Details

analyze51.0ms (1.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
25%	74.9%	0.1%	4
37.5%	62.4%	0.1%	5
56.2%	43.7%	0.1%	6
65.6%	34.3%	0.1%	7
76.5%	23.4%	0.1%	8
82%	18%	0.1%	9
87.8%	12.1%	0.1%	10
90.7%	9.2%	0.1%	11
93.8%	6.1%	0.1%	12
95.3%	4.6%	0.1%	13
96.8%	3.1%	0.1%	14

Compiler

Compiled 6 to 5 computations (16.7% saved)

sample11.0ms (0.3%)

Algorithm

1×

intervals

Results

4.0ms

256×

body

128

valid

Compiler

Compiled 11 to 11 computations (0% saved)

simplify93.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	13	7
1	13	7

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

0.0b

Counts

2 → 1

Compiler

Compiled 10 to 8 computations (20% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (+.f64 x y) x)
0.0b	(+.f64 (+.f64 x y) x)

rewrite8.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64_16105` `add-log-exp_binary64_16144`
3×	`sum-log_binary64_16196` `distribute-lft-out_binary64_16056`
1×	`flip-+_binary64_16079` `add-cube-cbrt_binary64_16140` `add-sqr-sqrt_binary64_16127` `associate-+l+_binary64_16038` `add-exp-log_binary64_16143` `+-commutative_binary64_16035` `flip3-+_binary64_16108` `pow1_binary64_16166` `add-cbrt-cube_binary64_16141`

Counts

1 → 15

Calls

2 calls:

7.0ms	(+.f64 (+.f64 x y) x)
0.0ms	(+.f64 (+.f64 x y) x)

series60.0ms (1.9%)

Counts

1 → 12

Calls

1 calls:

59.0ms

(+.f64 (+.f64 x y) x)

Compiler

Compiled 72 to 78 computations (-8.3% saved)

simplify54.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4958	205
1	4958	205

prune15.0ms (0.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

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

Error

0.0b

Counts

28 → 2

Compiler

Compiled 190 to 43 computations (77.4% saved)

localize6.0ms (0.2%)

Local error

Found 6 expressions with local error:

0.3b	(*.f64 (sqrt.f64 (+.f64 x (+.f64 x y))) (sqrt.f64 (+.f64 x (+.f64 x y))))
0.0b	(+.f64 x (+.f64 x y))
0.0b	(+.f64 x (+.f64 x y))
0.0b	(+.f64 x (+.f64 x y))
0.0b	(+.f64 x (+.f64 x y))
0.3b	(*.f64 (sqrt.f64 (+.f64 x (+.f64 x y))) (sqrt.f64 (+.f64 x (+.f64 x y))))

rewrite41.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`*-un-lft-identity_binary64_16105`
38×	`sqrt-prod_binary64_16121`
30×	`distribute-lft-out_binary64_16056`
25×	`add-sqr-sqrt_binary64_16127`
18×	`pow1_binary64_16166`
16×	`swap-sqr_binary64_16072`
13×	`add-log-exp_binary64_16144`
12×	`sqrt-div_binary64_16122`
11×	`add-cube-cbrt_binary64_16140`
8×	`flip-+_binary64_16079` `sqrt-pow1_binary64_16123` `flip3-+_binary64_16108` `associate-r_binary64_16045` `pow1/2_binary64_16185` `associate-l_binary64_16046`
6×	`sum-log_binary64_16196`
5×	`pow-prod-up_binary64_16175` `add-exp-log_binary64_16143` `add-cbrt-cube_binary64_16141`
4×	`frac-times_binary64_16115` `unswap-sqr_binary64_16073`
3×	`pow-sqr_binary64_16078` `pow-prod-down_binary64_16176`
2×	`associate-r/_binary64_16047` `rem-sqrt-square_binary64_16118` `+-commutative_binary64_16035` `associate-l/_binary64_16048` `associate-+r+_binary64_16037`
1×	`rem-square-sqrt_binary64_16117` `cbrt-unprod_binary64_16138` `pow-plus_binary64_16168` `*-commutative_binary64_16036` `prod-exp_binary64_16154` `sqrt-unprod_binary64_16125` `sqr-abs_binary64_16120` `pow2_binary64_16186`

Counts

3 → 100

Calls

6 calls:

20.0ms	(*.f64 (sqrt.f64 (+.f64 x (+.f64 x y))) (sqrt.f64 (+.f64 x (+.f64 x y))))
6.0ms	(+.f64 x (+.f64 x y))
6.0ms	(+.f64 x (+.f64 x y))
0.0ms	(+.f64 x (+.f64 x y))
0.0ms	(*.f64 (sqrt.f64 (+.f64 x (+.f64 x y))) (sqrt.f64 (+.f64 x (+.f64 x y))))

series179.0ms (5.6%)

Counts

3 → 36

Calls

3 calls:

64.0ms	(+.f64 x (+.f64 x y))
58.0ms	(*.f64 (sqrt.f64 (+.f64 x (+.f64 x y))) (sqrt.f64 (+.f64 x (+.f64 x y))))
57.0ms	(+.f64 x (+.f64 x y))

Compiler

Compiled 504 to 414 computations (17.9% saved)

simplify69.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5291	1314

prune78.0ms (2.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	135	3	138

Error

0.0b

Counts

138 → 3

Compiler

Compiled 1748 to 287 computations (83.6% saved)

localize9.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 x y))))
0.1b	(sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 x y))))
0.0b	(+.f64 x (+.f64 x y))
0.0b	(+.f64 x (+.f64 x y))
0.1b	(sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 x y))))
0.1b	(sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 x y))))
0.2b	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 x y)))) (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 x y)))) 3))
0.4b	(pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 x y)))) 3)

rewrite68.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

135×	`sqrt-prod_binary64_16121`
74×	`add-sqr-sqrt_binary64_16127`
60×	`*-un-lft-identity_binary64_16105`
36×	`sqrt-div_binary64_16122`
31×	`cube-prod_binary64_16133` `unpow-prod-down_binary64_16184`
28×	`associate-r_binary64_16045`
25×	`add-cube-cbrt_binary64_16140`
24×	`unswap-sqr_binary64_16073`
21×	`distribute-lft-out_binary64_16056`
12×	`sqrt-pow1_binary64_16123` `pow1_binary64_16166`
11×	`associate-l_binary64_16046`
10×	`add-exp-log_binary64_16143`
9×	`flip-+_binary64_16079` `flip3-+_binary64_16108`
8×	`cube-div_binary64_16134`
7×	`add-cbrt-cube_binary64_16141`
6×	`pow1/2_binary64_16185`
5×	`pow-pow_binary64_16177` `sqr-pow_binary64_16077`
4×	`rem-sqrt-square_binary64_16118` `frac-times_binary64_16115` `add-log-exp_binary64_16144`
3×	`pow-unpow_binary64_16182` `prod-exp_binary64_16154`
2×	`unpow3_binary64_16171` `associate-r/_binary64_16047` `pow-exp_binary64_16173` `pow-to-exp_binary64_16174` `associate-l/_binary64_16048` `cube-mult_binary64_16135`
1×	`sqrt-pow2_binary64_16124` `pow-prod-up_binary64_16175` `cbrt-unprod_binary64_16138` `rem-cube-cbrt_binary64_16128` `*-commutative_binary64_16036`

Counts

4 → 176

Calls

8 calls:

26.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 x y)))) (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 x y)))) 3))
10.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 x y)))) 3)
6.0ms	(sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 x y))))
6.0ms	(sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 x y))))
0.0ms	(+.f64 x (+.f64 x y))

series436.0ms (13.6%)

Counts

4 → 40

Calls

4 calls:

197.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 x y)))) 3)
92.0ms	(sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 x y))))
89.0ms	(sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 x y))))
58.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 x y)))) (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 x y)))) 3))

Compiler

Compiled 1404 to 1227 computations (12.6% saved)

simplify102.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4863	3357
1	4863	3357

prune165.0ms (5.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	214	2	216
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	215	4	219

Error

Counts

219 → 4

Compiler

Compiled 4153 to 1012 computations (75.6% saved)

localize7.0ms (0.2%)

Local error

Found 6 expressions with local error:

0.5b	(pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 x y)))) 4)
0.1b	(sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 x y))))
0.0b	(+.f64 x (+.f64 x y))
0.0b	(+.f64 x (+.f64 x y))
0.1b	(sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 x y))))
0.5b	(pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 x y)))) 4)

rewrite28.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`sqrt-prod_binary64_16121`
24×	`*-un-lft-identity_binary64_16105`
11×	`add-sqr-sqrt_binary64_16127` `unpow-prod-down_binary64_16184`
9×	`add-cube-cbrt_binary64_16140` `distribute-lft-out_binary64_16056`
8×	`sqrt-pow1_binary64_16123` `add-log-exp_binary64_16144` `pow1_binary64_16166`
5×	`pow-pow_binary64_16177`
4×	`sqrt-div_binary64_16122` `add-exp-log_binary64_16143` `pow1/2_binary64_16185`
3×	`sum-log_binary64_16196` `pow-unpow_binary64_16182` `add-cbrt-cube_binary64_16141`
2×	`flip-+_binary64_16079` `rem-sqrt-square_binary64_16118` `flip3-+_binary64_16108`
1×	`sqrt-pow2_binary64_16124` `pow-exp_binary64_16173` `pow-to-exp_binary64_16174` `+-commutative_binary64_16035` `associate-+r+_binary64_16037` `sqr-pow_binary64_16077`

Counts

3 → 68

Calls

6 calls:

11.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 x y)))) 4)
6.0ms	(sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 x y))))
6.0ms	(+.f64 x (+.f64 x y))
0.0ms	(+.f64 x (+.f64 x y))
0.0ms	(sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 x y))))

series893.0ms (27.9%)

Counts

3 → 31

Calls

3 calls:

746.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 x y)))) 4)
83.0ms	(sqrt.f64 (sqrt.f64 (+.f64 x (+.f64 x y))))
63.0ms	(+.f64 x (+.f64 x y))

Compiler

Compiled 667 to 657 computations (1.5% saved)

simplify83.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4862	997
1	4862	997

prune60.0ms (1.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	100	3	103

Error

Counts

103 → 3

Compiler

Compiled 1038 to 360 computations (65.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	174
1	44	174

regimes45.0ms (1.4%)

Compiler: Compiled 238 to 180 computations (24.4% saved)

bsearch0.0ms (0%)

regimes63.0ms (2%)

Compiler: Compiled 18 to 36 computations (-100% saved)

bsearch22.0ms (0.7%)

Steps

Iters	Range		Point
10	7.993236603686741e-35	1.2031916656546465e-22	7.788193505707118e-25
9	-9.404896261921963e-06	-1.686420950087121e-11	-1.894003570204116e-07

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes18.0ms (0.5%)

Compiler: Compiled 12 to 30 computations (-150% saved)

bsearch0.0ms (0%)

regimes18.0ms (0.6%)

Accuracy

Total 0.0b remaining (77.3%)

Threshold costs 0.0b (77.3%)

Compiler

Compiled 10 to 26 computations (-160% saved)

bsearch2.0ms (0.1%)

Compiler: Compiled 20 to 18 computations (10% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	27
1	20	27

end0.0ms (0%)

sample508.0ms (15.9%)

Algorithm

1×

intervals

Results

137.0ms	8000×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 148 to 116 computations (21.6% saved)

Pareto

0.49154105181442803

Details

analyze51.0ms (1.6%)

sample11.0ms (0.3%)

simplify93.0ms (2.9%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

rewrite8.0ms (0.3%)

series60.0ms (1.9%)

simplify54.0ms (1.7%)

prune15.0ms (0.5%)

localize6.0ms (0.2%)

rewrite41.0ms (1.3%)

series179.0ms (5.6%)

simplify69.0ms (2.2%)

prune78.0ms (2.4%)

localize9.0ms (0.3%)

rewrite68.0ms (2.1%)

series436.0ms (13.6%)

simplify102.0ms (3.2%)

prune165.0ms (5.1%)

localize7.0ms (0.2%)

rewrite28.0ms (0.9%)

series893.0ms (27.9%)

simplify83.0ms (2.6%)

prune60.0ms (1.9%)

simplify4.0ms (0.1%)

regimes45.0ms (1.4%)

bsearch0.0ms (0%)

regimes63.0ms (2%)

bsearch22.0ms (0.7%)

regimes18.0ms (0.5%)

bsearch0.0ms (0%)

regimes18.0ms (0.6%)

bsearch2.0ms (0.1%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample508.0ms (15.9%)

Profiling