b	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

rewrite127.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Rules

310×	`*-un-lft-identity_binary64_14059`
290×	`sqrt-prod_binary64_14075`
172×	`times-frac_binary64_14065`
144×	`add-sqr-sqrt_binary64_14081`
116×	`distribute-lft-out_binary64_14010`
88×	`add-cube-cbrt_binary64_14094`
43×	`swap-sqr_binary64_14026`
31×	`pow1_binary64_14120`
27×	`associate-r_binary64_13999` `sqrt-pow1_binary64_14077` `associate-l_binary64_14000`
16×	`unswap-sqr_binary64_14027`
14×	`associate-/r/_binary64_14005` `add-exp-log_binary64_14097`
12×	`associate-/r*_binary64_14003`
11×	`pow-flip_binary64_14133` `inv-pow_binary64_14144`
10×	`add-cbrt-cube_binary64_14095`
9×	`rem-sqrt-square_binary64_14072` `pow1/2_binary64_14139` `pow-prod-up_binary64_14129` `div-inv_binary64_14056`
7×	`flip-+_binary64_14033` `flip3-+_binary64_14062`
6×	`associate-/l*_binary64_14004`
5×	`sqrt-div_binary64_14076` `pow-prod-down_binary64_14130` `pow-sqr_binary64_14032`
4×	`add-log-exp_binary64_14098` `div-exp_binary64_14110`
3×	`sqr-abs_binary64_14074`
2×	`frac-2neg_binary64_14070` `clear-num_binary64_14058` `cbrt-undiv_binary64_14093` `rec-exp_binary64_14109` `1-exp_binary64_14103`
1×	`frac-times_binary64_14069` `pow2_binary64_14140` `associate-l/_binary64_14002` `prod-exp_binary64_14108` `cbrt-unprod_binary64_14092` `pow-plus_binary64_14122` `-commutative_binary64_13990` `sqrt-unprod_binary64_14079` `associate-*r/_binary64_14001` `rem-square-sqrt_binary64_14071`

Counts

4 → 281

Calls

8 calls:

48.0ms	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
11.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

series90.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
21.0ms	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
20.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
19.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

Compiler

Compiled 404 to 368 computations (8.9% saved)

simplify121.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5824	5963

prune528.0ms (15.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	288	5	293
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	290	10	300

Error

0.0b

Counts

300 → 10

Compiler

Compiled 7002 to 5179 computations (26% saved)

localize11.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.1b	(sqrt.f64 (pow.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 4))
0.1b	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.1b	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.1b	(sqrt.f64 (pow.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 4))
0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.4b	(pow.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 4)

rewrite77.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

158×	`sqrt-prod_binary64_14075`
142×	`*-un-lft-identity_binary64_14059`
76×	`times-frac_binary64_14065`
59×	`add-sqr-sqrt_binary64_14081`
58×	`unpow-prod-down_binary64_14138`
52×	`distribute-lft-out_binary64_14010`
49×	`add-cube-cbrt_binary64_14094`
10×	`pow1_binary64_14120`
9×	`rem-sqrt-square_binary64_14072` `add-exp-log_binary64_14097`
8×	`associate-/r/_binary64_14005`
7×	`sqrt-pow1_binary64_14077`
6×	`add-cbrt-cube_binary64_14095` `associate-/r*_binary64_14003`
5×	`pow-pow_binary64_14131`
4×	`add-log-exp_binary64_14098` `flip-+_binary64_14033` `div-inv_binary64_14056` `flip3-+_binary64_14062`
3×	`sqr-pow_binary64_14031` `pow1/2_binary64_14139` `pow-flip_binary64_14133` `pow-unpow_binary64_14136` `inv-pow_binary64_14144` `associate-/l*_binary64_14004`
2×	`div-exp_binary64_14110`
1×	`frac-2neg_binary64_14070` `sqrt-pow2_binary64_14078` `sqrt-div_binary64_14076` `clear-num_binary64_14058` `cbrt-undiv_binary64_14093` `pow-exp_binary64_14127` `rec-exp_binary64_14109` `1-exp_binary64_14103` `pow-to-exp_binary64_14128`

Counts

4 → 176

Calls

8 calls:

18.0ms	(sqrt.f64 (pow.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 4))
17.0ms	(pow.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 4)
13.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

series102.0ms (3%)

Counts

4 → 12

Calls

4 calls:

42.0ms	(pow.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 4)
24.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
18.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
18.0ms	(sqrt.f64 (pow.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 4))

Compiler

Compiled 268 to 268 computations (0% saved)

simplify107.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4873	3775
1	4873	3775

prune223.0ms (6.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	186	2	188
Fresh	2	6	8
Picked	0	1	1
Done	1	0	1
Total	189	9	198

Error

0.0b

Counts

198 → 9

Compiler

Compiled 3327 to 2586 computations (22.3% saved)

simplify16.0ms (0.5%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	155	1087
1	155	1087

regimes135.0ms (3.9%)

Compiler: Compiled 1451 to 1205 computations (17% saved)

bsearch0.0ms (0%)

regimes20.0ms (0.6%)

Compiler: Compiled 36 to 38 computations (-5.6% saved)

bsearch0.0ms (0%)

regimes8.0ms (0.2%)

Accuracy

Total 0.2b remaining (95.5%)

Threshold costs 0.2b (95.5%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch2.0ms (0.1%)

Compiler: Compiled 17 to 16 computations (5.9% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	26
1	21	26

end0.0ms (0%)

sample1.3s (38.1%)

Algorithm

1×

intervals

Results

193.0ms	1999×	body	1024	valid
118.0ms	4295×	body	128	valid
72.0ms	981×	body	512	valid
30.0ms	223×	body	2048	valid
27.0ms	502×	body	256	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 704 to 587 computations (16.6% saved)

Pareto

-0.9497068181173958

Details

analyze2.0ms (0.1%)

sample19.0ms (0.6%)

simplify100.0ms (2.9%)

prune2.0ms (0.1%)

localize9.0ms (0.3%)

rewrite11.0ms (0.3%)

series30.0ms (0.9%)

simplify62.0ms (1.8%)

prune48.0ms (1.4%)

localize6.0ms (0.2%)

rewrite23.0ms (0.7%)

series31.0ms (0.9%)

simplify109.0ms (3.2%)

prune90.0ms (2.6%)

localize11.0ms (0.3%)

rewrite127.0ms (3.7%)

series90.0ms (2.6%)

simplify121.0ms (3.5%)

prune528.0ms (15.4%)

localize11.0ms (0.3%)

rewrite77.0ms (2.3%)

series102.0ms (3%)

simplify107.0ms (3.1%)

prune223.0ms (6.5%)

simplify16.0ms (0.5%)

regimes135.0ms (3.9%)

bsearch0.0ms (0%)

regimes20.0ms (0.6%)

bsearch0.0ms (0%)

regimes8.0ms (0.2%)

bsearch2.0ms (0.1%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.3s (38.1%)

Profiling